Acausal measurement-based quantum computing
NASA Astrophysics Data System (ADS)
Morimae, Tomoyuki
2014-07-01
In measurement-based quantum computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of by-product operators. If we respect the no-signaling principle, by-product operators cannot be avoided. Here we study the possibility of acausal measurement-based quantum computing by using the process matrix framework [Oreshkov, Costa, and Brukner, Nat. Commun. 3, 1092 (2012), 10.1038/ncomms2076]. We construct a resource process matrix for acausal measurement-based quantum computing restricting local operations to projective measurements. The resource process matrix is an analog of the resource state of the standard causal measurement-based quantum computing. We find that if we restrict local operations to projective measurements the resource process matrix is (up to a normalization factor and trivial ancilla qubits) equivalent to the decorated graph state created from the graph state of the corresponding causal measurement-based quantum computing. We also show that it is possible to consider a causal game whose causal inequality is violated by acausal measurement-based quantum computing.
Blind topological measurement-based quantum computation
NASA Astrophysics Data System (ADS)
Morimae, Tomoyuki; Fujii, Keisuke
2012-09-01
Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3×10-3, which is comparable to that (7.5×10-3) of non-blind topological quantum computation. As the error per gate of the order 10-3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.
Randomized benchmarking in measurement-based quantum computing
NASA Astrophysics Data System (ADS)
Alexander, Rafael N.; Turner, Peter S.; Bartlett, Stephen D.
2016-09-01
Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.
Closed timelike curves in measurement-based quantum computation
NASA Astrophysics Data System (ADS)
Dias da Silva, Raphael; Galvão, Ernesto F.; Kashefi, Elham
2011-01-01
Many results have been recently obtained regarding the power of hypothetical closed timelike curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum computation encompasses in a natural way the CTC model proposed by Bennett, Schumacher, and Svetlichny. We identify a class of CTCs in this model that can be simulated deterministically and point to a fundamental limitation of Deutsch’s CTC model which leads to predictions conflicting with those of the one-way model.
Closed timelike curves in measurement-based quantum computation
Dias da Silva, Raphael; Galvao, Ernesto F.; Kashefi, Elham
2011-01-15
Many results have been recently obtained regarding the power of hypothetical closed timelike curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum computation encompasses in a natural way the CTC model proposed by Bennett, Schumacher, and Svetlichny. We identify a class of CTCs in this model that can be simulated deterministically and point to a fundamental limitation of Deutsch's CTC model which leads to predictions conflicting with those of the one-way model.
Transitions in the computational power of thermal states for measurement-based quantum computation
Barrett, Sean D.; Bartlett, Stephen D.; Jennings, David; Doherty, Andrew C.; Rudolph, Terry
2009-12-15
We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct 'phases' - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical, or quantum in the underlying spin-lattice model.
Sequential measurement-based quantum computing with memories
Roncaglia, Augusto J.; Aolita, Leandro; Ferraro, Alessandro; Acin, Antonio
2011-06-15
We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the cluster state needed for the computation and its consumption by measurements are carried out simultaneously. As a consequence, effective clusters of one spatial dimension fewer than in the standard approach are sufficient for computation. In particular, universal computation requires only a one-dimensional array of memories. The scheme applies to discrete-variable systems of any dimension as well as to continuous-variable ones, and both are treated equivalently under the light of local complementation of graphs. In this way our formalism introduces a general framework that encompasses and generalizes in a unified manner some previous system-dependent proposals. The procedure is intrinsically well suited for implementations with atom-photon interfaces.
Fault-tolerant measurement-based quantum computing with continuous-variable cluster states.
Menicucci, Nicolas C
2014-03-28
A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes. Initial squeezing in the cluster above a threshold value of 20.5 dB ensures that errors from finite squeezing acting on encoded qubits are below the fault-tolerance threshold of known qubit-based error-correcting codes. By concatenating with one of these codes and using ancilla-based error correction, fault-tolerant measurement-based quantum computation of theoretically indefinite length is possible with finitely squeezed cluster states.
Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model
Alsing, Paul; Fanto, Michael; Lott, Capt. Gordon; Tison, Christoper C.
2014-01-01
We provide a set of prescriptions for implementing a quantum circuit model algorithm as measurement based quantum computing (MBQC) algorithm1, 2 via a large cluster state. As means of illustration we draw upon our numerical modeling experience to describe a large graph state capable of searching a logical 8 element list (a non-trivial version of Grover's algorithm3 with feedforward). We develop several prescriptions based on analytic evaluation of cluster states and graph state equations which can be generalized into any circuit model operations. Such a resulting cluster state will be able to carry out the desired operation with appropriate measurements and feed forward error correction. We also discuss the physical implementation and the analysis of the principal 3-qubit entangling gate (Toffoli) required for a non-trivial feedforward realization of an 8-element Grover search algorithm.
Measurement-based quantum computation beyond the one-way model
NASA Astrophysics Data System (ADS)
Gross, D.; Eisert, J.; Schuch, N.; Perez-Garcia, D.
2007-11-01
We introduce schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in Gross and Eisert [Phys. Rev. Lett. 98, 220503 (2007); quant-ph/0609149]. Our method makes use of tools from many-body physics—matrix product states, finitely correlated states, or projected entangled pairs states—to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem—how to realize quantum computation—was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting and present a large number of examples. We find computational schemes, which differ from the original one-way computer, for example, in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may, for example, exhibit nonvanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev’s toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.
Measurement-based quantum computation on two-body interacting qubits with adiabatic evolution.
Kyaw, Thi Ha; Li, Ying; Kwek, Leong-Chuan
2014-10-31
A cluster state cannot be a unique ground state of a two-body interacting Hamiltonian. Here, we propose the creation of a cluster state of logical qubits encoded in spin-1/2 particles by adiabatically weakening two-body interactions. The proposal is valid for any spatial dimensional cluster states. Errors induced by thermal fluctuations and adiabatic evolution within finite time can be eliminated ensuring fault-tolerant quantum computing schemes.
D'Souza, Adam G.; Feder, David L.
2011-10-15
We examine cluster states transformed by stochastic local operations and classical communication, as a resource for deterministic universal computation driven strictly by projective measurements. We identify circumstances under which such states in one dimension constitute resources for random-length single-qubit rotations, in one case quasideterministically (N-U-N states) and in another probabilistically (B-U-B states). In contrast to the cluster states, the N-U-N states exhibit spin correlation functions that decay exponentially with distance, while the B-U-B states can be arbitrarily locally pure. A two-dimensional square N-U-N lattice is a universal resource for quasideterministic measurement-based quantum computation. Measurements on cubic B-U-B states yield two-dimensional cluster states with bond defects, whose connectivity exceeds the percolation threshold for a critical value of the local purity.
Li, Shu-Shen; Long, Gui-Lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi
2001-01-01
Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization. PMID:11562459
Scalable optical quantum computer
Manykin, E A; Mel'nichenko, E V
2014-12-31
A way of designing a scalable optical quantum computer based on the photon echo effect is proposed. Individual rare earth ions Pr{sup 3+}, regularly located in the lattice of the orthosilicate (Y{sub 2}SiO{sub 5}) crystal, are suggested to be used as optical qubits. Operations with qubits are performed using coherent and incoherent laser pulses. The operation protocol includes both the method of measurement-based quantum computations and the technique of optical computations. Modern hybrid photon echo protocols, which provide a sufficient quantum efficiency when reading recorded states, are considered as most promising for quantum computations and communications. (quantum computer)
Demonstration of blind quantum computing.
Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip
2012-01-20
Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.
Gross, D.; Eisert, J.
2010-10-15
We discuss the notion of quantum computational webs: These are quantum states universal for measurement-based computation, which can be built up from a collection of simple primitives. The primitive elements--reminiscent of building blocks in a construction kit--are (i) one-dimensional states (computational quantum wires) with the power to process one logical qubit and (ii) suitable couplings, which connect the wires to a computationally universal web. All elements are preparable by nearest-neighbor interactions in a single pass, of the kind accessible in a number of physical architectures. We provide a complete classification of qubit wires, a physically well-motivated class of universal resources that can be fully understood. Finally, we sketch possible realizations in superlattices and explore the power of coupling mechanisms based on Ising or exchange interactions.
Continuous-Variable Blind Quantum Computation
NASA Astrophysics Data System (ADS)
Morimae, Tomoyuki
2012-12-01
Blind quantum computation is a secure delegated quantum computing protocol where Alice, who does not have sufficient quantum technology at her disposal, delegates her computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice’s input, output, and algorithm. Protocols of blind quantum computation have been proposed for several qudit measurement-based computation models, such as the graph state model, the Affleck-Kennedy-Lieb-Tasaki model, and the Raussendorf-Harrington-Goyal topological model. Here, we consider blind quantum computation for the continuous-variable measurement-based model. We show that blind quantum computation is possible for the infinite squeezing case. We also show that the finite squeezing causes no additional problem in the blind setup apart from the one inherent to the continuous-variable measurement-based quantum computation.
Kendon, Viv
2014-12-04
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.
Quantum Computer Games: Quantum Minesweeper
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Measurement-based method for verifying quantum discord
NASA Astrophysics Data System (ADS)
Rahimi-Keshari, Saleh; Caves, Carlton M.; Ralph, Timothy C.
2013-01-01
We introduce a measurement-based method for verifying quantum discord of any bipartite quantum system. We show that by performing an informationally complete positive operator valued measurement (IC-POVM) on one subsystem and checking the commutativity of the conditional states of the other subsystem, quantum discord from the second subsystem to the first can be verified. This is an improvement upon previous methods, which enables us to efficiently apply our method to continuous-variable systems, as IC-POVM's are readily available from homodyne or heterodyne measurements. We show that quantum discord for Gaussian states can be verified by checking whether the peaks of the conditional Wigner functions corresponding to two different outcomes of heterodyne measurement coincide at the same point in the phase space. Using this method, we also prove that the only Gaussian states with zero discord are product states; hence, Gaussian states with Gaussian discord have nonzero quantum discord.
Efficient Universal Blind Quantum Computation
NASA Astrophysics Data System (ADS)
Giovannetti, Vittorio; Maccone, Lorenzo; Morimae, Tomoyuki; Rudolph, Terry G.
2013-12-01
We give a cheat sensitive protocol for blind universal quantum computation that is efficient in terms of computational and communication resources: it allows one party to perform an arbitrary computation on a second party’s quantum computer without revealing either which computation is performed, or its input and output. The first party’s computational capabilities can be extremely limited: she must only be able to create and measure single-qubit superposition states. The second party is not required to use measurement-based quantum computation. The protocol requires the (optimal) exchange of O(Jlog2(N)) single-qubit states, where J is the computational depth and N is the number of qubits needed for the computation.
Introduction to Quantum Computation
NASA Astrophysics Data System (ADS)
Ekert, A.
A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement in order to perform computation. In this series of lectures I want to elaborate on the computational power of such machines.
Quantum computing and probability.
Ferry, David K
2009-11-25
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.
Kendon, Vivien M; Nemoto, Kae; Munro, William J
2010-08-13
We briefly review what a quantum computer is, what it promises to do for us and why it is so hard to build one. Among the first applications anticipated to bear fruit is the quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data are encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error-correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous-variable quantum computers, becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.
Derandomizing Quantum Circuits with Measurement-Based Unitary Designs
NASA Astrophysics Data System (ADS)
Turner, Peter S.; Markham, Damian
2016-05-01
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state techniques, we show that these resources can "derandomize" circuit results by sampling the same kinds of ensembles quantum mechanically, analogously to a quantum random number generator. Furthermore, we find simple examples that give rise to new ensembles whose statistical moments exactly match those of the uniformly random distribution over all unitaries up to order t , while foregoing adaptive feedforward entirely. Such ensembles—known as t designs—often cannot be distinguished from the "truly" random ensemble, and so they find use in many applications that require this implied notion of pseudorandomness.
Derandomizing Quantum Circuits with Measurement-Based Unitary Designs.
Turner, Peter S; Markham, Damian
2016-05-20
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state techniques, we show that these resources can "derandomize" circuit results by sampling the same kinds of ensembles quantum mechanically, analogously to a quantum random number generator. Furthermore, we find simple examples that give rise to new ensembles whose statistical moments exactly match those of the uniformly random distribution over all unitaries up to order t, while foregoing adaptive feedforward entirely. Such ensembles-known as t designs-often cannot be distinguished from the "truly" random ensemble, and so they find use in many applications that require this implied notion of pseudorandomness. PMID:27258858
Derandomizing Quantum Circuits with Measurement-Based Unitary Designs.
Turner, Peter S; Markham, Damian
2016-05-20
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state techniques, we show that these resources can "derandomize" circuit results by sampling the same kinds of ensembles quantum mechanically, analogously to a quantum random number generator. Furthermore, we find simple examples that give rise to new ensembles whose statistical moments exactly match those of the uniformly random distribution over all unitaries up to order t, while foregoing adaptive feedforward entirely. Such ensembles-known as t designs-often cannot be distinguished from the "truly" random ensemble, and so they find use in many applications that require this implied notion of pseudorandomness.
Adiabatic topological quantum computing
NASA Astrophysics Data System (ADS)
Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; Flammia, Steven T.; Neels, Alice
2015-07-01
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.
Quantum computing with incoherent resources and quantum jumps.
Santos, M F; Cunha, M Terra; Chaves, R; Carvalho, A R R
2012-04-27
Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that, when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify this by showing how to efficiently prepare graph states for the implementation of measurement-based quantum computation.
Quantum information and computation
Bennett, C.H.
1995-10-01
A new quantum theory of communication and computation is emerging, in which the stuff transmitted or processed is not classical information, but arbitrary superpositions of quantum states. {copyright} 1995 {ital American} {ital Institute} {ital of} {ital Physics}.
Quantum computing classical physics.
Meyer, David A
2002-03-15
In the past decade, quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice-gas automata--and show how to implement them efficiently on standard quantum computers.
Measurement-based noiseless linear amplification for quantum communication
NASA Astrophysics Data System (ADS)
Chrzanowski, H. M.; Walk, N.; Haw, J. Y.; Thearle, O.; Assad, S. M.; Janousek, J.; Hosseini, S.; Ralph, T. C.; Symul, T.; Lam, P. K.
2014-11-01
Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require non-trivial experimental techniques such as noiseless amplification. We show that noiseless amplification could be achieved by performing a post-selective filtering of measurement outcomes. We termed this protocol measurement-based noiseless linear amplification (MBNLA). We apply this protocol to entanglement that suffers transmission loss of up to the equivalent of 100km of optical fibre and show that it is capable of distilling entanglement to a level stronger than that achievable by transmitting a maximally entangled state through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime via MBNLA. Compared to its physical counterpart, MBNLA not only is easier in term of implementation, but also allows one to achieve near optimal probability of success.
Dissipative quantum computing with open quantum walks
Sinayskiy, Ilya; Petruccione, Francesco
2014-12-04
An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.
Probabilistic Cloning and Quantum Computation
NASA Astrophysics Data System (ADS)
Gao, Ting; Yan, Feng-Li; Wang, Zhi-Xi
2004-06-01
We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which the cloning offers an advantage which cannot be matched by any approach that does not resort to quantum cloning. In these quantum computations, we need to distribute quantum information contained in the states about which we have some partial information. To perform quantum computations, we use a state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.
NASA Technical Reports Server (NTRS)
Zak, M.
1998-01-01
Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.
Quantum computing with trapped ions
Hughes, R.J.
1998-01-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
Castagnoli, G. )
1991-08-10
This paper reports that current conceptions of quantum mechanical computers inherit from conventional digital machines two apparently interacting features, machine imperfection and temporal development of the computational process. On account of machine imperfection, the process would become ideally reversible only in the limiting case of zero speed. Therefore the process is irreversible in practice and cannot be considered to be a fundamental quantum one. By giving up classical features and using a linear, reversible and non-sequential representation of the computational process - not realizable in classical machines - the process can be identified with the mathematical form of a quantum steady state. This form of steady quantum computation would seem to have an important bearing on the notion of cognition.
Experimental verification of quantum computation
NASA Astrophysics Data System (ADS)
Barz, Stefanie; Fitzsimons, Joseph F.; Kashefi, Elham; Walther, Philip
2013-11-01
Quantum computers are expected to offer substantial speed-ups over their classical counterparts and to solve problems intractable for classical computers. Beyond such practical significance, the concept of quantum computation opens up fundamental questions, among them the issue of whether quantum computations can be certified by entities that are inherently unable to compute the results themselves. Here we present the first experimental verification of quantum computation. We show, in theory and experiment, how a verifier with minimal quantum resources can test a significantly more powerful quantum computer. The new verification protocol introduced here uses the framework of blind quantum computing and is independent of the experimental quantum-computation platform used. In our scheme, the verifier is required only to generate single qubits and transmit them to the quantum computer. We experimentally demonstrate this protocol using four photonic qubits and show how the verifier can test the computer's ability to perform quantum computation.
Entanglement and adiabatic quantum computation
NASA Astrophysics Data System (ADS)
Ahrensmeier, D.
2006-06-01
Adiabatic quantum computation provides an alternative approach to quantum computation using a time-dependent Hamiltonian. The time evolution of entanglement during the adiabatic quantum search algorithm is studied, and its relevance as a resource is discussed.
NASA Astrophysics Data System (ADS)
Kashefi, Elham
Over the next five to ten years we will see a state of flux as quantum devices become part of the mainstream computing landscape. However adopting and applying such a highly variable and novel technology is both costly and risky as this quantum approach has an acute verification and validation problem: On the one hand, since classical computations cannot scale up to the computational power of quantum mechanics, verifying the correctness of a quantum-mediated computation is challenging; on the other hand, the underlying quantum structure resists classical certification analysis. Our grand aim is to settle these key milestones to make the translation from theory to practice possible. Currently the most efficient ways to verify a quantum computation is to employ cryptographic methods. I will present the current state of the art of various existing protocols where generally there exists a trade-off between the practicality of the scheme versus their generality, trust assumptions and security level. EK gratefully acknowledges funding through EPSRC Grants EP/N003829/1 and EP/M013243/1.
Quantum entanglement, quantum communication and the limits of quantum computing
NASA Astrophysics Data System (ADS)
Ambainis, Andris
Quantum entanglement is a term describing the quantum correlations between different parts of a quantum system. Quantum information theory has developed sophisticated techniques to quantify and study quantum entanglement. In this thesis, we show how to apply those techniques to problems in quantum algorithms, complexity theory, communication and cryptography. The main results are: (1) quantum communication protocols that are exponentially more efficient that conventional (classical) communication protocols, (2) unconditionally secure quantum protocols for cryptographic problems, (3) a new "quantum adversary" method for proving lower bounds on quantum algorithms, (4) a study of "one clean qubit computation", a model related to the experimental implementation of quantum computers using NMR (nucleo-magnetic resonance) technology.
Computational quantum-classical boundary of noisy commuting quantum circuits.
Fujii, Keisuke; Tamate, Shuhei
2016-01-01
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039
Computational quantum-classical boundary of noisy commuting quantum circuits
NASA Astrophysics Data System (ADS)
Fujii, Keisuke; Tamate, Shuhei
2016-05-01
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.
Computational quantum-classical boundary of noisy commuting quantum circuits
Fujii, Keisuke; Tamate, Shuhei
2016-01-01
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039
O'Brien, Jeremy L
2007-12-01
In 2001, all-optical quantum computing became feasible with the discovery that scalable quantum computing is possible using only single-photon sources, linear optical elements, and single-photon detectors. Although it was in principle scalable, the massive resource overhead made the scheme practically daunting. However, several simplifications were followed by proof-of-principle demonstrations, and recent approaches based on cluster states or error encoding have dramatically reduced this worrying resource overhead, making an all-optical architecture a serious contender for the ultimate goal of a large-scale quantum computer. Key challenges will be the realization of high-efficiency sources of indistinguishable single photons, low-loss, scalable optical circuits, high-efficiency single-photon detectors, and low-loss interfacing of these components.
Computational quantum chemistry website
1997-08-22
This report contains the contents of a web page related to research on the development of quantum chemistry methods for computational thermochemistry and the application of quantum chemistry methods to problems in material chemistry and chemical sciences. Research programs highlighted include: Gaussian-2 theory; Density functional theory; Molecular sieve materials; Diamond thin-film growth from buckyball precursors; Electronic structure calculations on lithium polymer electrolytes; Long-distance electronic coupling in donor/acceptor molecules; and Computational studies of NOx reactions in radioactive waste storage.
Abstract quantum computing machines and quantum computational logics
NASA Astrophysics Data System (ADS)
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto
2016-06-01
Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.
Measurements-based Moving Target Detection in Quantum Video
NASA Astrophysics Data System (ADS)
Yan, Fei; Iliyasu, Abdullah M.; Khan, Asif R.; Yang, Huamin
2016-04-01
A method to detect a moving target in multi-channel quantum video is proposed based on multiple measurements on the video strip. The proposed method is capable of detecting the location of the moving target in each frame of the quantum video thereby ensuring that the motion trail of the object is easily and efficiently retrieved. Three experiments, i.e. moving target detection (MTD) of a pixel, MTD of an object in complex shape, and MTD of a pixel whose color is conterminous with that of its background, are implemented to demonstrate the feasibility of the proposal. This study presents a modest attempt to focus on the moving target detection and its applications in quantum video.
Experimental realization of generalized qubit measurements based on quantum walks
NASA Astrophysics Data System (ADS)
Zhao, Yuan-yuan; Yu, Neng-kun; Kurzyński, Paweł; Xiang, Guo-yong; Li, Chuan-Feng; Guo, Guang-Can
2015-04-01
We report an experimental implementation of a single-qubit generalized measurement scenario, the positive-operator valued measure (POVM), based on a quantum walk model. The qubit is encoded in a single-photon polarization. The photon performs a quantum walk on an array of optical elements, where the polarization-dependent translation is performed via birefringent beam displacers and a change of the polarization is implemented with the help of wave plates. We implement: (i) trine POVM, i.e., the POVM elements uniformly distributed on an equatorial plane of the Bloch sphere; (ii) symmetric-informationally-complete (SIC) POVM; and (iii) unambiguous discrimination of two nonorthogonal qubit states.
NASA Astrophysics Data System (ADS)
Yepez, Jeffrey
This paper discusses a computing architecture that uses both classical parallelism and quantum parallelism. We consider a large parallel array of small quantum computers, connected together by classical communication channels. This kind of computer is called a type-II quantum computer, to differentiate it from a globally phase-coherent quantum computer, which is the first type of quantum computer that has received nearly exclusive attention in the literature. Although a hybrid, a type-II quantum computer retains the crucial advantage allowed by quantum mechanical superposition that its computational power grows exponentially in the number of phase-coherent qubits per node, only short-range and short time phase-coherence is needed, which significantly reduces the level of engineering facility required to achieve its construction. Therefore, the primary factor limiting its computational power is an economic one and not a technological one, since the volume of its computational medium can in principle scale indefinitely.
Measurement-based teleportation along quantum spin chains.
Barjaktarevic, J P; McKenzie, R H; Links, J; Milburn, G J
2005-12-01
We examine the teleportation of an unknown spin-1/2 quantum state along a quantum spin chain with an even number of sites. Our protocol, using a sequence of Bell measurements, may be viewed as an iterated version of the 2-qubit protocol of C. H. Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)]. A decomposition of the Hilbert space of the spin chain into 4 vector spaces, called Bell subspaces, is given. It is established that any state from a Bell subspace may be used as a channel to perform unit fidelity teleportation. The space of all spin-0 many-body states, which includes the ground states of many known antiferromagnetic systems, belongs to a common Bell subspace. A channel-dependent teleportation parameter [symbol: see text] is introduced, and a bound on the teleportation fidelity is given in terms of [symbol: see text].
Holographic quantum computing.
Tordrup, Karl; Negretti, Antonio; Mølmer, Klaus
2008-07-25
We propose to use a single mesoscopic ensemble of trapped polar molecules for quantum computing. A "holographic quantum register" with hundreds of qubits is encoded in collective excitations with definite spatial phase variations. Each phase pattern is uniquely addressed by optical Raman processes with classical optical fields, while one- and two-qubit gates and qubit readout are accomplished by transferring the qubit states to a stripline microwave cavity field and a Cooper pair box where controllable two-level unitary dynamics and detection is governed by classical microwave fields.
Investigating photonic quantum computation
NASA Astrophysics Data System (ADS)
Myers, Casey Robert
The use of photons as qubits is a promising implementation for quantum computation. The inability of photons to interact, especially with the environment, makes them an ideal physical candidate. However, this also makes them a difficult system to perform two qubit gates on. Recent breakthroughs in photonic quantum computing have shown methods around the requirement of direct photon-photon interaction. In this thesis we study three recently discovered schemes for optical quantum computation. We first investigate the so called linear optical quantum computing (LOQC) scheme, exploring a method to improve the original proposal by constructing a photon-number QND detector that succeeds with a high probability. In doing this we present a new type of LOQC teleporter, one that can detect the presence of a single photon in an arbitrary polarisation state when the input state is a sum of vacuum and multi-photon terms. This new type of teleporter is an improvement on the original scheme in that the entangled states required can be made offline with fewer entangling operations. We next investigate the so called quantum bus (qubus) scheme for photonic quantum computing. We show a scheme to measure the party of n qubit states by using a single qubus mode, controlled rotations and displacements. This allows for the syndrome measurements of any stabilizer quantum error correcting code. We extend these results to a fault tolerant scheme to measure an arbitrary Pauli operator of weight n, incorporating so called single bit teleportations. We investigate the construction of a Toffoli gate by using a single qubus mode, controlled rotations and displacements that works with a success probability of at least 25%. We also investigate the use of single bit teleportations to construct a universal set of gates on coherent state type logic and in the construction of cluster states. We finally investigate the optical Zeno gate, a gate that uses the Zeno effect in the form of two photon
Quantum computers: Definition and implementations
Perez-Delgado, Carlos A.; Kok, Pieter
2011-01-15
The DiVincenzo criteria for implementing a quantum computer have been seminal in focusing both experimental and theoretical research in quantum-information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. Therefore, the question is what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that, according to this definition, a device is a quantum computer if it obeys the following criteria: Any quantum computer must consist of a quantum memory, with an additional structure that (1) facilitates a controlled quantum evolution of the quantum memory; (2) includes a method for information theoretic cooling of the memory; and (3) provides a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault tolerantly. We discuss various existing quantum computing paradigms and how they fit within this framework. Finally, we present a decision tree for selecting an avenue toward building a quantum computer. This is intended to help experimentalists determine the most natural paradigm given a particular physical implementation.
Quantum computers: Definition and implementations
NASA Astrophysics Data System (ADS)
Pérez-Delgado, Carlos A.; Kok, Pieter
2011-01-01
The DiVincenzo criteria for implementing a quantum computer have been seminal in focusing both experimental and theoretical research in quantum-information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. Therefore, the question is what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that, according to this definition, a device is a quantum computer if it obeys the following criteria: Any quantum computer must consist of a quantum memory, with an additional structure that (1) facilitates a controlled quantum evolution of the quantum memory; (2) includes a method for information theoretic cooling of the memory; and (3) provides a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault tolerantly. We discuss various existing quantum computing paradigms and how they fit within this framework. Finally, we present a decision tree for selecting an avenue toward building a quantum computer. This is intended to help experimentalists determine the most natural paradigm given a particular physical implementation.
Quantum Walk Schemes for Universal Quantum Computation
NASA Astrophysics Data System (ADS)
Underwood, Michael S.
Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction
Quantum computation vs. firewalls
NASA Astrophysics Data System (ADS)
Harlow, Daniel; Hayden, Patrick
2013-06-01
In this paper we discuss quantum computational restrictions on the types of thought experiments recently used by Almheiri, Marolf, Polchinski, and Sully to argue against the smoothness of black hole horizons. We argue that the quantum computations required to do these experiments would take a time which is exponential in the entropy of the black hole under study, and we show that for a wide variety of black holes this prevents the experiments from being done. We interpret our results as motivating a broader type of nonlocality than is usually considered in the context of black hole thought experiments, and claim that once this type of nonlocality is allowed there may be no need for firewalls. Our results do not threaten the unitarity of black hole evaporation or the ability of advanced civilizations to test it.
Quantum computing of semiclassical formulas.
Georgeot, B; Giraud, O
2008-04-01
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from classical trajectories, and which alternatively test the semiclassical approximation by computing classical actions from quantum evolution. The gain over classical computation is in general quadratic, and can be larger in some specific cases.
Quantum computing on encrypted data.
Fisher, K A G; Broadbent, A; Shalm, L K; Yan, Z; Lavoie, J; Prevedel, R; Jennewein, T; Resch, K J
2014-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
Quantum Computing's Classical Problem, Classical Computing's Quantum Problem
NASA Astrophysics Data System (ADS)
Van Meter, Rodney
2014-08-01
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that out-compute classical systems capable of some logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends.
Quantum computing with defects.
Weber, J R; Koehl, W F; Varley, J B; Janotti, A; Buckley, B B; Van de Walle, C G; Awschalom, D D
2010-05-11
Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantum computer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV(-1)) center stands out for its robustness--its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV(-1) center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors.
Quantum computing with defects
Weber, J. R.; Koehl, W. F.; Varley, J. B.; Janotti, A.; Buckley, B. B.; Van de Walle, C. G.; Awschalom, D. D.
2010-01-01
Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantum computer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV-1) center stands out for its robustness—its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV-1 center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors. PMID:20404195
Measurement-based quantum lattice gas model of fluid dynamics in 2+1 dimensions.
Micci, Michael M; Yepez, Jeffrey
2015-09-01
Presented are quantum simulation results using a measurement-based quantum lattice gas algorithm for Navier-Stokes fluid dynamics in 2+1 dimensions. Numerical prediction of the kinematic viscosity was measured by the decay rate of an initial sinusoidal flow profile. Due to local quantum entanglement in the quantum lattice gas, the minimum kinematic viscosity in the measurement-based quantum lattice gas is lower than achievable in a classical lattice gas. The numerically predicted viscosities precisely match the theoretical predictions obtained with a mean field approximation. Uniform flow profile with double shear layers, on a 16K×8K lattice, leads to the Kelvin-Helmholtz instability, breaking up the shear layer into pairs of counter-rotating vortices that eventually merge via vortex fusion and dissipate because of the nonzero shear viscosity.
Universal quantum computation by discontinuous quantum walk
Underwood, Michael S.; Feder, David L.
2010-10-15
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum ''walker'' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This ''discontinuous'' quantum walk employs perfect quantum-state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one time step apart.
Towards quantum chemistry on a quantum computer.
Lanyon, B P; Whitfield, J D; Gillett, G G; Goggin, M E; Almeida, M P; Kassal, I; Biamonte, J D; Mohseni, M; Powell, B J; Barbieri, M; Aspuru-Guzik, A; White, A G
2010-02-01
Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications. PMID:21124400
Intermediate quantum maps for quantum computation
Giraud, O.; Georgeot, B.
2005-10-15
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.
Quasicrystals and Quantum Computing
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
1997-03-01
In Quantum (Q) Computing qubits form Q-superpositions for macroscopic times. One scheme for ultra-fast (Q) computing can be based on quasicrystals. Ultrafast processing in Q-coherent structures (and the very existence of durable Q-superpositions) may be 'consequence' of presence of entire manifold of integer arithmetic (A0, aleph-naught of Georg Cantor) at any 4-point of space-time, furthermore, at any point of any multidimensional phase space of (any) N-particle Q-system. The latter, apart from quasicrystals, can include dispersed and/or diluted systems (Berezin, 1994). In such systems such alleged centrepieces of Q-Computing as ability for fast factorization of long integers can be processed by sheer virtue of the fact that entire infinite pattern of prime numbers is instantaneously available as 'free lunch' at any instant/point. Infinitely rich pattern of A0 (including pattern of primes and almost primes) acts as 'independent' physical effect which directly generates Q-dynamics (and physical world) 'out of nothing'. Thus Q-nonlocality can be ultimately based on instantaneous interconnectedness through ever- the-same structure of A0 ('Platonic field' of integers).
Quantum Computing: Solving Complex Problems
DiVincenzo, David [IBM Watson Research Center
2016-07-12
One of the motivating ideas of quantum computation was that there could be a new kind of machine that would solve hard problems in quantum mechanics. There has been significant progress towards the experimental realization of these machines (which I will review), but there are still many questions about how such a machine could solve computational problems of interest in quantum physics. New categorizations of the complexity of computational problems have now been invented to describe quantum simulation. The bad news is that some of these problems are believed to be intractable even on a quantum computer, falling into a quantum analog of the NP class. The good news is that there are many other new classifications of tractability that may apply to several situations of physical interest.
The Physics of Quantum Computation
NASA Astrophysics Data System (ADS)
Falci, Giuseppe; Paladino, Elisabette
2015-10-01
Quantum Computation has emerged in the past decades as a consequence of down-scaling of electronic devices to the mesoscopic regime and of advances in the ability of controlling and measuring microscopic quantum systems. QC has many interdisciplinary aspects, ranging from physics and chemistry to mathematics and computer science. In these lecture notes we focus on physical hardware, present day challenges and future directions for design of quantum architectures.
Duality quantum computer and the efficient quantum simulations
NASA Astrophysics Data System (ADS)
Wei, Shi-Jie; Long, Gui-Lu
2016-03-01
Duality quantum computing is a new mode of a quantum computer to simulate a moving quantum computer passing through a multi-slit. It exploits the particle wave duality property for computing. A quantum computer with n qubits and a qudit simulates a moving quantum computer with n qubits passing through a d-slit. Duality quantum computing can realize an arbitrary sum of unitaries and therefore a general quantum operator, which is called a generalized quantum gate. All linear bounded operators can be realized by the generalized quantum gates, and unitary operators are just the extreme points of the set of generalized quantum gates. Duality quantum computing provides flexibility and a clear physical picture in designing quantum algorithms, and serves as a powerful bridge between quantum and classical algorithms. In this paper, after a brief review of the theory of duality quantum computing, we will concentrate on the applications of duality quantum computing in simulations of Hamiltonian systems. We will show that duality quantum computing can efficiently simulate quantum systems by providing descriptions of the recent efficient quantum simulation algorithm of Childs and Wiebe (Quantum Inf Comput 12(11-12):901-924, 2012) for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al. (Phys Rev Lett 114:090502, 2015), which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.
Toward a superconducting quantum computer
Tsai, Jaw-Shen
2010-01-01
Intensive research on the construction of superconducting quantum computers has produced numerous important achievements. The quantum bit (qubit), based on the Josephson junction, is at the heart of this research. This macroscopic system has the ability to control quantum coherence. This article reviews the current state of quantum computing as well as its history, and discusses its future. Although progress has been rapid, the field remains beset with unsolved issues, and there are still many new research opportunities open to physicists and engineers. PMID:20431256
Quantum Information and Computing
NASA Astrophysics Data System (ADS)
Accardi, L.; Ohya, Masanori; Watanabe, N.
2006-03-01
Preface -- Coherent quantum control of [symbol]-atoms through the stochastic limit / L. Accardi, S. V. Kozyrev and A. N. Pechen -- Recent advances in quantum white noise calculus / L. Accardi and A. Boukas -- Control of quantum states by decoherence / L. Accardi and K. Imafuku -- Logical operations realized on the Ising chain of N qubits / M. Asano, N. Tateda and C. Ishii -- Joint extension of states of fermion subsystems / H. Araki -- Quantum filtering and optimal feedback control of a Gaussian quantum free particle / S. C. Edwards and V. P. Belavkin -- On existence of quantum zeno dynamics / P. Exner and T. Ichinose -- Invariant subspaces and control of decoherence / P. Facchi, V. L. Lepore and S. Pascazio -- Clauser-Horner inequality for electron counting statistics in multiterminal mesoscopic conductors / L. Faoro, F. Taddei and R. Fazio -- Fidelity of quantum teleportation model using beam splittings / K.-H. Fichtner, T. Miyadera and M. Ohya -- Quantum logical gates realized by beam splittings / W. Freudenberg ... [et al.] -- Information divergence for quantum channels / S. J. Hammersley and V. P. Belavkin -- On the uniqueness theorem in quantum information geometry / H. Hasegawa -- Noncanonical representations of a multi-dimensional Brownian motion / Y. Hibino -- Some of future directions of white noise theory / T. Hida -- Information, innovation and elemental random field / T. Hida -- Generalized quantum turing machine and its application to the SAT chaos algorithm / S. Iriyama, M. Ohya and I. Volovich -- A Stroboscopic approach to quantum tomography / A. Jamiolkowski -- Positive maps and separable states in matrix algebras / A. Kossakowski -- Simulating open quantum systems with trapped ions / S. Maniscalco -- A purification scheme and entanglement distillations / H. Nakazato, M. Unoki and K. Yuasa -- Generalized sectors and adjunctions to control micro-macro transitions / I. Ojima -- Saturation of an entropy bound and quantum Markov states / D. Petz -- An
Quantum computation and hidden variables
NASA Astrophysics Data System (ADS)
Aristov, V. V.; Nikulov, A. V.
2008-03-01
Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass delusion concerning the problem, how a quantum computer can be made. The idea of quantum computation can be described within the limits of quantum formalism. But in order to understand how this idea can be put into practice one should realize the question: "What could the quantum formalism describe?", in spite of the absence of an universally recognized answer. Only a realization of this question and the undecided problem of quantum foundations allows to see in which quantum systems the superposition and EPR correlation could be expected. Because of the "specialization barbarism" many authors are sure that Bell proved full impossibility of any hidden-variables interpretation. Therefore it is important to emphasize that in reality Bell has restricted to validity limits of the no-hidden-variables proof and has shown that two-state quantum system can be described by hidden variables. The later means that no experimental result obtained on two-state quantum system can prove the existence of superposition and violation of the realism. One should not assume before unambiguous experimental evidence that any two-state quantum system is quantum bit. No experimental evidence of superposition of macroscopically distinct quantum states and of a quantum bit on base of superconductor structure was obtained for the present. Moreover same experimental results can not be described in the limits of the quantum formalism.
Cryptography, quantum computation and trapped ions
Hughes, Richard J.
1998-03-01
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.
Experimental quantum computing without entanglement.
Lanyon, B P; Barbieri, M; Almeida, M P; White, A G
2008-11-14
Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.
PERTURBATION APPROACH FOR QUANTUM COMPUTATION
G. P. BERMAN; D. I. KAMENEV; V. I. TSIFRINOVICH
2001-04-01
We discuss how to simulate errors in the implementation of simple quantum logic operations in a nuclear spin quantum computer with many qubits, using radio-frequency pulses. We verify our perturbation approach using the exact solutions for relatively small (L = 10) number of qubits.
Quantum chromodynamics with advanced computing
Kronfeld, Andreas S.; /Fermilab
2008-07-01
We survey results in lattice quantum chromodynamics from groups in the USQCD Collaboration. The main focus is on physics, but many aspects of the discussion are aimed at an audience of computational physicists.
Quantum Compiling for Topological Quantum Computing
NASA Astrophysics Data System (ADS)
Svore, Krysta
2014-03-01
In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations for non-abelian quasiparticles described by the Fibonacci anyon model. We develop a probabilistically polynomial algorithm that outputs a braid pattern to approximate a given single-qubit unitary to a desired precision. We also classify the single-qubit unitaries that can be implemented exactly by a Fibonacci anyon braid pattern and present an efficient algorithm to produce their braid patterns. Our techniques produce braid patterns that meet the uniform asymptotic lower bound on the compiled circuit depth and thus are depth-optimal asymptotically. Our compiled circuits are significantly shorter than those output by prior state-of-the-art methods, resulting in improvements in depth by factors ranging from 20 to 1000 for precisions ranging between 10-10 and 10-30.
Fast graph operations in quantum computation
NASA Astrophysics Data System (ADS)
Zhao, Liming; Pérez-Delgado, Carlos A.; Fitzsimons, Joseph F.
2016-03-01
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in the reverse direction to yield a graph data structure, which allows for more efficient manipulation and comparison of graphs than any possible classical structure. We introduce efficient algorithms for many transformation and comparison operations on graphs represented as graph states, and prove that no classical data structure can have similar performance for the full set of operations studied.
Quantumness, Randomness and Computability
NASA Astrophysics Data System (ADS)
Solis, Aldo; Hirsch, Jorge G.
2015-06-01
Randomness plays a central role in the quantum mechanical description of our interactions. We review the relationship between the violation of Bell inequalities, non signaling and randomness. We discuss the challenge in defining a random string, and show that algorithmic information theory provides a necessary condition for randomness using Borel normality. We close with a view on incomputablity and its implications in physics.
Atomic physics: A milestone in quantum computing
NASA Astrophysics Data System (ADS)
Bartlett, Stephen D.
2016-08-01
Quantum computers require many quantum bits to perform complex calculations, but devices with more than a few bits are difficult to program. A device based on five atomic quantum bits shows a way forward. See Letter p.63
ASCR Workshop on Quantum Computing for Science
Aspuru-Guzik, Alan; Van Dam, Wim; Farhi, Edward; Gaitan, Frank; Humble, Travis; Jordan, Stephen; Landahl, Andrew J; Love, Peter; Lucas, Robert; Preskill, John; Muller, Richard P.; Svore, Krysta; Wiebe, Nathan; Williams, Carl
2015-06-01
This report details the findings of the DOE ASCR Workshop on Quantum Computing for Science that was organized to assess the viability of quantum computing technologies to meet the computational requirements of the DOE’s science and energy mission, and to identify the potential impact of quantum technologies. The workshop was held on February 17-18, 2015, in Bethesda, MD, to solicit input from members of the quantum computing community. The workshop considered models of quantum computation and programming environments, physical science applications relevant to DOE's science mission as well as quantum simulation, and applied mathematics topics including potential quantum algorithms for linear algebra, graph theory, and machine learning. This report summarizes these perspectives into an outlook on the opportunities for quantum computing to impact problems relevant to the DOE’s mission as well as the additional research required to bring quantum computing to the point where it can have such impact.
Course 10: Basic Concepts in Quantum Computation
NASA Astrophysics Data System (ADS)
Ekert, A.; Hayden, P. M.; Inamori, H.
Contents 1 Qubits, gates and networks 2 Quantum arithmetic and function evaluations 3 Algorithms and their complexity 4 From interferometers to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase estimation 8 Periodicity and quantum factoring 9 Cryptography 10 Conditional quantum dynamics 11 Decoherence and recoherence 12 Concluding remarks
General Quantum Interference Principle and Duality Computer
NASA Astrophysics Data System (ADS)
Long, Gui-Lu
2006-05-01
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
Brain Neurons as Quantum Computers:
NASA Astrophysics Data System (ADS)
Bershadskii, A.; Dremencov, E.; Bershadskii, J.; Yadid, G.
The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of brain neurons, has been actively discussed in the last years. A positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In the present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied in vivo on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in the generation of pleasure and in the development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a quantum system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental (in vivo) indication in the favor of the quantum (at least partially) nature of brain neurons activity.
Quantum computing with parafermions
NASA Astrophysics Data System (ADS)
Hutter, Adrian; Loss, Daniel
2016-03-01
Zd parafermions are exotic non-Abelian quasiparticles generalizing Majorana fermions, which correspond to the case d =2 . In contrast to Majorana fermions, braiding of parafermions with d >2 allows one to perform an entangling gate. This has spurred interest in parafermions, and a variety of condensed matter systems have been proposed as potential hosts for them. In this work, we study the computational power of braiding parafermions more systematically. We make no assumptions on the underlying physical model but derive all our results from the algebraical relations that define parafermions. We find a family of 2 d representations of the braid group that are compatible with these relations. The braiding operators derived this way reproduce those derived previously from physical grounds as special cases. We show that if a d -level qudit is encoded in the fusion space of four parafermions, braiding of these four parafermions allows one to generate the entire single-qudit Clifford group (up to phases), for any d . If d is odd, then we show that in fact the entire many-qudit Clifford group can be generated.
Geometry of discrete quantum computing
NASA Astrophysics Data System (ADS)
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Exploiting Locality in Quantum Computation for Quantum Chemistry.
McClean, Jarrod R; Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-12-18
Accurate prediction of chemical and material properties from first-principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route toward highly accurate solutions with polynomial cost; however, this solution still carries a large overhead. In this Perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provides numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.
Universal computation by multiparticle quantum walk.
Childs, Andrew M; Gosset, David; Webb, Zak
2013-02-15
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. We consider a generalization to interacting systems with more than one walker, such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions, and show that multiparticle quantum walk is capable of universal quantum computation. Our construction could, in principle, be used as an architecture for building a scalable quantum computer with no need for time-dependent control. PMID:23413349
Computational multiqubit tunnelling in programmable quantum annealers.
Boixo, Sergio; Smelyanskiy, Vadim N; Shabani, Alireza; Isakov, Sergei V; Dykman, Mark; Denchev, Vasil S; Amin, Mohammad H; Smirnov, Anatoly Yu; Mohseni, Masoud; Neven, Hartmut
2016-01-07
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.
Computational multiqubit tunnelling in programmable quantum annealers
Boixo, Sergio; Smelyanskiy, Vadim N.; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Denchev, Vasil S.; Amin, Mohammad H.; Smirnov, Anatoly Yu; Mohseni, Masoud; Neven, Hartmut
2016-01-01
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive. PMID:26739797
Computational multiqubit tunnelling in programmable quantum annealers
NASA Astrophysics Data System (ADS)
Boixo, Sergio; Smelyanskiy, Vadim N.; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Denchev, Vasil S.; Amin, Mohammad H.; Smirnov, Anatoly Yu; Mohseni, Masoud; Neven, Hartmut
2016-01-01
Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational multiqubit tunnelling has not yet been observed, and a theory of co-tunnelling under high- and low-frequency noises is lacking. Here we show that 8-qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. In support of the design of quantum annealers we develop a nonperturbative theory of open quantum dynamics under realistic noise characteristics. This theory accurately predicts the rate of many-body dissipative quantum tunnelling subject to the polaron effect. Furthermore, we experimentally demonstrate that quantum tunnelling outperforms thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive.
Experimental one-way quantum computing.
Walther, P; Resch, K J; Rudolph, T; Schenck, E; Weinfurter, H; Vedral, V; Aspelmeyer, M; Zeilinger, A
2005-03-10
Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.
Universal quantum computation using the discrete-time quantum walk
Lovett, Neil B.; Cooper, Sally; Everitt, Matthew; Trevers, Matthew; Kendon, Viv
2010-04-15
A proof that continuous-time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by A. M. Childs [Phys. Rev. Lett. 102, 180501 (2009)]. We present a version based instead on the discrete-time quantum walk. We show that the discrete-time quantum walk is able to implement the same universal gate set and thus both discrete and continuous-time quantum walks are computational primitives. Additionally, we give a set of components on which the discrete-time quantum walk provides perfect state transfer.
Layered Architectures for Quantum Computers and Quantum Repeaters
NASA Astrophysics Data System (ADS)
Jones, Nathan C.
This chapter examines how to organize quantum computers and repeaters using a systematic framework known as layered architecture, where machine control is organized in layers associated with specialized tasks. The framework is flexible and could be used for analysis and comparison of quantum information systems. To demonstrate the design principles in practice, we develop architectures for quantum computers and quantum repeaters based on optically controlled quantum dots, showing how a myriad of technologies must operate synchronously to achieve fault-tolerance. Optical control makes information processing in this system very fast, scalable to large problem sizes, and extendable to quantum communication.
Limitations of quantum computing with Gaussian cluster states
Ohliger, M.; Kieling, K.; Eisert, J.
2010-10-15
We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian-projected entangled pair states, we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information are not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states and points toward the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.
The Quantum Human Computer (QHC) Hypothesis
ERIC Educational Resources Information Center
Salmani-Nodoushan, Mohammad Ali
2008-01-01
This article attempts to suggest the existence of a human computer called Quantum Human Computer (QHC) on the basis of an analogy between human beings and computers. To date, there are two types of computers: Binary and Quantum. The former operates on the basis of binary logic where an object is said to exist in either of the two states of 1 and…
Symmetry-protected topologically ordered states for universal quantum computation
NASA Astrophysics Data System (ADS)
Poulsen Nautrup, Hendrik; Wei, Tzu-Chieh
Measurement-based quantum computation (MBQC) is a model for quantum information processing utilizing only local measurements on suitably entangled resource states for the implementation of quantum gates. A complete characterization for universal resource states is still missing. It has been shown that symmetry-protected topological order (SPTO) in one dimension can be exploited for the protection of certain quantum gates in MBQC. Here we investigate whether any 2D nontrivial SPTO states can serve as resource for MBQC. In particular, we show that the nontrivial SPTO ground state of the CZX model on the square lattice by Chen et al. [Phys. Rev. B 84, 235141 (2011)] can be reduced to a 2D cluster state by local measurement, hence a universal resource state. Such ground states have been generalized to qudits with symmetry action described by three cocycles of a finite group G of order d and shown to exhibit nontrivial SPTO. We also extend these to arbitary lattices and show that the generalized two-dimensional plaquette states on arbitrary lattices exhibit nontrivial SPTO in terms of symmetry fractionalization and that they are universal resource states for quantum computation. SPTO states therefore can provide a new playground for measurement-based quantum computation. This work was supported in part by the National Science Foundation.
Universal quantum computation with qudits
NASA Astrophysics Data System (ADS)
Luo, MingXing; Wang, XiaoJun
2014-09-01
Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm. Most of previous algorithms are based on the qubit systems. Herein a proposal for a universal circuit is given based on the qudit system, which is larger and can store more information. In order to prove its universality for quantum applications, an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation. The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions. In comparison to previous quantum qudit logical gates, each primitive qudit gate is only dependent on two free parameters and may be easily implemented. In experimental implementation, multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates. The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.
Non-unitary probabilistic quantum computing
NASA Technical Reports Server (NTRS)
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
Embracing the quantum limit in silicon computing.
Morton, John J L; McCamey, Dane R; Eriksson, Mark A; Lyon, Stephen A
2011-11-17
Quantum computers hold the promise of massive performance enhancements across a range of applications, from cryptography and databases to revolutionary scientific simulation tools. Such computers would make use of the same quantum mechanical phenomena that pose limitations on the continued shrinking of conventional information processing devices. Many of the key requirements for quantum computing differ markedly from those of conventional computers. However, silicon, which plays a central part in conventional information processing, has many properties that make it a superb platform around which to build a quantum computer. PMID:22094695
Embracing the quantum limit in silicon computing.
Morton, John J L; McCamey, Dane R; Eriksson, Mark A; Lyon, Stephen A
2011-11-16
Quantum computers hold the promise of massive performance enhancements across a range of applications, from cryptography and databases to revolutionary scientific simulation tools. Such computers would make use of the same quantum mechanical phenomena that pose limitations on the continued shrinking of conventional information processing devices. Many of the key requirements for quantum computing differ markedly from those of conventional computers. However, silicon, which plays a central part in conventional information processing, has many properties that make it a superb platform around which to build a quantum computer.
Adaptive quantum computation in changing environments using projective simulation
Tiersch, M.; Ganahl, E. J.; Briegel, H. J.
2015-01-01
Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent’s learning behavior in static and time-varying fields and explore composition strategies in the projective simulator to improve the agent’s performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover’s search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks. PMID:26260263
Adaptive quantum computation in changing environments using projective simulation
NASA Astrophysics Data System (ADS)
Tiersch, M.; Ganahl, E. J.; Briegel, H. J.
2015-08-01
Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent’s learning behavior in static and time-varying fields and explore composition strategies in the projective simulator to improve the agent’s performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover’s search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks.
Contextuality supplies the 'magic' for quantum computation.
Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph
2014-06-19
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms. PMID:24919152
Contextuality supplies the 'magic' for quantum computation.
Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph
2014-06-19
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.
Contextuality supplies the `magic' for quantum computation
NASA Astrophysics Data System (ADS)
Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph
2014-06-01
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via `magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple `hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.
Quantum computing with steady state spin currents
NASA Astrophysics Data System (ADS)
Sutton, Brian M.
Many approaches to quantum computing use spatially confined qubits in the presence of dynamic fields to perform computation. These approaches are contrasted with proposals using mobile qubits in the presence of static fields. In this thesis, steady state quantum computing using mobile electrons is explored using numerical modeling. Firstly, a foundational introduction to the case of spatially confined qubits embodied via quantum dots is provided. A collection of universal gates implemented with dynamic fields is described using simulations. These gates are combined to implement a five-qubit Grover search to provide further insight on the time-dependent field approach. Secondly, the quantum dot description is contrasted with quantum computing using steady state spin currents. Leveraging the Non-Equilibrium Greens Function formalism to perform numerical simulations, the quantum aspects of steady state spin currents are explored by revisiting the Stern-Gerlach experiment using spin-polarized contacts on a one-dimensional channel. After demonstrating the quantum nature of mobile electrons at steady state, arbitrary single qubit operations using static fields are explored. The model is further extended to incorporate two-qubit interactions to realize the square root of SWAP gate. The two-qubit CNOT gate is used to prepare a Bell state, which is read via quantum state tomography. Finally, Grover's search is revisited to explore the performance benefits of steady state quantum computing. The described multi-particle model is applicable to mobile qubit quantum computing proposals leveraging synchronized electron transport in static fields to perform quantum computing.
Assumptions for fault tolerant quantum computing
Knill, E.; Laflamme, R.
1996-06-01
Assumptions useful for fault tolerant quantum computing are stated and briefly discussed. We focus on assumptions related to properties of the computational system. The strongest form of the assumptions seems to be sufficient for achieving highly fault tolerant quantum computation. We discuss weakenings which are also likely to suffice.
Quantum computing. Defining and detecting quantum speedup.
Rønnow, Troels F; Wang, Zhihui; Job, Joshua; Boixo, Sergio; Isakov, Sergei V; Wecker, David; Martinis, John M; Lidar, Daniel A; Troyer, Matthias
2014-07-25
The development of small-scale quantum devices raises the question of how to fairly assess and detect quantum speedup. Here, we show how to define and measure quantum speedup and how to avoid pitfalls that might mask or fake such a speedup. We illustrate our discussion with data from tests run on a D-Wave Two device with up to 503 qubits. By using random spin glass instances as a benchmark, we found no evidence of quantum speedup when the entire data set is considered and obtained inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results do not rule out the possibility of speedup for other classes of problems and illustrate the subtle nature of the quantum speedup question.
Molecular Realizations of Quantum Computing 2007
NASA Astrophysics Data System (ADS)
Nakahara, Mikio; Ota, Yukihiro; Rahimi, Robabeh; Kondo, Yasushi; Tada-Umezaki, Masahito
2009-06-01
Liquid-state NMR quantum computer: working principle and some examples / Y. Kondo -- Flux qubits, tunable coupling and beyond / A. O. Niskanen -- Josephson phase qubits, and quantum communication via a resonant cavity / M. A. Sillanpää -- Quantum computing using pulse-based electron-nuclear double resonance (ENDOR): molecular spin-qubits / K. Sato ... [et al.] -- Fullerene C[symbol]: a possible molecular quantum computer / T. Wakabayashi -- Molecular magnets for quantum computation / T. Kuroda -- Errors in a plausible scheme of quantum gates in Kane's model / Y. Ota -- Yet another formulation for quantum simultaneous noncooperative bimatrix games / A. SaiToh, R. Rahimi, M. Nakahara -- Continuous-variable teleportation of single-photon states and an accidental cloning of a photonic qubit in two-channel teleportation / T. Ide.
Quantum Computational Logics and Possible Applications
NASA Astrophysics Data System (ADS)
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Leporini, Roberto; di Francia, Giuliano Toraldo
2008-01-01
In quantum computational logics meanings of formulas are identified with quantum information quantities: systems of qubits or, more generally, mixtures of systems of qubits. We consider two kinds of quantum computational semantics: (1) a compositional semantics, where the meaning of a compound formula is determined by the meanings of its parts; (2) a holistic semantics, which makes essential use of the characteristic “holistic” features of the quantum-theoretic formalism. The compositional and the holistic semantics turn out to characterize the same logic. In this framework, one can introduce the notion of quantum-classical truth table, which corresponds to the most natural way for a quantum computer to calculate classical tautologies. Quantum computational logics can be applied to investigate different kinds of semantic phenomena where holistic, contextual and gestaltic patterns play an essential role (from natural languages to musical compositions).
Prospects for quantum computation with trapped ions
Hughes, R.J.; James, D.F.V.
1997-12-31
Over the past decade information theory has been generalized to allow binary data to be represented by two-state quantum mechanical systems. (A single two-level system has come to be known as a qubit in this context.) The additional freedom introduced into information physics with quantum systems has opened up a variety of capabilities that go well beyond those of conventional information. For example, quantum cryptography allows two parties to generate a secret key even in the presence of eavesdropping. But perhaps the most remarkable capabilities have been predicted in the field of quantum computation. Here, a brief survey of the requirements for quantum computational hardware, and an overview of the in trap quantum computation project at Los Alamos are presented. The physical limitations to quantum computation with trapped ions are discussed.
Some Thoughts Regarding Practical Quantum Computing
NASA Astrophysics Data System (ADS)
Ghoshal, Debabrata; Gomez, Richard; Lanzagorta, Marco; Uhlmann, Jeffrey
2006-03-01
Quantum computing has become an important area of research in computer science because of its potential to provide more efficient algorithmic solutions to certain problems than are possible with classical computing. The ability of performing parallel operations over an exponentially large computational space has proved to be the main advantage of the quantum computing model. In this regard, we are particularly interested in the potential applications of quantum computers to enhance real software systems of interest to the defense, industrial, scientific and financial communities. However, while much has been written in popular and scientific literature about the benefits of the quantum computational model, several of the problems associated to the practical implementation of real-life complex software systems in quantum computers are often ignored. In this presentation we will argue that practical quantum computation is not as straightforward as commonly advertised, even if the technological problems associated to the manufacturing and engineering of large-scale quantum registers were solved overnight. We will discuss some of the frequently overlooked difficulties that plague quantum computing in the areas of memories, I/O, addressing schemes, compilers, oracles, approximate information copying, logical debugging, error correction and fault-tolerant computing protocols.
Disciplines, models, and computers: the path to computational quantum chemistry.
Lenhard, Johannes
2014-12-01
Many disciplines and scientific fields have undergone a computational turn in the past several decades. This paper analyzes this sort of turn by investigating the case of computational quantum chemistry. The main claim is that the transformation from quantum to computational quantum chemistry involved changes in three dimensions. First, on the side of instrumentation, small computers and a networked infrastructure took over the lead from centralized mainframe architecture. Second, a new conception of computational modeling became feasible and assumed a crucial role. And third, the field of computa- tional quantum chemistry became organized in a market-like fashion and this market is much bigger than the number of quantum theory experts. These claims will be substantiated by an investigation of the so-called density functional theory (DFT), the arguably pivotal theory in the turn to computational quantum chemistry around 1990.
The Heisenberg representation of quantum computers
Gottesman, D.
1998-06-24
Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.
Quantum computing with realistically noisy devices.
Knill, E
2005-03-01
In theory, quantum computers offer a means of solving problems that would be intractable on conventional computers. Assuming that a quantum computer could be constructed, it would in practice be required to function with noisy devices called 'gates'. These gates cause decoherence of the fragile quantum states that are central to the computer's operation. The goal of so-called 'fault-tolerant quantum computing' is therefore to compute accurately even when the error probability per gate (EPG) is high. Here we report a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent. Such EPGs have been experimentally demonstrated, but to avoid excessive resource overheads required by the necessary architecture, lower EPGs are needed. Assuming the availability of quantum resources comparable to the digital resources available in today's computers, we show that non-trivial quantum computations at EPGs of as high as one per cent could be implemented.
Quantum Computer Games: Schrodinger Cat and Hounds
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2012-01-01
The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…
Pattern recognition on a quantum computer
Schuetzhold, Ralf
2003-06-01
By means of a simple example, it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (dataset) can be accomplished efficiently by a quantum computer. Employing the powerful tool of the quantum Fourier transform, the proposed quantum algorithm exhibits an exponential speedup in comparison with its classical counterpart.
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-01
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.
Quantum and classical dynamics in adiabatic computation
NASA Astrophysics Data System (ADS)
Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.
2014-10-01
Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing—though inconclusive—results.
Functional quantum computing: An optical approach
NASA Astrophysics Data System (ADS)
Rambo, Timothy M.; Altepeter, Joseph B.; Kumar, Prem; D'Ariano, G. Mauro
2016-05-01
Recent theoretical investigations treat quantum computations as functions, quantum processes which operate on other quantum processes, rather than circuits. Much attention has been given to the N -switch function which takes N black-box quantum operators as input, coherently permutes their ordering, and applies the result to a target quantum state. This is something which cannot be equivalently done using a quantum circuit. Here, we propose an all-optical system design which implements coherent operator permutation for an arbitrary number of input operators.
Embedding quantum simulators for quantum computation of entanglement.
Di Candia, R; Mejia, B; Castillo, H; Pedernales, J S; Casanova, J; Solano, E
2013-12-13
We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum dynamics in the enlarged Hilbert space of an embedding quantum simulator. In this manner, entanglement monotones are conveniently mapped onto physical observables, overcoming the necessity of full tomography and reducing drastically the experimental requirements. Furthermore, this method is directly applicable to pure states and, assisted by classical algorithms, to the mixed-state case. Finally, we expect that the proposed embedding framework paves the way for a general theory of enhanced one-to-one quantum simulators.
Measurement-based quantum phase estimation algorithm for finding eigenvalues of non-unitary matrices
Wang Hefeng; Nori, Franco; Wu Lianao; Liu Yuxi
2010-12-15
We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues and eigenvectors. This proposal combines ideas of frequent measurement, measured quantum Fourier transform, and quantum state tomography. It provides a generalization of the conventional phase estimation algorithm, which is limited to Hermitian or unitary matrices.
Quantum error correction and fault-tolerant quantum computation
NASA Astrophysics Data System (ADS)
Lai, Ching-Yi
Quantum computers need to be protected by quantum error-correcting codes against decoherence. One of the most interesting and useful classes of quantum codes is the class of quantum stabilizer codes. Entanglement-assisted (EA) quantum codes are a class of stabilizer codes that make use of preshared entanglement between the sender and the receiver. We provide several code constructions for entanglement-assisted quantum codes. The MacWilliams identity for quantum codes leads to linear programming bounds on the minimum distance. We find new constraints on the simplified stabilizer group and the logical group, which help improve the linear programming bounds on entanglement-assisted quantum codes. The results also can be applied to standard stabilizer codes. In the real world, quantum gates are faulty. To implement quantum computation fault-tolerantly, quantum codes with certain properties are needed. We first analyze Knill's postselection scheme in a two-dimensional architecture. The error performance of this scheme is better than other known concatenated codes. Then we propose several methods to protect syndrome extraction against measurement errors.
Experimental demonstration of deterministic one-way quantum computation on a NMR quantum computer
Ju, Chenyong; Zhu Jing; Peng Xinhua; Chong Bo; Zhou Xianyi; Du Jiangfeng
2010-01-15
One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report an experimental realization of the complete process of deterministic one-way quantum Deutsch-Josza algorithm in NMR, including graph state preparation, single-qubit measurements, and feed-forward corrections. The findings in our experiment may shed light on the future scalable one-way quantum computation.
Adiabatic Quantum Computation and the Theory of Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Kaminsky, William; Lloyd, Seth
2007-03-01
We present a general approach to determining the asymptotic scaling of adiabatic quantum computational resources (space, time, energy, and precision) on random instances of NP-complete graph theory problems. By utilizing the isomorphisms between certain NP-complete graph theory problems and certain frustrated spin models, we demonstrate that the asymptotic scaling of the minimum spectral gap that determines the asymptotic running time of adiabatic algorithms is itself determined by the presence and character of quantum phase transitions in these frustrated models. Most notably, we draw the conclusion that adiabatic quantum computers based on quantum Ising models are much less likely to be efficient than those based on quantum rotor or Heisenberg models. We then exhibit practical rotor and Heisenberg model based architectures using Josephson junction and quantum dot circuits.
Cavity QED Deutsch quantum computer
NASA Astrophysics Data System (ADS)
Hollenberg, Lloyd C. L.; Salgueiro, A. N.; Nemes, M. C.
2001-10-01
The two-atom correlation scheme originally proposed by Davidovich, Brune, Raimond, and Haroche for measuring the decoherence of a mesoscopic superposition of coherent states of a QED cavity field is shown to be equivalent to a quantum computer solving Deutsch's problem. Using the existing analysis of decoherence in the Master equation formalism, and other important losses in this system, the final probability for obtaining the correct result for the computation is found in terms of the time period between atom traversals, the number of photons in the cavity, and the precision of the atomic velocity. The error due to decoherence in this system amounts to a phase error, and in the Master equation approach is a linear effect at small time scales. By explicitly considering the dynamics of the decoherence process when the system is coupled to a bath of oscillators with finite mode cutoff the error due to decoherence is found to decrease significantly and becomes a quadratic effect at short-time scales.
Universal quantum computation with little entanglement.
Van den Nest, Maarten
2013-02-01
We show that universal quantum computation can be achieved in the standard pure-state circuit model while the entanglement entropy of every bipartition is small in each step of the computation. The entanglement entropy required for large-scale quantum computation even tends to zero. Moreover we show that the same conclusion applies to many entanglement measures commonly used in the literature. This includes e.g., the geometric measure, localizable entanglement, multipartite concurrence, squashed entanglement, witness-based measures, and more generally any entanglement measure which is continuous in a certain natural sense. These results demonstrate that many entanglement measures are unsuitable tools to assess the power of quantum computers.
The case for biological quantum computer elements
NASA Astrophysics Data System (ADS)
Baer, Wolfgang; Pizzi, Rita
2009-05-01
An extension to vonNeumann's analysis of quantum theory suggests self-measurement is a fundamental process of Nature. By mapping the quantum computer to the brain architecture we will argue that the cognitive experience results from a measurement of a quantum memory maintained by biological entities. The insight provided by this mapping suggests quantum effects are not restricted to small atomic and nuclear phenomena but are an integral part of our own cognitive experience and further that the architecture of a quantum computer system parallels that of a conscious brain. We will then review the suggestions for biological quantum elements in basic neural structures and address the de-coherence objection by arguing for a self- measurement event model of Nature. We will argue that to first order approximation the universe is composed of isolated self-measurement events which guaranties coherence. Controlled de-coherence is treated as the input/output interactions between quantum elements of a quantum computer and the quantum memory maintained by biological entities cognizant of the quantum calculation results. Lastly we will present stem-cell based neuron experiments conducted by one of us with the aim of demonstrating the occurrence of quantum effects in living neural networks and discuss future research projects intended to reach this objective.
Performing quantum computing experiments in the cloud
NASA Astrophysics Data System (ADS)
Devitt, Simon J.
2016-09-01
Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.
Graph isomorphism and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Gaitan, Frank; Clark, Lane
2014-02-01
In the graph isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G →G'. If yes, then G and G' are said to be isomorphic; otherwise they are nonisomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. In this paper we present a quantum algorithm that solves arbitrary instances of GI and which also provides an approach to determining all automorphisms of a given graph. We show how the GI problem can be converted to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. We numerically simulate the algorithm's quantum dynamics and show that it correctly (i) distinguishes nonisomorphic graphs; (ii) recognizes isomorphic graphs and determines the permutation(s) that connect them; and (iii) finds the automorphism group of a given graph G. We then discuss the GI quantum algorithm's experimental implementation, and close by showing how it can be leveraged to give a quantum algorithm that solves arbitrary instances of the NP-complete subgraph isomorphism problem. The computational complexity of an adiabatic quantum algorithm is largely determined by the minimum energy gap Δ (N) separating the ground and first-excited states in the limit of large problem size N ≫1. Calculating Δ (N) in this limit is a fundamental open problem in adiabatic quantum computing, and so it is not possible to determine the computational complexity of adiabatic quantum algorithms in general, nor consequently, of the specific adiabatic quantum algorithms presented here. Adiabatic quantum computing has been shown to be equivalent to the circuit model of quantum computing, and so development of adiabatic quantum algorithms continues to be of great interest.
Universal quantum computation with weakly integral anyons
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Hong, Seung-Moon; Wang, Zhenghan
2015-08-01
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral—anyons whose squared quantum dimensions are integers. We analyze the computational power of the first non-abelian anyon system with only integral quantum dimensions—, the quantum double of . Since all anyons in have finite images of braid group representations, they cannot be universal for quantum computation by braiding alone. Based on our knowledge of the images of the braid group representations, we set up three qutrit computational models. Supplementing braidings with some measurements and ancillary states, we find a universal gate set for each model.
Video Encryption and Decryption on Quantum Computers
NASA Astrophysics Data System (ADS)
Yan, Fei; Iliyasu, Abdullah M.; Venegas-Andraca, Salvador E.; Yang, Huamin
2015-08-01
A method for video encryption and decryption on quantum computers is proposed based on color information transformations on each frame encoding the content of the encoding the content of the video. The proposed method provides a flexible operation to encrypt quantum video by means of the quantum measurement in order to enhance the security of the video. To validate the proposed approach, a tetris tile-matching puzzle game video is utilized in the experimental simulations. The results obtained suggest that the proposed method enhances the security and speed of quantum video encryption and decryption, both properties required for secure transmission and sharing of video content in quantum communication.
Quantum Computation Using Optically Coupled Quantum Dot Arrays
NASA Technical Reports Server (NTRS)
Pradhan, Prabhakar; Anantram, M. P.; Wang, K. L.; Roychowhury, V. P.; Saini, Subhash (Technical Monitor)
1998-01-01
A solid state model for quantum computation has potential advantages in terms of the ease of fabrication, characterization, and integration. The fundamental requirements for a quantum computer involve the realization of basic processing units (qubits), and a scheme for controlled switching and coupling among the qubits, which enables one to perform controlled operations on qubits. We propose a model for quantum computation based on optically coupled quantum dot arrays, which is computationally similar to the atomic model proposed by Cirac and Zoller. In this model, individual qubits are comprised of two coupled quantum dots, and an array of these basic units is placed in an optical cavity. Switching among the states of the individual units is done by controlled laser pulses via near field interaction using the NSOM technology. Controlled rotations involving two or more qubits are performed via common cavity mode photon. We have calculated critical times, including the spontaneous emission and switching times, and show that they are comparable to the best times projected for other proposed models of quantum computation. We have also shown the feasibility of accessing individual quantum dots using the NSOM technology by calculating the photon density at the tip, and estimating the power necessary to perform the basic controlled operations. We are currently in the process of estimating the decoherence times for this system; however, we have formulated initial arguments which seem to indicate that the decoherence times will be comparable, if not longer, than many other proposed models.
Measurement-based performance evaluation technique for high-performance computers
NASA Technical Reports Server (NTRS)
Sharma, S.; Natarajan, C.; Iyer, R. K.
1993-01-01
A measurement-based performance evaluation technique has been used to characterize the OS performance of Cedar, a hierarchical shared-memory multiprocessor system. Thirteen OS performance meters were used to capture the operating system activities for compute-bound workloads. Three representative applications from the Perfect Benchmark Suite were used to measure the OS performance in a dedicated system and in multiprogrammed workloads. It was found that 13-23 percent of the total execution time on a dedicated system was spent in executing OS-related activities. Under multiprogramming, 12-14 percent of the total execution time was used by the OS. The impact of multiprogramming on the operating system performance meters was also measured.
Conceptual aspects of geometric quantum computation
NASA Astrophysics Data System (ADS)
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-07-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Conceptual aspects of geometric quantum computation
NASA Astrophysics Data System (ADS)
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-10-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Hyper-parallel photonic quantum computation with coupled quantum dots.
Ren, Bao-Cang; Deng, Fu-Guo
2014-04-11
It is well known that a parallel quantum computer is more powerful than a classical one. So far, there are some important works about the construction of universal quantum logic gates, the key elements in quantum computation. However, they are focused on operating on one degree of freedom (DOF) of quantum systems. Here, we investigate the possibility of achieving scalable hyper-parallel quantum computation based on two DOFs of photon systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating on both the spatial-mode and the polarization DOFs of a two-photon system simultaneously, by exploiting the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics (QED). This hyper-CNOT gate is implemented by manipulating the four qubits in the two DOFs of a two-photon system without auxiliary spatial modes or polarization modes. It reduces the operation time and the resources consumed in quantum information processing, and it is more robust against the photonic dissipation noise, compared with the integration of several cascaded CNOT gates in one DOF.
One-way quantum computation with circuit quantum electrodynamics
Wu Chunwang; Han Yang; Chen Pingxing; Li Chengzu; Zhong Xiaojun
2010-03-15
In this Brief Report, we propose a potential scheme to implement one-way quantum computation with circuit quantum electrodynamics (QED). Large cluster states of charge qubits can be generated in just one step with a superconducting transmission line resonator (TLR) playing the role of a dispersive coupler. A single-qubit measurement in the arbitrary basis can be implemented using a single electron transistor with the help of one-qubit gates. By examining the main decoherence sources, we show that circuit QED is a promising architecture for one-way quantum computation.
Materials Frontiers to Empower Quantum Computing
Taylor, Antoinette Jane; Sarrao, John Louis; Richardson, Christopher
2015-06-11
This is an exciting time at the nexus of quantum computing and materials research. The materials frontiers described in this report represent a significant advance in electronic materials and our understanding of the interactions between the local material and a manufactured quantum state. Simultaneously, directed efforts to solve materials issues related to quantum computing provide an opportunity to control and probe the fundamental arrangement of matter that will impact all electronic materials. An opportunity exists to extend our understanding of materials functionality from electronic-grade to quantum-grade by achieving a predictive understanding of noise and decoherence in qubits and their origins in materials defects and environmental coupling. Realizing this vision systematically and predictively will be transformative for quantum computing and will represent a qualitative step forward in materials prediction and control.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-01
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Superadiabatic Controlled Evolutions and Universal Quantum Computation
Santos, Alan C.; Sarandy, Marcelo S.
2015-01-01
Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts. PMID:26511064
Reducing computational complexity of quantum correlations
NASA Astrophysics Data System (ADS)
Chanda, Titas; Das, Tamoghna; Sadhukhan, Debasis; Pal, Amit Kumar; SenDe, Aditi; Sen, Ujjwal
2015-12-01
We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures such as quantum discord and quantum work deficit in two qubits and higher-dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having nonpositive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.
Is the Brain a Quantum Computer?
ERIC Educational Resources Information Center
Litt, Abninder; Eliasmith, Chris; Kroon, Frederick W.; Weinstein, Steven; Thagard, Paul
2006-01-01
We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic…
Directional coupling for quantum computing and communication.
Nikolopoulos, Georgios M
2008-11-14
We introduce the concept of directional coupling, i.e., the selective transfer of a state between adjacent quantum wires, in the context of quantum computing and communication. Our analysis rests upon a mathematical analogy between a dual-channel directional coupler and a composite spin system.
Quantum computation with optical coherent states
Ralph, T.C.; Gilchrist, A.; Milburn, G.J.; Munro, W.J.; Glancy, S.
2003-10-01
We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and 'small' coherent superposition resource states.
Quantum computing Hyper Terahertz Facility opens
NASA Astrophysics Data System (ADS)
Singh Chadha, Kulvinder
2016-01-01
A new facility has opened at the University of Surrey to use terahertz radiation for quantum computing. The Hyper Terahertz Facility (HTF) is a joint collaboration between the University of Surrey and the National Physical Laboratory (NPL).
Iterated Gate Teleportation and Blind Quantum Computation.
Pérez-Delgado, Carlos A; Fitzsimons, Joseph F
2015-06-01
Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraint only holds in limited scenarios, and show how to overcome it using a novel method of iterated gate teleportations. This technique enables drastic reductions in the communication required for distributed quantum protocols, extending beyond the blind computation setting. Applied to blind quantum computation, this technique offers significant efficiency improvements, and in some scenarios offers an exponential reduction in communication requirements. PMID:26196609
Iterated Gate Teleportation and Blind Quantum Computation.
Pérez-Delgado, Carlos A; Fitzsimons, Joseph F
2015-06-01
Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraint only holds in limited scenarios, and show how to overcome it using a novel method of iterated gate teleportations. This technique enables drastic reductions in the communication required for distributed quantum protocols, extending beyond the blind computation setting. Applied to blind quantum computation, this technique offers significant efficiency improvements, and in some scenarios offers an exponential reduction in communication requirements.
Braid group representation on quantum computation
Aziz, Ryan Kasyfil; Muchtadi-Alamsyah, Intan
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
Cat-qubits for quantum computation
NASA Astrophysics Data System (ADS)
Mirrahimi, Mazyar
2016-08-01
The development of quantum Josephson circuits has created a strong expectation for reliable processing of quantum information. While this progress has already led to various proof-of-principle experiments on small-scale quantum systems, a major scaling step is required towards many-qubit protocols. Fault-tolerant computation with protected logical qubits usually comes at the expense of a significant overhead in the hardware. Each of the involved physical qubits still needs to satisfy the best achieved properties (coherence times, coupling strengths and tunability). Here, and in the aim of addressing alternative approaches to deal with these obstacles, I overview a series of recent theoretical proposals, and the experimental developments following these proposals, to enable a hardware-efficient paradigm for quantum memory protection and universal quantum computation.
Robust dynamical decoupling for quantum computing and quantum memory.
Souza, Alexandre M; Alvarez, Gonzalo A; Suter, Dieter
2011-06-17
Dynamical decoupling (DD) is a popular technique for protecting qubits from the environment. However, unless special care is taken, experimental errors in the control pulses used in this technique can destroy the quantum information instead of preserving it. Here, we investigate techniques for making DD sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment. We present experimental data from solid-state nuclear spin qubits and introduce a new DD sequence that is suitable for quantum computing and quantum memory.
Irreconcilable difference between quantum walks and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Wong, Thomas G.; Meyer, David A.
2016-06-01
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.
Efficient quantum circuits for one-way quantum computing.
Tanamoto, Tetsufumi; Liu, Yu-Xi; Hu, Xuedong; Nori, Franco
2009-03-13
While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show an efficient way of generating cluster states directly using either the imaginary SWAP (iSWAP) gate for the XY model, or the sqrt[SWAP] gate for the Heisenberg model. Our approach thus makes one-way quantum computing more feasible for solid-state devices.
Nondissipative decoherence bounds on quantum computation
NASA Astrophysics Data System (ADS)
Mancini, Stefano; Bonifacio, Rodolfo
2001-03-01
We investigate the capabilities of a quantum computer based on cold trapped ions in the presence of nondissipative decoherence. The latter is accounted by using the evolution time as a random variable and then averaging on a properly defined probability distribution. Severe bounds on computational performances are found.
Qubus ancilla-driven quantum computation
NASA Astrophysics Data System (ADS)
Brown, Katherine Louise; De, Suvabrata; Kendon, Viv; Munro, Bill
2014-12-01
Hybrid matter-optical systems offer a robust, scalable path to quantum computation. Such systems have an ancilla which acts as a bus connecting the qubits. We demonstrate how using a continuous variable qubus as the ancilla provides savings in the total number of operations required when computing with many qubits.
Qubus ancilla-driven quantum computation
Brown, Katherine Louise; De, Suvabrata; Kendon, Viv; Munro, Bill
2014-12-04
Hybrid matter-optical systems offer a robust, scalable path to quantum computation. Such systems have an ancilla which acts as a bus connecting the qubits. We demonstrate how using a continuous variable qubus as the ancilla provides savings in the total number of operations required when computing with many qubits.
Biologically inspired path to quantum computer
NASA Astrophysics Data System (ADS)
Ogryzko, Vasily; Ozhigov, Yuri
2014-12-01
We describe an approach to quantum computer inspired by the information processing at the molecular level in living cells. It is based on the separation of a small ensemble of qubits inside the living system (e.g., a bacterial cell), such that coherent quantum states of this ensemble remain practically unchanged for a long time. We use the notion of a quantum kernel to describe such an ensemble. Quantum kernel is not strictly connected with certain particles; it permanently exchanges atoms and molecules with the environment, which makes quantum kernel a virtual notion. There are many reasons to expect that the state of quantum kernel of a living system can be treated as the stationary state of some Hamiltonian. While the quantum kernel is responsible for the stability of dynamics at the time scale of cellular life, at the longer inter-generation time scale it can change, varying smoothly in the course of biological evolution. To the first level of approximation, quantum kernel can be described in the framework of qubit modification of Jaynes-Cummings-Hubbard model, in which the relaxation corresponds to the exchange of matter between quantum kernel and the rest of the cell and is represented as Lindblad super-operators.
Power of one qumode for quantum computation
NASA Astrophysics Data System (ADS)
Liu, Nana; Thompson, Jayne; Weedbrook, Christian; Lloyd, Seth; Vedral, Vlatko; Gu, Mile; Modi, Kavan
2016-05-01
Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class of problems where quantum computers possess an advantage is phase estimation, which includes applications like factoring. We introduce a computational model based on a single squeezed state resource that can perform phase estimation, which we call the power of one qumode. This model is inspired by an interesting computational model known as deterministic quantum computing with one quantum bit (DQC1). Using the power of one qumode, we identify that the amount of squeezing is sufficient to quantify the resource requirements of different computational problems based on phase estimation. In particular, we can use the amount of squeezing to quantitatively relate the resource requirements of DQC1 and factoring. Furthermore, we can connect the squeezing to other known resources like precision, energy, qudit dimensionality, and qubit number. We show the circumstances under which they can likewise be considered good resources.
Accelerating commutation circuits in quantum computer networks
NASA Astrophysics Data System (ADS)
Jiang, Min; Huang, Xu; Chen, Xiaoping; Zhang, Zeng-ke
2012-12-01
In a high speed and packet-switched quantum computer network, a packet routing delay often leads to traffic jams, becoming a severe bottleneck for speeding up the transmission rate. Based on the delayed commutation circuit proposed in Phys. Rev. Lett. 97, 110502 (2006), we present an improved scheme for accelerating network transmission. For two more realistic scenarios, we utilize the characteristic of a quantum state to simultaneously implement a data switch and transmission that makes it possible to reduce the packet delay and route a qubit packet even before its address is determined. This circuit is further extended to the quantum network for the transmission of the unknown quantum information. The analysis demonstrates that quantum communication technology can considerably reduce the processing delay time and build faster and more efficient packet-switched networks.
Entanglement and Quantum Computation: An Overview
Perez, R.B.
2000-06-27
This report presents a selective compilation of basic facts from the fields of particle entanglement and quantum information processing prepared for those non-experts in these fields that may have interest in an area of physics showing counterintuitive, ''spooky'' (Einstein's words) behavior. In fact, quantum information processing could, in the near future, provide a new technology to sustain the benefits to the U.S. economy due to advanced computer technology.
Information-theoretic temporal Bell inequality and quantum computation
Morikoshi, Fumiaki
2006-05-15
An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation.
Quantum computation with ions in microscopic traps
NASA Astrophysics Data System (ADS)
Šašura, Marek; Steane, Andrew M.
2002-12-01
We discuss a possible experimental realization of fast quantum gates with high fidelity with ions confined in microscopic traps. The original proposal of this physical system for quantum computation comes from Cirac and Zoller (Nature 404, 579 (2000)). In this paper we analyse a sensitivity of the ion-trap quantum gate on various experimental parameters which was omitted in the original proposal. We address imprecision of laser pulses, impact of photon scattering, nonzero temperature effects and influence of laser intensity fluctuations on the total fidelity of the two-qubit phase gate.
Computations in quantum mechanics made easy
NASA Astrophysics Data System (ADS)
Korsch, H. J.; Rapedius, K.
2016-09-01
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.
Quantum computation with ``hot`` trapped ions
James, D.F.V.; Schneider, S. |; Milburn, G.J.
1998-12-31
The authors describe two methods that have been proposed to circumvent the problem of heating by external electromagnetic fields in ion trap quantum computers. Firstly the higher order modes of ion oscillation (i.e., modes other than the center-of-mass mode) have much slower heating rates, and can therefore be employed as a reliable quantum information bus. Secondly they discuss a recently proposed method combining adiabatic passage and a number-state dependent phase shift which allows quantum gates to be performed using the center-of-mass mode as the information bus, regardless of its initial state.
Universal dephasing control during quantum computation
Gordon, Goren; Kurizki, Gershon
2007-10-15
Dephasing is a ubiquitous phenomenon that leads to the loss of coherence in quantum systems and the corruption of quantum information. We present a universal dynamical control approach to combat dephasing during all stages of quantum computation, namely, storage and single- and two-qubit operators. We show that (a) tailoring multifrequency gate pulses to the dephasing dynamics can increase fidelity; (b) cross-dephasing, introduced by entanglement, can be eliminated by appropriate control fields; (c) counterintuitively and contrary to previous schemes, one can increase the gate duration, while simultaneously increasing the total gate fidelity.
Quantum Computing: Theoretical versus Practical Possibility
NASA Astrophysics Data System (ADS)
Paraoanu, G. S.
2011-09-01
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle—there are no known laws of Nature that prevent it—yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I distinguish between "strong" and "weak" emergentist positions. The former assumes that a critical value of a parameter exists (one that is most likely related to the complexity of the states involved) at which the quantum-mechanical description breaks down, in other words, that quantum mechanics will turn out to be an incomplete description of reality. The latter assumes that quantum mechanics will remain as a universally valid theory, but that the classical resources required to build a real quantum computer scale up with the number of qubits, which hints that a limiting principle is at work.
Can the human brain do quantum computing?
Rocha, A F; Massad, E; Coutinho, F A B
2004-01-01
The electrical membrane properties have been the key issues in the understanding of the cerebral physiology for more than almost two centuries. But, molecular neurobiology has now discovered that biochemical transactions play an important role in neuronal computations. Quantum computing (QC) is becoming a reality both from the theoretical point of view as well as from practical applications. Quantum mechanics is the most accurate description at atomic level and it lies behind all chemistry that provides the basis for biology ... maybe the magic of entanglement is also crucial for life. The purpose of the present paper is to discuss the dendrite spine as a quantum computing device, taking into account what is known about the physiology of the glutamate receptors and the cascade of biochemical transactions triggered by the glutamate binding to these receptors.
Ultrafast quantum nondemolition measurement based on diamond-shaped artificial atom
NASA Astrophysics Data System (ADS)
Küng, Bruno; Dumur, Etienne; Diniz, Igor; Feofanov, Alexey; Weissl, Thomas; Naud, Cécile; Guichard, Wiebke; Auffèves, Alexia; Buisson, Olivier
2014-03-01
We present a theoretical study of a quantum nondemolition readout scheme based on a superconducting artificial atom with two internal degrees of freedom. In comparison with the most widely employed readout scheme for superconducting qubits, the dispersive readout in a circuit quantum electrodynamics architecture, our approach promises a significantly stronger measurement signal. This should allow for a high-fidelity readout in a single shot. Our device consists of two transmons (i.e., small capacitively shunted Josephson junctions) coupled via a large inductance. The resulting circuit exhibits a symmetric and an antisymmetric oscillation which we use as a logical and ancilla qubit, respectively. The Josephson non-linearity leads to a cross-Kerr-like coupling of the two oscillations. This allows us to read out the logical qubit state by measuring the ancilla qubit frequency. To measure the ancilla qubit frequency, we couple it to a superconducting microwave resonator, allowing for a large amplitude and a fast response of the transmitted microwave signal. At the same time, the logical qubit remains weakly coupled and far detuned from the resonator, preventing qubit relaxation due to the Purcell effect.
Silicon enhancement mode nanostructures for quantum computing.
Carroll, Malcolm S.
2010-03-01
Development of silicon, enhancement mode nanostructures for solid-state quantum computing will be described. A primary motivation of this research is the recent unprecedented manipulation of single electron spins in GaAs quantum dots, which has been used to demonstrate a quantum bit. Long spin decoherence times are predicted possible in silicon qubits. This talk will focus on silicon enhancement mode quantum dot structures that emulate the GaAs lateral quantum dot qubit but use an enhancement mode field effect transistor (FET) structure. One critical concern for silicon quantum dots that use oxides as insulators in the FET structure is that defects in the metal oxide semiconductor (MOS) stack can produce both detrimental electrostatic and paramagnetic effects on the qubit. Understanding the implications of defects in the Si MOS system is also relevant for other qubit architectures that have nearby dielectric passivated surfaces. Stable, lithographically defined, single-period Coulomb-blockade and single-electron charge sensing in a quantum dot nanostructure using a MOS stack will be presented. A combination of characterization of defects, modeling and consideration of modified approaches that incorporate SiGe or donors provides guidance about the enhancement mode MOS approach for future qubits and quantum circuit micro-architecture.
Trading Classical and Quantum Computational Resources
NASA Astrophysics Data System (ADS)
Bravyi, Sergey; Smith, Graeme; Smolin, John A.
2016-04-01
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First, we consider sparse quantum circuits such that each qubit participates in O (1 ) two-qubit gates. It is shown that any sparse circuit on n +k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time 2O (k )poly (n ) . Second, we study Pauli-based computation (PBC), where allowed operations are nondestructive eigenvalue measurements of n -qubit Pauli operators. The computation begins by initializing each qubit in the so-called magic state. This model is known to be equivalent to the universal quantum computer. We show that any PBC on n +k qubits can be simulated by PBCs on n qubits and a classical processing that takes time 2O (k )poly (n ). Finally, we propose a purely classical algorithm that can simulate a PBC on n qubits in a time 2α npoly (n ) , where α ≈0.94 . This improves upon the brute-force simulation method, which takes time 2npoly (n ). Our algorithm exploits the fact that n -fold tensor products of magic states admit a low-rank decomposition into n -qubit stabilizer states.
Tempel, David G; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
Tempel, David G.; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms. PMID:22553483
Towards universal quantum computation through relativistic motion
Bruschi, David Edward; Sabín, Carlos; Kok, Pieter; Johansson, Göran; Delsing, Per; Fuentes, Ivette
2016-01-01
We show how to use relativistic motion to generate continuous variable Gaussian cluster states within cavity modes. Our results can be demonstrated experimentally using superconducting circuits where tuneable boundary conditions correspond to mirrors moving with velocities close to the speed of light. In particular, we propose the generation of a quadripartite square cluster state as a first example that can be readily implemented in the laboratory. Since cluster states are universal resources for universal one-way quantum computation, our results pave the way for relativistic quantum computation schemes. PMID:26860584
Topics in linear optical quantum computation
NASA Astrophysics Data System (ADS)
Glancy, Scott Charles
This thesis covers several topics in optical quantum computation. A quantum computer is a computational device which is able to manipulate information by performing unitary operations on some physical system whose state can be described as a vector (or mixture of vectors) in a Hilbert space. The basic unit of information, called the qubit, is considered to be a system with two orthogonal states, which are assigned logical values of 0 and 1. Photons make excellent candidates to serve as qubits. They have little interactions with the environment. Many operations can be performed using very simple linear optical devices such as beam splitters and phase shifters. Photons can easily be processed through circuit-like networks. Operations can be performed in very short times. Photons are ideally suited for the long-distance communication of quantum information. The great difficulty in constructing an optical quantum computer is that photons naturally interact weakly with one another. This thesis first gives a brief review of two early approaches to optical quantum computation. It will describe how any discrete unitary operation can be performed using a single photon and a network of beam splitters, and how the Kerr effect can be used to construct a two photon logic gate. Second, this work provides a thorough introduction to the linear optical quantum computer developed by Knill, Laflamme, and Milburn. It then presents this author's results on the reliability of this scheme when implemented using imperfect photon detectors. This author finds that quantum computers of this sort cannot be built using current technology. Third, this dissertation describes a method for constructing a linear optical quantum computer using nearly orthogonal coherent states of light as the qubits. It shows how a universal set of logic operations can be performed, including calculations of the fidelity with which these operations may be accomplished. It discusses methods for reducing and
Towards universal quantum computation through relativistic motion
NASA Astrophysics Data System (ADS)
Bruschi, David Edward; Sabín, Carlos; Kok, Pieter; Johansson, Göran; Delsing, Per; Fuentes, Ivette
2016-02-01
We show how to use relativistic motion to generate continuous variable Gaussian cluster states within cavity modes. Our results can be demonstrated experimentally using superconducting circuits where tuneable boundary conditions correspond to mirrors moving with velocities close to the speed of light. In particular, we propose the generation of a quadripartite square cluster state as a first example that can be readily implemented in the laboratory. Since cluster states are universal resources for universal one-way quantum computation, our results pave the way for relativistic quantum computation schemes.
Processor core model for quantum computing.
Yung, Man-Hong; Benjamin, Simon C; Bose, Sougato
2006-06-01
We describe an architecture based on a processing "core," where multiple qubits interact perpetually, and a separate "store," where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the core, and free evolution of the core. This enables computation using physical systems where the entangling interactions are "always on." Alternatively, for switchable systems, our model constitutes a prescription for optimizing many-qubit gates. We discuss implementations of the quantum Fourier transform, Hamiltonian simulation, and quantum error correction.
Random Numbers and Quantum Computers
ERIC Educational Resources Information Center
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
Ultrafast quantum nondemolition measurements based on a diamond-shaped artificial atom
NASA Astrophysics Data System (ADS)
Diniz, I.; Dumur, E.; Buisson, O.; Auffèves, A.
2013-03-01
We propose a quantum nondemolition (QND) readout scheme for a superconducting artificial atom coupled to a resonator in a circuit QED architecture, for which we estimate a very high measurement fidelity without Purcell effect limitations. The device consists of two transmons coupled by a large inductance, giving rise to a diamond-shaped artificial atom with a logical qubit and an ancilla qubit interacting through a cross-Kerr-like term. The ancilla is strongly coupled to a transmission line resonator. Depending on the qubit state, the ancilla is resonantly or dispersively coupled to the resonator, leading to a large contrast in the transmitted microwave signal amplitude. This original method can be implemented with a state-of-the-art Josephson parametric amplifier, leading to QND measurements in a few tens of nanoseconds with fidelity as large as 99.9%.
Mizel, Ari
2004-07-01
Ground-state quantum computers mimic quantum-mechanical time evolution within the amplitudes of a time-independent quantum state. We explore the principles that constrain this mimicking. A no-cloning argument is found to impose strong restrictions. It is shown, however, that there is flexibility that can be exploited using quantum teleportation methods to improve ground-state quantum computer design.
A surface code quantum computer in silicon
Hill, Charles D.; Peretz, Eldad; Hile, Samuel J.; House, Matthew G.; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.
2015-01-01
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310
A surface code quantum computer in silicon.
Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L
2015-10-01
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310
A surface code quantum computer in silicon.
Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L
2015-10-01
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.
The quantum cryptograpy: Communication and computation
NASA Astrophysics Data System (ADS)
Delicado, Raquel Fernandez; Cabello, David Bellver; Boada, Ivan Lloro
2005-07-01
Nowadays there are two secure ways of encrypting information, the public key cryptography (PKC), and the symmetric cryptography (SC). With the arrival of the quantum computation, both methods become vulnerable, thanks to its exponential-growing calculation capacity. To solve this lack of security, quantum physics nowadays offers us two satisfactory methods which have been proposed successfully from a theoretical point of view: the two non-commuting observables, based on the Bennet and Brassard protocol, and the quantum entanglement combined with the Bell's inequality theorem, based on the Ekert protocol. Since some experiments have demonstrated the viability of the conduction of free space quantum cryptography at the surface of the Earth, we propose that this could be a boost for secure ground-to-satellite or satellite-to-satellite communications.
Industrial Superconducting Quantum Computer Development in Canada
NASA Astrophysics Data System (ADS)
Rose, Geordie
2002-05-01
Quantum computation is one of the most active areas of research in academia. Nearly every university in the world that has a science department has researchers who are working on either trying to build hardware or develop algorithms for these machines. In this talk I will describe D-Wave's goals and achievements in assembling a global research network, centered in Canada, whose purpose is the development of superconducting quantum computer hardware. In addition I will describe the technical approach that we are concentrating on, involving cuprate-based flux qubits and niobium RSFQ control circuitry. Finally I will introduce a very important application of these machines, namely their use as simulators of other quantum systems, in the context of human pharmaceutical drug and vaccine design.
Realizing universal Majorana fermionic quantum computation
NASA Astrophysics Data System (ADS)
Wu, Ya-Jie; He, Jing; Kou, Su-Peng
2014-08-01
Majorana fermionic quantum computation (MFQC) was proposed by S. B. Bravyi and A. Yu. Kitaev [Ann. Phys. (NY) 298, 210 (2002), 10.1006/aphy.2002.6254], who indicated that a (nontopological) fault-tolerant quantum computer built from Majorana fermions may be more efficient than that built from distinguishable two-state systems. However, until now scientists have not known how to realize a MFQC in a physical system. In this paper we propose a possible realization of MFQC. We find that the end of a line defect of a p-wave superconductor or superfluid in a honeycomb lattice traps a Majorana zero mode, which becomes the starting point of MFQC. Then we show how to manipulate Majorana fermions to perform universal MFQC, which possesses possibilities for high-level local controllability through individually addressing the quantum states of individual constituent elements by using timely cold-atom technology.
Universality of computation in real quantum theory
NASA Astrophysics Data System (ADS)
Belenchia, A.; D'Ariano, G. M.; Perinotti, P.
2013-10-01
Recently de la Torre et al. (Phys. Rev. Lett., 109 (2012) 090403) reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result relies on universality of any entangling gate for quantum computation. Here we prove universality of C-NOT with local gates for Real Quantum Theory (RQT), showing that the universality requirement would not be sufficient for the result, whereas local discriminability and the local qubit structure play a crucial role. For reversible computation, generally an extra rebit is needed for RQT. As a by-product we also provide a short proof of universality of C-NOT for CQT.
Hybrid quantum computing: semicloning for general database retrieval
NASA Astrophysics Data System (ADS)
Lanzagorta, Marco; Uhlmann, Jeffrey K.
2005-05-01
Quantum computing (QC) has become an important area of research in computer science because of its potential to provide more efficient algorithmic solutions to certain problems than are possible with classical computing (CC). In particular, QC is able to exploit the special properties of quantum superposition to achieve computational parallelism beyond what can be achieved with parallel CC computers. However, these special properties are not applicable for general computation. Therefore, we propose the use of "hybrid quantum computers" (HQCs) that combine both classical and quantum computing architectures in order to leverage the benefits of both. We demonstrate how an HQC can exploit quantum search to support general database operations more efficiently than is possible with CC. Our solution is based on new quantum results that are of independent significance to the field of quantum computing. More specifically, we demonstrate that the most restrictive implications of the quantum No-Cloning Theorem can be avoided through the use of semiclones.
The quantum computer game: citizen science
NASA Astrophysics Data System (ADS)
Damgaard, Sidse; Mølmer, Klaus; Sherson, Jacob
2013-05-01
Progress in the field of quantum computation is hampered by daunting technical challenges. Here we present an alternative approach to solving these by enlisting the aid of computer players around the world. We have previously examined a quantum computation architecture involving ultracold atoms in optical lattices and strongly focused tweezers of light. In The Quantum Computer Game (see http://www.scienceathome.org/), we have encapsulated the time-dependent Schrödinger equation for the problem in a graphical user interface allowing for easy user input. Players can then search the parameter space with real-time graphical feedback in a game context with a global high-score that rewards short gate times and robustness to experimental errors. The game which is still in a demo version has so far been tried by several hundred players. Extensions of the approach to other models such as Gross-Pitaevskii and Bose-Hubbard are currently under development. The game has also been incorporated into science education at high-school and university level as an alternative method for teaching quantum mechanics. Initial quantitative evaluation results are very positive. AU Ideas Center for Community Driven Research, CODER.
Towards fault tolerant adiabatic quantum computation.
Lidar, Daniel A
2008-04-25
I show how to protect adiabatic quantum computation (AQC) against decoherence and certain control errors, using a hybrid methodology involving dynamical decoupling, subsystem and stabilizer codes, and energy gaps. Corresponding error bounds are derived. As an example, I show how to perform decoherence-protected AQC against local noise using at most two-body interactions.
Blind quantum computing with weak coherent pulses.
Dunjko, Vedran; Kashefi, Elham; Leverrier, Anthony
2012-05-18
The universal blind quantum computation (UBQC) protocol [A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual IEEE Symposiumon Foundations of Computer Science (IEEE Computer Society, Los Alamitos, CA, USA, 2009), pp. 517-526.] allows a client to perform quantum computation on a remote server. In an ideal setting, perfect privacy is guaranteed if the client is capable of producing specific, randomly chosen single qubit states. While from a theoretical point of view, this may constitute the lowest possible quantum requirement, from a pragmatic point of view, generation of such states to be sent along long distances can never be achieved perfectly. We introduce the concept of ϵ blindness for UBQC, in analogy to the concept of ϵ security developed for other cryptographic protocols, allowing us to characterize the robustness and security properties of the protocol under possible imperfections. We also present a remote blind single qubit preparation protocol with weak coherent pulses for the client to prepare, in a delegated fashion, quantum states arbitrarily close to perfect random single qubit states. This allows us to efficiently achieve ϵ-blind UBQC for any ϵ>0, even if the channel between the client and the server is arbitrarily lossy.
Simulations of Probabilities for Quantum Computing
NASA Technical Reports Server (NTRS)
Zak, M.
1996-01-01
It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.
Deterministic quantum computation with one photonic qubit
NASA Astrophysics Data System (ADS)
Hor-Meyll, M.; Tasca, D. S.; Walborn, S. P.; Ribeiro, P. H. Souto; Santos, M. M.; Duzzioni, E. I.
2015-07-01
We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the computation of the trace of a high-dimension matrix, being limited by the resolution of the modulator panel and the technical imperfections. In order to illustrate the method, we compute the normalized trace of unitary matrices and implement the Deutsch-Jozsa algorithm. The largest matrix that can be manipulated with our setup is 1080 ×1920 , which is able to represent a system with approximately 21 qubits.
Scheme for Quantum Computing Immune to Decoherence
NASA Technical Reports Server (NTRS)
Williams, Colin; Vatan, Farrokh
2008-01-01
A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic. Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1.2 particle. It can be surprisingly difficult to achieve certain gate operations . most notably, those of arbitrary 1-qubit gates . in spintronic hardware according to this model. However, ironically, certain 2-qubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware. Therefore, it would be fortunate if it were possible to implement any 1-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any 1-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report
Efficient quantum computing using coherent photon conversion.
Langford, N K; Ramelow, S; Prevedel, R; Munro, W J; Milburn, G J; Zeilinger, A
2011-10-12
Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting
Ensemble quantum computing by NMR spectroscopy
Cory, David G.; Fahmy, Amr F.; Havel, Timothy F.
1997-01-01
A quantum computer (QC) can operate in parallel on all its possible inputs at once, but the amount of information that can be extracted from the result is limited by the phenomenon of wave function collapse. We present a new computational model, which differs from a QC only in that the result of a measurement is the expectation value of the observable, rather than a random eigenvalue thereof. Such an expectation value QC can solve nondeterministic polynomial-time complete problems in polynomial time. This observation is significant precisely because the computational model can be realized, to a certain extent, by NMR spectroscopy on macroscopic ensembles of quantum spins, namely molecules in a test tube. This is made possible by identifying a manifold of statistical spin states, called pseudo-pure states, the mathematical description of which is isomorphic to that of an isolated spin system. The result is a novel NMR computer that can be programmed much like a QC, but in other respects more closely resembles a DNA computer. Most notably, when applied to intractable combinatorial problems, an NMR computer can use an amount of sample, rather than time, which grows exponentially with the size of the problem. Although NMR computers will be limited by current technology to exhaustive searches over only 15 to 20 bits, searches over as much as 50 bits are in principle possible, and more advanced algorithms could greatly extend the range of applicability of such machines. PMID:9050830
Measurement and Information Extraction in Complex Dynamics Quantum Computation
NASA Astrophysics Data System (ADS)
Casati, Giulio; Montangero, Simone
Quantum Information processing has several di.erent applications: some of them can be performed controlling only few qubits simultaneously (e.g. quantum teleportation or quantum cryptography) [1]. Usually, the transmission of large amount of information is performed repeating several times the scheme implemented for few qubits. However, to exploit the advantages of quantum computation, the simultaneous control of many qubits is unavoidable [2]. This situation increases the experimental di.culties of quantum computing: maintaining quantum coherence in a large quantum system is a di.cult task. Indeed a quantum computer is a many-body complex system and decoherence, due to the interaction with the external world, will eventually corrupt any quantum computation. Moreover, internal static imperfections can lead to quantum chaos in the quantum register thus destroying computer operability [3]. Indeed, as it has been shown in [4], a critical imperfection strength exists above which the quantum register thermalizes and quantum computation becomes impossible. We showed such e.ects on a quantum computer performing an e.cient algorithm to simulate complex quantum dynamics [5,6].
Quantum computation: algorithms and implementation in quantum dot devices
NASA Astrophysics Data System (ADS)
Gamble, John King
In this thesis, we explore several aspects of both the software and hardware of quantum computation. First, we examine the computational power of multi-particle quantum random walks in terms of distinguishing mathematical graphs. We study both interacting and non-interacting multi-particle walks on strongly regular graphs, proving some limitations on distinguishing powers and presenting extensive numerical evidence indicative of interactions providing more distinguishing power. We then study the recently proposed adiabatic quantum algorithm for Google PageRank, and show that it exhibits power-law scaling for realistic WWW-like graphs. Turning to hardware, we next analyze the thermal physics of two nearby 2D electron gas (2DEG), and show that an analogue of the Coulomb drag effect exists for heat transfer. In some distance and temperature, this heat transfer is more significant than phonon dissipation channels. After that, we study the dephasing of two-electron states in a single silicon quantum dot. Specifically, we consider dephasing due to the electron-phonon coupling and charge noise, separately treating orbital and valley excitations. In an ideal system, dephasing due to charge noise is strongly suppressed due to a vanishing dipole moment. However, introduction of disorder or anharmonicity leads to large effective dipole moments, and hence possibly strong dephasing. Building on this work, we next consider more realistic systems, including structural disorder systems. We present experiment and theory, which demonstrate energy levels that vary with quantum dot translation, implying a structurally disordered system. Finally, we turn to the issues of valley mixing and valley-orbit hybridization, which occurs due to atomic-scale disorder at quantum well interfaces. We develop a new theoretical approach to study these effects, which we name the disorder-expansion technique. We demonstrate that this method successfully reproduces atomistic tight-binding techniques
Scalable Quantum Computing Over the Rainbow
NASA Astrophysics Data System (ADS)
Pfister, Olivier; Menicucci, Nicolas C.; Flammia, Steven T.
2011-03-01
The physical implementation of nontrivial quantum computing is an experimental challenge due to decoherence and the need for scalability. Recently we proved a novel theoretical scheme for realizing a scalable quantum register of very large size, entangled in a cluster state, in the optical frequency comb (OFC) defined by the eigenmodes of a single optical parametric oscillator (OPO). The classical OFC is well known as implemented by the femtosecond, carrier-envelope-phase- and mode-locked lasers which have redefined frequency metrology in recent years. The quantum OFC is a set of harmonic oscillators, or Qmodes, whose amplitude and phase quadratures are continuous variables, the manipulation of which is a mature field for one or two Qmodes. We have shown that the nonlinear optical medium of a single OPO can be engineered, in a sophisticated but already demonstrated manner, so as to entangle in constant time the OPO's OFC into a finitely squeezed, Gaussian cluster state suitable for universal quantum computing over continuous variables. Here we summarize our theoretical result and survey the ongoing experimental efforts in this direction.
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Scalable quantum computer architecture with coupled donor-quantum dot qubits
Schenkel, Thomas; Lo, Cheuk Chi; Weis, Christoph; Lyon, Stephen; Tyryshkin, Alexei; Bokor, Jeffrey
2014-08-26
A quantum bit computing architecture includes a plurality of single spin memory donor atoms embedded in a semiconductor layer, a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, wherein a first voltage applied across at least one pair of the aligned quantum dot and donor atom controls a donor-quantum dot coupling. A method of performing quantum computing in a scalable architecture quantum computing apparatus includes arranging a pattern of single spin memory donor atoms in a semiconductor layer, forming a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, applying a first voltage across at least one aligned pair of a quantum dot and donor atom to control a donor-quantum dot coupling, and applying a second voltage between one or more quantum dots to control a Heisenberg exchange J coupling between quantum dots and to cause transport of a single spin polarized electron between quantum dots.
Hierarchy of Efficiently Computable and Faithful Lower Bounds to Quantum Discord.
Piani, Marco
2016-08-19
Quantum discord expresses a fundamental nonclassicality of correlations that is more general than entanglement, but that, in its standard definition, is not easily evaluated. We derive a hierarchy of computationally efficient lower bounds to the standard quantum discord. Every nontrivial element of the hierarchy constitutes by itself a valid discordlike measure, based on a fundamental feature of quantum correlations: their lack of shareability. Our approach emphasizes how the difference between entanglement and discord depends on whether shareability is intended as a static property or as a dynamical process. PMID:27588837
Hierarchy of Efficiently Computable and Faithful Lower Bounds to Quantum Discord
NASA Astrophysics Data System (ADS)
Piani, Marco
2016-08-01
Quantum discord expresses a fundamental nonclassicality of correlations that is more general than entanglement, but that, in its standard definition, is not easily evaluated. We derive a hierarchy of computationally efficient lower bounds to the standard quantum discord. Every nontrivial element of the hierarchy constitutes by itself a valid discordlike measure, based on a fundamental feature of quantum correlations: their lack of shareability. Our approach emphasizes how the difference between entanglement and discord depends on whether shareability is intended as a static property or as a dynamical process.
Universal quantum gates for Single Cooper Pair Box based quantum computing
NASA Technical Reports Server (NTRS)
Echternach, P.; Williams, C. P.; Dultz, S. C.; Braunstein, S.; Dowling, J. P.
2000-01-01
We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.
Non-unitary probabilistic quantum computing circuit and method
NASA Technical Reports Server (NTRS)
Williams, Colin P. (Inventor); Gingrich, Robert M. (Inventor)
2009-01-01
A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.
Atomic Fock states and quantum computing
NASA Astrophysics Data System (ADS)
Wan, Shoupu
The potential impact of quantum computing has stimulated a world-wide effort to develop the necessary experimental and theoretical resources. In the race for the quantum computer, several candidate systems have emerged, but the ultimate system is still unclear. We study theoretically how to realize atomic Fock states both for fermionic and bosonic atoms, mainly in one-dimensional optical traps. We demonstrate a new approach of quantum computing based on ultracold fermionic atomic Fock states in optical traps. With the Pauli exclusion principle, producing fermionic atomic Fock states in optical traps is straightforward. We find that laser culling of fermionic atoms in optical traps can produce a scalable number of ultra-high fidelity qubits. We show how each qubit can be independently prepared, and how to perform the required entanglement operations and detect the qubit states with spatially resolved, single-atom detection with adiabatic trap-splitting and fluorescence imaging. On the other hand, bosonic atoms have a strong tendency to stay together. One must rely on strong repulsive interactions to produce bosonic atomic Fock states. To simulate the physical conditions of producing Fock states with ultracold bosonic atoms, we study a many-boson system with arbitrary interaction strength using the Bethe ansatz method. This approach provides a general framework, enabling the study of Fock state production over a wide range of realistic experimental parameters.
Universal quantum computation with metaplectic anyons
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Wang, Zhenghan
2015-03-01
We show that braidings of the metaplectic anyons Xɛ in SO(3)2 = SU(2)4 with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p)2 for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.
Universal quantum computation with metaplectic anyons
Cui, Shawn X.; Wang, Zhenghan E-mail: zhenghwa@microsoft.com
2015-03-15
We show that braidings of the metaplectic anyons X{sub ϵ} in SO(3){sub 2} = SU(2){sub 4} with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p){sub 2} for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.
PREFACE: Quantum Information, Communication, Computation and Cryptography
NASA Astrophysics Data System (ADS)
Benatti, F.; Fannes, M.; Floreanini, R.; Petritis, D.
2007-07-01
The application of quantum mechanics to information related fields such as communication, computation and cryptography is a fast growing line of research that has been witnessing an outburst of theoretical and experimental results, with possible practical applications. On the one hand, quantum cryptography with its impact on secrecy of transmission is having its first important actual implementations; on the other hand, the recent advances in quantum optics, ion trapping, BEC manipulation, spin and quantum dot technologies allow us to put to direct test a great deal of theoretical ideas and results. These achievements have stimulated a reborn interest in various aspects of quantum mechanics, creating a unique interplay between physics, both theoretical and experimental, mathematics, information theory and computer science. In view of all these developments, it appeared timely to organize a meeting where graduate students and young researchers could be exposed to the fundamentals of the theory, while senior experts could exchange their latest results. The activity was structured as a school followed by a workshop, and took place at The Abdus Salam International Center for Theoretical Physics (ICTP) and The International School for Advanced Studies (SISSA) in Trieste, Italy, from 12-23 June 2006. The meeting was part of the activity of the Joint European Master Curriculum Development Programme in Quantum Information, Communication, Cryptography and Computation, involving the Universities of Cergy-Pontoise (France), Chania (Greece), Leuven (Belgium), Rennes1 (France) and Trieste (Italy). This special issue of Journal of Physics A: Mathematical and Theoretical collects 22 contributions from well known experts who took part in the workshop. They summarize the present day status of the research in the manifold aspects of quantum information. The issue is opened by two review articles, the first by G Adesso and F Illuminati discussing entanglement in continuous variable
Hard chaos, quantum billiards, and quantum dot computers
Mainieri, R.; Cvitanovic, P.; Hasslacher, B.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Research was performed in analytic and computational techniques for dealing with hard chaos, especially the powerful tool of cycle expansions. This work has direct application to the understanding of electrons in nanodevices, such as junctions of quantum wires, or in arrays of dots or antidots. We developed a series of techniques for computing the properties of quantum systems with hard chaos, in particular the flow of electrons through nanodevices. These techniques are providing the insight and tools to design computers with nanoscale components. Recent efforts concentrated on understanding the effects of noise and orbit pruning in chaotic dynamical systems. We showed that most complicated chaotic systems (not just those equivalent to a finite shift) will develop branch points in their cycle expansion. Once the singularity is known to exist, it can be removed with a dramatic increase in the speed of convergence of quantities of physical interest.
Compact quantum circuits from one-way quantum computation
NASA Astrophysics Data System (ADS)
Dias da Silva, Raphael; Galvão, Ernesto F.
2013-07-01
In this paper we address the problem of translating one-way quantum computation (1WQC) into the circuit model. We start by giving a straightforward circuit representation of any 1WQC, at the cost of introducing many ancilla wires. We then propose a set of simple circuit identities that explore the relationship between the entanglement resource and correction structure of a 1WQC, allowing one to obtain equivalent circuits acting on fewer qubits. We conclude with some examples and a discussion of open problems.
Symmetrically private information retrieval based on blind quantum computing
NASA Astrophysics Data System (ADS)
Sun, Zhiwei; Yu, Jianping; Wang, Ping; Xu, Lingling
2015-05-01
Universal blind quantum computation (UBQC) is a new secure quantum computing protocol which allows a user Alice who does not have any sophisticated quantum technology to delegate her computing to a server Bob without leaking any privacy. Using the features of UBQC, we propose a protocol to achieve symmetrically private information retrieval, which allows a quantum limited Alice to query an item from Bob with a fully fledged quantum computer; meanwhile, the privacy of both parties is preserved. The security of our protocol is based on the assumption that malicious Alice has no quantum computer, which avoids the impossibility proof of Lo. For the honest Alice, she is almost classical and only requires minimal quantum resources to carry out the proposed protocol. Therefore, she does not need any expensive laboratory which can maintain the coherence of complicated quantum experimental setups.
Novel systems and methods for quantum communication, quantum computation, and quantum simulation
NASA Astrophysics Data System (ADS)
Gorshkov, Alexey Vyacheslavovich
Precise control over quantum systems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators that can elucidate the physics of complex condensed matter systems. However, the fragility of quantum effects makes it very difficult to harness the power of quantum mechanics. In this thesis, we present novel systems and tools for gaining fundamental insights into the complex quantum world and for bringing practical applications of quantum mechanics closer to reality. We first optimize and show equivalence between a wide range of techniques for storage of photons in atomic ensembles. We describe experiments demonstrating the potential of our optimization algorithms for quantum communication and computation applications. Next, we combine the technique of photon storage with strong atom-atom interactions to propose a robust protocol for implementing the two-qubit photonic phase gate, which is an important ingredient in many quantum computation and communication tasks. In contrast to photon storage, many quantum computation and simulation applications require individual addressing of closely-spaced atoms, ions, quantum dots, or solid state defects. To meet this requirement, we propose a method for coherent optical far-field manipulation of quantum systems with a resolution that is not limited by the wavelength of radiation. While alkali atoms are currently the system of choice for photon storage and many other applications, we develop new methods for quantum information processing and quantum simulation with ultracold alkaline-earth atoms in optical lattices. We show how multiple qubits can be encoded in individual alkaline-earth atoms and harnessed for quantum computing and precision measurements applications. We also demonstrate that alkaline-earth atoms can be used to simulate highly symmetric systems exhibiting spin-orbital interactions and capable of providing valuable insights into strongly
Applicability of Rydberg atoms to quantum computers
NASA Astrophysics Data System (ADS)
Ryabtsev, Igor I.; Tretyakov, Denis B.; Beterov, Ilya I.
2005-01-01
The applicability of Rydberg atoms to quantum computers is examined from an experimental point of view. In many recent theoretical proposals, the excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole-dipole interactions that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analysed. We also present the results of modelling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S1/2 → 37P1/2 and two-photon 37S1/2 → 38S1/2 transitions in an ensemble of a few sodium Rydberg atoms. The microwave spectra were investigated for various final states of the ensemble initially prepared in its ground state. The results may be applied to the studies on collective laser excitation of ground-state atoms aiming to realize quantum gates.
Software Systems for High-performance Quantum Computing
Humble, Travis S; Britt, Keith A
2016-01-01
Quantum computing promises new opportunities for solving hard computational problems, but harnessing this novelty requires breakthrough concepts in the design, operation, and application of computing systems. We define some of the challenges facing the development of quantum computing systems as well as software-based approaches that can be used to overcome these challenges. Following a brief overview of the state of the art, we present models for the quantum programming and execution models, the development of architectures for hybrid high-performance computing systems, and the realization of software stacks for quantum networking. This leads to a discussion of the role that conventional computing plays in the quantum paradigm and how some of the current challenges for exascale computing overlap with those facing quantum computing.
Quantum computation over the butterfly network
Soeda, Akihito; Kinjo, Yoshiyuki; Turner, Peter S.; Murao, Mio
2011-07-15
In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider deterministically performing a two-qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource setting introduced by M. Hayashi [Phys. Rev. A 76, 040301(R) (2007)], which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that unitary operations can be performed without adding any entanglement resource, if and only if the unitary operations are locally unitary equivalent to controlled unitary operations. Our protocol is optimal in the sense that the unitary operations cannot be implemented if we relax the specifications of any of the channels. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.
Multiple-server Flexible Blind Quantum Computation in Networks
NASA Astrophysics Data System (ADS)
Kong, Xiaoqin; Li, Qin; Wu, Chunhui; Yu, Fang; He, Jinjun; Sun, Zhiyuan
2016-06-01
Blind quantum computation (BQC) can allow a client with limited quantum power to delegate his quantum computation to a powerful server and still keep his own data private. In this paper, we present a multiple-server flexible BQC protocol, where a client who only needs the ability of accessing qua ntum channels can delegate the computational task to a number of servers. Especially, the client's quantum computation also can be achieved even when one or more delegated quantum servers break down in networks. In other words, when connections to certain quantum servers are lost, clients can adjust flexibly and delegate their quantum computation to other servers. Obviously it is trivial that the computation will be unsuccessful if all servers are interrupted.
Milestones Toward Majorana-Based Quantum Computing
NASA Astrophysics Data System (ADS)
Aasen, David; Hell, Michael; Mishmash, Ryan V.; Higginbotham, Andrew; Danon, Jeroen; Leijnse, Martin; Jespersen, Thomas S.; Folk, Joshua A.; Marcus, Charles M.; Flensberg, Karsten; Alicea, Jason
2016-07-01
We introduce a scheme for preparation, manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current, (2) validation of a prototype topological qubit, and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and read out schemes as well.
Minimal computational-space implementation of multiround quantum protocols
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Chiribella, Giulio
2011-02-15
A single-party strategy in a multiround quantum protocol can be implemented by sequential networks of quantum operations connected by internal memories. Here, we provide an efficient realization in terms of computational-space resources.
Semiquantum key distribution with secure delegated quantum computation
Li, Qin; Chan, Wai Hong; Zhang, Shengyu
2016-01-01
Semiquantum key distribution allows a quantum party to share a random key with a “classical” party who only can prepare and measure qubits in the computational basis or reorder some qubits when he has access to a quantum channel. In this work, we present a protocol where a secret key can be established between a quantum user and an almost classical user who only needs the quantum ability to access quantum channels, by securely delegating quantum computation to a quantum server. We show the proposed protocol is robust even when the delegated quantum server is a powerful adversary, and is experimentally feasible with current technology. As one party of our protocol is the most quantum-resource efficient, it can be more practical and significantly widen the applicability scope of quantum key distribution. PMID:26813384
Semiquantum key distribution with secure delegated quantum computation.
Li, Qin; Chan, Wai Hong; Zhang, Shengyu
2016-01-01
Semiquantum key distribution allows a quantum party to share a random key with a "classical" party who only can prepare and measure qubits in the computational basis or reorder some qubits when he has access to a quantum channel. In this work, we present a protocol where a secret key can be established between a quantum user and an almost classical user who only needs the quantum ability to access quantum channels, by securely delegating quantum computation to a quantum server. We show the proposed protocol is robust even when the delegated quantum server is a powerful adversary, and is experimentally feasible with current technology. As one party of our protocol is the most quantum-resource efficient, it can be more practical and significantly widen the applicability scope of quantum key distribution. PMID:26813384
Semiquantum key distribution with secure delegated quantum computation
NASA Astrophysics Data System (ADS)
Li, Qin; Chan, Wai Hong; Zhang, Shengyu
2016-01-01
Semiquantum key distribution allows a quantum party to share a random key with a “classical” party who only can prepare and measure qubits in the computational basis or reorder some qubits when he has access to a quantum channel. In this work, we present a protocol where a secret key can be established between a quantum user and an almost classical user who only needs the quantum ability to access quantum channels, by securely delegating quantum computation to a quantum server. We show the proposed protocol is robust even when the delegated quantum server is a powerful adversary, and is experimentally feasible with current technology. As one party of our protocol is the most quantum-resource efficient, it can be more practical and significantly widen the applicability scope of quantum key distribution.
A measurement-based X-ray source model characterization for CT dosimetry computations.
Sommerville, Mitchell; Poirier, Yannick; Tambasco, Mauro
2015-11-08
The purpose of this study was to show that the nominal peak tube voltage potential (kVp) and measured half-value layer (HVL) can be used to generate energy spectra and fluence profiles for characterizing a computed tomography (CT) X-ray source, and to validate the source model and an in-house kV X-ray dose computation algorithm (kVDoseCalc) for computing machine- and patient-specific CT dose. Spatial variation of the X-ray source spectra of a Philips Brilliance and a GE Optima Big Bore CT scanner were found by measuring the HVL along the direction of the internal bow-tie filter axes. Third-party software, Spektr, and the nominal kVp settings were used to generate the energy spectra. Beam fluence was calculated by dividing the integral product of the spectra and the in-air NIST mass-energy attenuation coefficients by in-air dose measurements along the filter axis. The authors found the optimal number of photons to seed in kVDoseCalc to achieve dose convergence. The Philips Brilliance beams were modeled for 90, 120, and 140 kVp tube settings. The GE Optima beams were modeled for 80, 100, 120, and 140 kVp tube settings. Relative doses measured using a Capintec Farmer-type ionization chamber (0.65 cc) placed in a cylindrical polymethyl methacrylate (PMMA) phantom and irradiated by the Philips Brilliance, were compared to those computed with kVDoseCalc. Relative doses in an anthropomorphic thorax phantom (E2E SBRT Phantom) irradiated by the GE Optima were measured using a (0.015 cc) PTW Freiburg ionization chamber and compared to computations from kVDoseCalc. The number of photons required to reduce the average statistical uncertainty in dose to < 0.3% was 2 × 105. The average percent difference between calculation and measurement over all 12 PMMA phantom positions was found to be 1.44%, 1.47%, and 1.41% for 90, 120, and 140 kVp, respectively. The maximum percent difference between calculation and measurement for all energies, measurement positions, and phantoms was
A measurement-based X-ray source model characterization for CT dosimetry computations.
Sommerville, Mitchell; Poirier, Yannick; Tambasco, Mauro
2015-01-01
The purpose of this study was to show that the nominal peak tube voltage potential (kVp) and measured half-value layer (HVL) can be used to generate energy spectra and fluence profiles for characterizing a computed tomography (CT) X-ray source, and to validate the source model and an in-house kV X-ray dose computation algorithm (kVDoseCalc) for computing machine- and patient-specific CT dose. Spatial variation of the X-ray source spectra of a Philips Brilliance and a GE Optima Big Bore CT scanner were found by measuring the HVL along the direction of the internal bow-tie filter axes. Third-party software, Spektr, and the nominal kVp settings were used to generate the energy spectra. Beam fluence was calculated by dividing the integral product of the spectra and the in-air NIST mass-energy attenuation coefficients by in-air dose measurements along the filter axis. The authors found the optimal number of photons to seed in kVDoseCalc to achieve dose convergence. The Philips Brilliance beams were modeled for 90, 120, and 140 kVp tube settings. The GE Optima beams were modeled for 80, 100, 120, and 140 kVp tube settings. Relative doses measured using a Capintec Farmer-type ionization chamber (0.65 cc) placed in a cylindrical polymethyl methacrylate (PMMA) phantom and irradiated by the Philips Brilliance, were compared to those computed with kVDoseCalc. Relative doses in an anthropomorphic thorax phantom (E2E SBRT Phantom) irradiated by the GE Optima were measured using a (0.015 cc) PTW Freiburg ionization chamber and compared to computations from kVDoseCalc. The number of photons required to reduce the average statistical uncertainty in dose to < 0.3% was 2 × 105. The average percent difference between calculation and measurement over all 12 PMMA phantom positions was found to be 1.44%, 1.47%, and 1.41% for 90, 120, and 140 kVp, respectively. The maximum percent difference between calculation and measurement for all energies, measurement positions, and phantoms was
One-way quantum computing in the optical frequency comb.
Menicucci, Nicolas C; Flammia, Steven T; Pfister, Olivier
2008-09-26
One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.
Measurement-only verifiable blind quantum computing with quantum input verification
NASA Astrophysics Data System (ADS)
Morimae, Tomoyuki
2016-10-01
Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness), and the correctness of the computation is verifiable by the client despite her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state, whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.
NASA Astrophysics Data System (ADS)
Tassoulas, E.; Vereses, A.; Agiakatsikas, D.; Koulouras, Gr.; Nomicos, C.
2010-05-01
A few years ago, real time communication, data collection and transmission from a field station measuring electromagnetic variations in the middle of nowhere, was a very expensive accomplishment. Nowadays, wireless communications and Internet access reach end users much easier and they are less expensive. WIFI, GPRS, 3G or Satellite Internet connections enable this to come true even at the most detached areas of our world where no cables can easily reach at a low cost. Except for the effective potential range, these communication technologies can also give high speed, constant and low cost Internet access. As the Internet access speeds grow, a new term is coming to the foreground. Cloud Computing. The terminology of Cloud Computing refers to a wide subset of Internet technologies usage that the clients: A)Do not need to store any valuable information in any physical infrastructure owned by themselves. B)Consume on-line resources from a third party provider, enabling them to focus on their productivity without having to worry about their data or any other possible local hardware failure. C)Collaborate and share between associates faster and easier, as they can access their work from anywhere, just with the existence of Internet access. This telemetric system, relies on Cloud Computing for the delivery of collected data from the field station to an on-line storage. Collaborators and scientists, can be synchronized with the on-line storage, make changes and synchronize vice versa. Local storage at the field station end, is only needed in the case of an Internet connection failure, so that the data can be stored until the Internet connection is regained. Local storage at the user's side is optional, however desirable thus giving the ability to work off-line and synchronize again the changes when one goes on-line.
Das Sarma, Sankar
2012-10-03
I will discuss the revolutionary new concept of topological quantum computation, which is fault-tolerant at the hardware level with no need, in principle, of any quantum error correction protocols. Errors simply do not occur since the physical qubits and the computation steps are protected against decoherence by non-local topological correlations in the underlying physical system. The key idea is non-Abelian statistics of the quasiparticles (called 'anyons' as opposed to fermions or bosons), where the space-time braiding of the anyons around each other, i.e. quantum 'knots', form topologically protected quantum gate operations. I will describe in detail the theoretical principles guiding the experimental search for the appropriate topological phases of matter where such non-Abelian anyons, which are low-dimensional solid state versions of the elusive and exotic Majorana fermions hypothesized seventy-five years ago, may exist. I will critically discuss the recent experimental claims of observing the Majorana modes in semiconductor nanowire structures following earlier theoretical proposals, outlining the future developments which would be necessary to eventually build a topological quantum computer.
Do multipartite correlations speed up adiabatic quantum computation or quantum annealing?
NASA Astrophysics Data System (ADS)
Batle, J.; Ooi, C. H. Raymond; Farouk, Ahmed; Abutalib, M.; Abdalla, S.
2016-08-01
Quantum correlations are thought to be the reason why certain quantum algorithms overcome their classical counterparts. Since the nature of this resource is still not fully understood, we shall investigate how multipartite entanglement and non-locality among qubits vary as the quantum computation runs. We shall encounter that quantum measures on the whole system cannot account for their corresponding speedup.
Waitzman, A A; Posnick, J C; Armstrong, D C; Pron, G E
1992-03-01
Computed tomography (CT) is a useful modality for the management of craniofacial anomalies. A study was undertaken to assess whether CT measurements of the upper craniofacial skeleton accurately represent the bony region imaged. Measurements taken directly from five dry skulls (approximate ages: adults, over 18 years; child, 4 years; infant, 6 months) were compared to those from axial CT scans of these skulls. Excellent agreement was found between the direct (dry skull) and indirect (CT) measurements. The effect of head tilt on the accuracy of these measurements was investigated. The error was within clinically acceptable limits (less than 5 percent) if the angle was no more than +/- 4 degrees from baseline (0 degrees). Objective standardized information gained from CT should complement the subjective clinical data usually collected for the treatment of craniofacial deformities. PMID:1571344
Graph isomorphism and adiabatic quantum computing
NASA Astrophysics Data System (ADS)
Gaitan, Frank; Clark, Lane
2014-03-01
In the Graph Isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and maps G --> G'. If yes (no), then G and G' are said to be isomorphic (non-isomorphic). The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. We present a quantum algorithm that solves arbitrary instances of GI, and which provides a novel approach to determining all automorphisms of a graph. The algorithm converts a GI instance to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. Numerical simulation of the algorithm's quantum dynamics shows that it correctly distinguishes non-isomorphic graphs; recognizes isomorphic graphs; and finds the automorphism group of a graph. We also discuss the algorithm's experimental implementation and show how it can be leveraged to solve arbitrary instances of the NP-Complete Sub-Graph Isomorphism problem.
Parallelism for quantum computation with qudits
O'Leary, Dianne P.; Brennen, Gavin K.; Bullock, Stephen S.
2006-09-15
Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high-fidelity two-qudit gates. We first describe how to implement parallel single-qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth (time) of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the alkali-metal atoms {sup 87}Rb and {sup 133}Cs. Second, we provide a protocol for implementing parallelized nonlocal two-qudit gates using the assistance of entangled qubit pairs. Using known protocols for qubit entanglement purification, this offers the possibility of high-fidelity two-qudit gates.
Quantum computing accelerator I/O : LDRD 52750 final report.
Schroeppel, Richard Crabtree; Modine, Normand Arthur; Ganti, Anand; Pierson, Lyndon George; Tigges, Christopher P.
2003-12-01
In a superposition of quantum states, a bit can be in both the states '0' and '1' at the same time. This feature of the quantum bit or qubit has no parallel in classical systems. Currently, quantum computers consisting of 4 to 7 qubits in a 'quantum computing register' have been built. Innovative algorithms suited to quantum computing are now beginning to emerge, applicable to sorting and cryptanalysis, and other applications. A framework for overcoming slightly inaccurate quantum gate interactions and for causing quantum states to survive interactions with surrounding environment is emerging, called quantum error correction. Thus there is the potential for rapid advances in this field. Although quantum information processing can be applied to secure communication links (quantum cryptography) and to crack conventional cryptosystems, the first few computing applications will likely involve a 'quantum computing accelerator' similar to a 'floating point arithmetic accelerator' interfaced to a conventional Von Neumann computer architecture. This research is to develop a roadmap for applying Sandia's capabilities to the solution of some of the problems associated with maintaining quantum information, and with getting data into and out of such a 'quantum computing accelerator'. We propose to focus this work on 'quantum I/O technologies' by applying quantum optics on semiconductor nanostructures to leverage Sandia's expertise in semiconductor microelectronic/photonic fabrication techniques, as well as its expertise in information theory, processing, and algorithms. The work will be guided by understanding of practical requirements of computing and communication architectures. This effort will incorporate ongoing collaboration between 9000, 6000 and 1000 and between junior and senior personnel. Follow-on work to fabricate and evaluate appropriate experimental nano/microstructures will be proposed as a result of this work.
Topological quantum computing with only one mobile quasiparticle.
Simon, S H; Bonesteel, N E; Freedman, M H; Petrovic, N; Hormozi, L
2006-02-24
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2 + 1 dimensional space-time. In this Letter we show that any such quantum computation that can be done by braiding n identical quasiparticles can also be done by moving a single quasiparticle around n - 1 other identical quasiparticles whose positions remain fixed.
Control aspects of quantum computing using pure and mixed states.
Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J
2012-10-13
Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.
Control aspects of quantum computing using pure and mixed states
Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J.
2012-01-01
Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems. PMID:22946034
Waitzman, A A; Posnick, J C; Armstrong, D C; Pron, G E
1992-03-01
Current diagnosis and surgical correction of craniofacial anomalies would benefit from accurate quantitative and standardized points of reference. A retrospective study was undertaken to define normal values for a series of craniofacial measurements and to evaluate the growth patterns of the craniofacial complex through axial computed tomography (CT). Fifteen measurements were taken from 542 CT scan series of skeletally normal subjects. The measurement values were then divided into 1-year age categories from 1 to 17 years, and into four age groups for those under 1 year of age. The normal range and growth pattern of measurement values for the cranial vault, orbital region, and upper midface are presented. The overall size of the cranio-orbito-zygomatic skeleton reaches more than 85 percent of adult size by age 5 years. The cranial vault grows rapidly in the first year of life but growth levels off early. The upper midface grows at a slower rate in infancy, but continues to grow later in childhood and early adolescence. Knowledge of the differential growth patterns and normal measurement values in the craniofacial region will help improve diagnostic accuracy, staging of reconstruction, precision of corrective surgery, and follow-up of patients. PMID:1571345
Samlan, Robin A.; Story, Brad H.; Bunton, Kate
2014-01-01
Purpose To determine 1) how specific vocal fold structural and vibratory features relate to breathy voice quality and 2) the relation of perceived breathiness to four acoustic correlates of breathiness. Method A computational, kinematic model of the vocal fold medial surfaces was used to specify features of vocal fold structure and vibration in a manner consistent with breathy voice. Four model parameters were altered: vocal process separation, surface bulging, vibratory nodal point, and epilaryngeal constriction. Twelve naïve listeners rated breathiness of 364 samples relative to a reference. The degree of breathiness was then compared to 1) the underlying kinematic profile and 2) four acoustic measures: cepstral peak prominence (CPP), harmonics-to-noise ratio, and two measures of spectral slope. Results Vocal process separation alone accounted for 61.4% of the variance in perceptual rating. Adding nodal point ratio and bulging to the equation increased the explained variance to 88.7%. The acoustic measure CPP accounted for 86.7% of the variance in perceived breathiness, and explained variance increased to 92.6% with the addition of one spectral slope measure. Conclusions Breathiness ratings were best explained kinematically by the degree of vocal process separation and acoustically by CPP. PMID:23785184
Multiple network alignment on quantum computers
NASA Astrophysics Data System (ADS)
Daskin, Anmer; Grama, Ananth; Kais, Sabre
2014-12-01
Comparative analyses of graph-structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large biomolecules, and recurring patterns of interactions in social networks. A large class of such analyses methods quantify the topological similarity of nodes across networks. The resulting correspondence of nodes across networks, also called node alignment, can be used to identify invariant subgraphs across the input graphs. Given graphs as input, alignment algorithms use topological information to assign a similarity score to each -tuple of nodes, with elements (nodes) drawn from each of the input graphs. Nodes are considered similar if their neighbors are also similar. An alternate, equivalent view of these network alignment algorithms is to consider the Kronecker product of the input graphs and to identify high-ranked nodes in the Kronecker product graph. Conventional methods such as PageRank and HITS (Hypertext-Induced Topic Selection) can be used for this purpose. These methods typically require computation of the principal eigenvector of a suitably modified Kronecker product matrix of the input graphs. We adopt this alternate view of the problem to address the problem of multiple network alignment. Using the phase estimation algorithm, we show that the multiple network alignment problem can be efficiently solved on quantum computers. We characterize the accuracy and performance of our method and show that it can deliver exponential speedups over conventional (non-quantum) methods.
Measurement-only topological quantum computation via anyonic interferometry
Bonderson, Parsa Freedman, Michael Nayak, Chetan
2009-04-15
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using 'forced measurement' protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.
Quantum computation of multifractal exponents through the quantum wavelet transform
Garcia-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand
2009-05-15
We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant, e.g., for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition.
Computer Visualization of Many-Particle Quantum Dynamics
Ozhigov, A. Y.
2009-03-10
In this paper I show the importance of computer visualization in researching of many-particle quantum dynamics. Such a visualization becomes an indispensable illustrative tool for understanding the behavior of dynamic swarm-based quantum systems. It is also an important component of the corresponding simulation framework, and can simplify the studies of underlying algorithms for multi-particle quantum systems.
Computer Visualization of Many-Particle Quantum Dynamics
NASA Astrophysics Data System (ADS)
Ozhigov, A. Y.
2009-03-01
In this paper I show the importance of computer visualization in researching of many-particle quantum dynamics. Such a visualization becomes an indispensable illustrative tool for understanding the behavior of dynamic swarm-based quantum systems. It is also an important component of the corresponding simulation framework, and can simplify the studies of underlying algorithms for multi-particle quantum systems.
Heterotic quantum and classical computing on convergence spaces
NASA Astrophysics Data System (ADS)
Patten, D. R.; Jakel, D. W.; Irwin, R. J.; Blair, H. A.
2015-05-01
Category-theoretic characterizations of heterotic models of computation, introduced by Stepney et al., combine computational models such as classical/quantum, digital/analog, synchronous/asynchronous, etc. to obtain increased computational power. A highly informative classical/quantum heterotic model of computation is represented by Abramsky's simple sequential imperative quantum programming language which extends the classical simple imperative programming language to encompass quantum computation. The mathematical (denotational) semantics of this classical language serves as a basic foundation upon which formal verification methods can be developed. We present a more comprehensive heterotic classical/quantum model of computation based on heterotic dynamical systems on convergence spaces. Convergence spaces subsume topological spaces but admit finer structure from which, in prior work, we obtained differential calculi in the cartesian closed category of convergence spaces allowing us to define heterotic dynamical systems, given by coupled systems of first order differential equations whose variables are functions from the reals to convergence spaces.
QCMPI: A parallel environment for quantum computing
NASA Astrophysics Data System (ADS)
Tabakin, Frank; Juliá-Díaz, Bruno
2009-06-01
QCMPI is a quantum computer (QC) simulation package written in Fortran 90 with parallel processing capabilities. It is an accessible research tool that permits rapid evaluation of quantum algorithms for a large number of qubits and for various "noise" scenarios. The prime motivation for developing QCMPI is to facilitate numerical examination of not only how QC algorithms work, but also to include noise, decoherence, and attenuation effects and to evaluate the efficacy of error correction schemes. The present work builds on an earlier Mathematica code QDENSITY, which is mainly a pedagogic tool. In that earlier work, although the density matrix formulation was featured, the description using state vectors was also provided. In QCMPI, the stress is on state vectors, in order to employ a large number of qubits. The parallel processing feature is implemented by using the Message-Passing Interface (MPI) protocol. A description of how to spread the wave function components over many processors is provided, along with how to efficiently describe the action of general one- and two-qubit operators on these state vectors. These operators include the standard Pauli, Hadamard, CNOT and CPHASE gates and also Quantum Fourier transformation. These operators make up the actions needed in QC. Codes for Grover's search and Shor's factoring algorithms are provided as examples. A major feature of this work is that concurrent versions of the algorithms can be evaluated with each version subject to alternate noise effects, which corresponds to the idea of solving a stochastic Schrödinger equation. The density matrix for the ensemble of such noise cases is constructed using parallel distribution methods to evaluate its eigenvalues and associated entropy. Potential applications of this powerful tool include studies of the stability and correction of QC processes using Hamiltonian based dynamics. Program summaryProgram title: QCMPI Catalogue identifier: AECS_v1_0 Program summary URL
Progress in silicon-based quantum computing.
Clark, R G; Brenner, R; Buehler, T M; Chan, V; Curson, N J; Dzurak, A S; Gauja, E; Goan, H S; Greentree, A D; Hallam, T; Hamilton, A R; Hollenberg, L C L; Jamieson, D N; McCallum, J C; Milburn, G J; O'Brien, J L; Oberbeck, L; Pakes, C I; Prawer, S D; Reilly, D J; Ruess, F J; Schofield, S R; Simmons, M Y; Stanley, F E; Starrett, R P; Wellard, C; Yang, C
2003-07-15
We review progress at the Australian Centre for Quantum Computer Technology towards the fabrication and demonstration of spin qubits and charge qubits based on phosphorus donor atoms embedded in intrinsic silicon. Fabrication is being pursued via two complementary pathways: a 'top-down' approach for near-term production of few-qubit demonstration devices and a 'bottom-up' approach for large-scale qubit arrays with sub-nanometre precision. The 'top-down' approach employs a low-energy (keV) ion beam to implant the phosphorus atoms. Single-atom control during implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure. In contrast, the 'bottom-up' approach uses scanning tunnelling microscope lithography and epitaxial silicon overgrowth to construct devices at an atomic scale. In both cases, surface electrodes control the qubit using voltage pulses, and dual single-electron transistors operating near the quantum limit provide fast read-out with spurious-signal rejection.
Random matrix model of adiabatic quantum computing
Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2005-05-15
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size.
Preparing ground states of quantum many-body systems on a quantum computer
NASA Astrophysics Data System (ADS)
Poulin, David
2009-03-01
The simulation of quantum many-body systems is a notoriously hard problem in condensed matter physics, but it could easily be handled by a quantum computer [4,1]. There is however one catch: while a quantum computer can naturally implement the dynamics of a quantum system --- i.e. solve Schr"odinger's equation --- there was until now no general method to initialize the computer in a low-energy state of the simulated system. We present a quantum algorithm [5] that can prepare the ground state and thermal states of a quantum many-body system in a time proportional to the square-root of its Hilbert space dimension. This is the same scaling as required by the best known algorithm to prepare the ground state of a classical many-body system on a quantum computer [3,2]. This provides strong evidence that for a quantum computer, preparing the ground state of a quantum system is in the worst case no more difficult than preparing the ground state of a classical system. 1 D. Aharonov and A. Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge, Proc. 35th Annual ACM Symp. on Theo. Comp., (2003), p. 20. F. Barahona, On the computational complexity of ising spin glass models, J. Phys. A. Math. Gen., 15 (1982), p. 3241. C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknessess of quantum computing, SIAM J. Comput., 26 (1997), pp. 1510--1523, quant-ph/9701001. S. Lloyd, Universal quantum simulators, Science, 273 (1996), pp. 1073--1078. D. Poulin and P. Wocjan, Preparing ground states of quantum many-body systems on a quantum computer, 2008, arXiv:0809.2705.
A scheme for efficient quantum computation with linear optics
NASA Astrophysics Data System (ADS)
Knill, E.; Laflamme, R.; Milburn, G. J.
2001-01-01
Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.
Demonstration of measurement-only blind quantum computing
NASA Astrophysics Data System (ADS)
Greganti, Chiara; Roehsner, Marie-Christine; Barz, Stefanie; Morimae, Tomoyuki; Walther, Philip
2016-01-01
Blind quantum computing allows for secure cloud networks of quasi-classical clients and a fully fledged quantum server. Recently, a new protocol has been proposed, which requires a client to perform only measurements. We demonstrate a proof-of-principle implementation of this measurement-only blind quantum computing, exploiting a photonic setup to generate four-qubit cluster states for computation and verification. Feasible technological requirements for the client and the device-independent blindness make this scheme very applicable for future secure quantum networks.
Number Partitioning via Quantum Adiabatic Computation
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadim N.; Toussaint, Udo; Clancy, Daniel (Technical Monitor)
2002-01-01
We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.
Trapped Ion Quantum Computation by Adiabatic Passage
Feng Xuni; Wu Chunfeng; Lai, C. H.; Oh, C. H.
2008-11-07
We propose a new universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.
Scalable quantum computation via local control of only two qubits
Burgarth, Daniel; Maruyama, Koji; Murphy, Michael; Montangero, Simone; Calarco, Tommaso; Nori, Franco; Plenio, Martin B.
2010-04-15
We apply quantum control techniques to a long spin chain by acting only on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on these qubits and indirect swap operations across the chain. It is shown that the control sequences can be computed and implemented efficiently. We discuss the application of these ideas to physical systems such as superconducting qubits in which full control of long chains is challenging.
The Brain Is both Neurocomputer and Quantum Computer
ERIC Educational Resources Information Center
Hameroff, Stuart R.
2007-01-01
In their article, "Is the Brain a Quantum Computer,?" Litt, Eliasmith, Kroon, Weinstein, and Thagard (2006) criticize the Penrose-Hameroff "Orch OR" quantum computational model of consciousness, arguing instead for neurocomputation as an explanation for mental phenomena. Here I clarify and defend Orch OR, show how Orch OR and neurocomputation are…
Demonstration of a small programmable quantum computer with atomic qubits
NASA Astrophysics Data System (ADS)
Debnath, S.; Linke, N. M.; Figgatt, C.; Landsman, K. A.; Wright, K.; Monroe, C.
2016-08-01
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch–Jozsa and Bernstein–Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.
Demonstration of a small programmable quantum computer with atomic qubits.
Debnath, S; Linke, N M; Figgatt, C; Landsman, K A; Wright, K; Monroe, C
2016-08-01
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels. PMID:27488798
Demonstration of a small programmable quantum computer with atomic qubits.
Debnath, S; Linke, N M; Figgatt, C; Landsman, K A; Wright, K; Monroe, C
2016-08-03
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.
Demonstration of a small programmable quantum computer with atomic qubits
NASA Astrophysics Data System (ADS)
Debnath, S.; Linke, N. M.; Figgatt, C.; Landsman, K. A.; Wright, K.; Monroe, C.
2016-08-01
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding.
Lau, Hoi-Kwan; Plenio, Martin B
2016-09-01
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding
NASA Astrophysics Data System (ADS)
Lau, Hoi-Kwan; Plenio, Martin B.
2016-09-01
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.
Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
NASA Astrophysics Data System (ADS)
Broadbent, Anne
2016-08-01
In instantaneous nonlocal quantum computation, two parties cooperate in order to perform a quantum computation on their joint inputs, while being restricted to a single round of simultaneous communication. Previous results showed that instantaneous nonlocal quantum computation is possible, at the cost of an exponential amount of prior shared entanglement (in the size of the input). Here, we show that a linear amount of entanglement suffices, (in the size of the computation), as long as the parties share nonlocal correlations as given by the Popescu-Rohrlich box. This means that communication is not required for efficient instantaneous nonlocal quantum computation. Exploiting the well-known relation to position-based cryptography, our result also implies the impossibility of secure position-based cryptography against adversaries with nonsignaling correlations. Furthermore, our construction establishes a quantum analog of the classical communication complexity collapse under nonsignaling correlations.
Universal Quantum Computing with Arbitrary Continuous-Variable Encoding.
Lau, Hoi-Kwan; Plenio, Martin B
2016-09-01
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified. PMID:27636459
Cluster State Quantum Computation and the Repeat-Until Scheme
NASA Astrophysics Data System (ADS)
Kwek, L. C.
Cluster state computation or the one way quantum computation (1WQC) relies on an initially highly entangled state (called a cluster state) and an appropriate sequence of single qubit measurements along different directions, together with feed-forward based on the measurement results, to realize a quantum computation process. The final result of the computation is obtained by measuring the last remaining qubits in the computational basis. In this short tutorial on cluster state quantum computation, we will also describe the basic ideas of a cluster state and proceed to describe how a single qubit operation can be done on a cluster state. Recently, we proposed a repeat-until-success (RUS) scheme that could effectively be used to realize one-way quantum computer on a hybrid system of photons and atoms. We will briefly describe this RUS scheme and show how it can be used to entangled two distant stationary qubits.
Experimental magic state distillation for fault-tolerant quantum computing.
Souza, Alexandre M; Zhang, Jingfu; Ryan, Colm A; Laflamme, Raymond
2011-01-25
Any physical quantum device for quantum information processing (QIP) is subject to errors in implementation. In order to be reliable and efficient, quantum computers will need error-correcting or error-avoiding methods. Fault-tolerance achieved through quantum error correction will be an integral part of quantum computers. Of the many methods that have been discovered to implement it, a highly successful approach has been to use transversal gates and specific initial states. A critical element for its implementation is the availability of high-fidelity initial states, such as |0〉 and the 'magic state'. Here, we report an experiment, performed in a nuclear magnetic resonance (NMR) quantum processor, showing sufficient quantum control to improve the fidelity of imperfect initial magic states by distilling five of them into one with higher fidelity.
Quantum Monte Carlo Endstation for Petascale Computing
Lubos Mitas
2011-01-26
NCSU research group has been focused on accomplising the key goals of this initiative: establishing new generation of quantum Monte Carlo (QMC) computational tools as a part of Endstation petaflop initiative for use at the DOE ORNL computational facilities and for use by computational electronic structure community at large; carrying out high accuracy quantum Monte Carlo demonstration projects in application of these tools to the forefront electronic structure problems in molecular and solid systems; expanding the impact of QMC methods and approaches; explaining and enhancing the impact of these advanced computational approaches. In particular, we have developed quantum Monte Carlo code (QWalk, www.qwalk.org) which was significantly expanded and optimized using funds from this support and at present became an actively used tool in the petascale regime by ORNL researchers and beyond. These developments have been built upon efforts undertaken by the PI's group and collaborators over the period of the last decade. The code was optimized and tested extensively on a number of parallel architectures including petaflop ORNL Jaguar machine. We have developed and redesigned a number of code modules such as evaluation of wave functions and orbitals, calculations of pfaffians and introduction of backflow coordinates together with overall organization of the code and random walker distribution over multicore architectures. We have addressed several bottlenecks such as load balancing and verified efficiency and accuracy of the calculations with the other groups of the Endstation team. The QWalk package contains about 50,000 lines of high quality object-oriented C++ and includes also interfaces to data files from other conventional electronic structure codes such as Gamess, Gaussian, Crystal and others. This grant supported PI for one month during summers, a full-time postdoc and partially three graduate students over the period of the grant duration, it has resulted in 13
Secure Multiparty Quantum Computation for Summation and Multiplication.
Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun
2016-01-01
As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics. PMID:26792197
Secure Multiparty Quantum Computation for Summation and Multiplication
Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun
2016-01-01
As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics. PMID:26792197
Secure Multiparty Quantum Computation for Summation and Multiplication
NASA Astrophysics Data System (ADS)
Shi, Run-Hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun
2016-01-01
As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantum mechanics.
Computable measure of total quantum correlations of multipartite systems
NASA Astrophysics Data System (ADS)
Behdani, Javad; Akhtarshenas, Seyed Javad; Sarbishaei, Mohsen
2016-04-01
Quantum discord as a measure of the quantum correlations cannot be easily computed for most of density operators. In this paper, we present a measure of the total quantum correlations that is operationally simple and can be computed effectively for an arbitrary mixed state of a multipartite system. The measure is based on the coherence vector of the party whose quantumness is investigated as well as the correlation matrix of this part with the remainder of the system. Being able to detect the quantumness of multipartite systems, such as detecting the quantum critical points in spin chains, alongside with the computability characteristic of the measure, makes it a useful indicator to be exploited in the cases which are out of the scope of the other known measures.
Continuous-variable quantum computing in optical time-frequency modes using quantum memories.
Humphreys, Peter C; Kolthammer, W Steven; Nunn, Joshua; Barbieri, Marco; Datta, Animesh; Walmsley, Ian A
2014-09-26
We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate, and measure two-dimensional cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that are a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures.
High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation
Yang, W. L.; Feng, M.; Yin, Z. Q.; Hu, Y.; Du, J. F.
2011-07-15
We study a hybrid quantum computing system using a nitrogen-vacancy center ensemble (NVE) as quantum memory, a current-biased Josephson junction (CBJJ) superconducting qubit fabricated in a transmission line resonator (TLR) as the quantum computing processor, and the microwave photons in TLR as the quantum data bus. The storage process is seriously treated by considering all kinds of decoherence mechanisms. Such a hybrid quantum device can also be used to create multiqubit W states of NVEs through a common CBJJ. The experimental feasibility is achieved using currently available technology.
Noisy one-way quantum computations: The role of correlations
Chaves, Rafael; Melo, Fernando de
2011-08-15
A scheme to evaluate computation fidelities within the one-way model is developed and explored to understand the role of correlations in the quality of noisy quantum computations. The formalism is promptly applied to many computation instances and unveils that a higher amount of entanglement in the noisy resource state does not necessarily imply a better computation.
NASA Astrophysics Data System (ADS)
Moll, Nikolaj; Fuhrer, Andreas; Staar, Peter; Tavernelli, Ivano
2016-07-01
Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the Fermionic problem in a system of qubits. By exploiting the block diagonality of a Fermionic Hamiltonian, we show that the number of required qubits can be reduced while the number of terms in the Hamiltonian will increase. All operations for this reduction can be performed in operator space. The scheme is conceived as a pre-computational step that would be performed prior to the actual quantum simulation. We apply this scheme to reduce the number of qubits necessary to simulate both the Hamiltonian of the two-site Fermi-Hubbard model and the hydrogen molecule. Both quantum systems can then be simulated with a two-qubit quantum computer. Despite the increase in the number of Hamiltonian terms, the scheme still remains a useful tool to reduce the dimensionality of specific quantum systems for quantum simulators with a limited number of resources.
NASA Astrophysics Data System (ADS)
Moll, Nikolaj; Fuhrer, Andreas; Staar, Peter; Tavernelli, Ivano
2016-07-01
Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the Fermionic problem in a system of qubits. By exploiting the block diagonality of a Fermionic Hamiltonian, we show that the number of required qubits can be reduced while the number of terms in the Hamiltonian will increase. All operations for this reduction can be performed in operator space. The scheme is conceived as a pre-computational step that would be performed prior to the actual quantum simulation. We apply this scheme to reduce the number of qubits necessary to simulate both the Hamiltonian of the two-site Fermi–Hubbard model and the hydrogen molecule. Both quantum systems can then be simulated with a two-qubit quantum computer. Despite the increase in the number of Hamiltonian terms, the scheme still remains a useful tool to reduce the dimensionality of specific quantum systems for quantum simulators with a limited number of resources.
Quantum computing with acceptor spins in silicon.
Salfi, Joe; Tong, Mengyang; Rogge, Sven; Culcer, Dimitrie
2016-06-17
The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin-orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin-orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin-orbit induced dipole-dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin-orbit terms are responsible for sweet spots in the dephasing time [Formula: see text] as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin-orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si. PMID:27171901
Quantum computing with acceptor spins in silicon.
Salfi, Joe; Tong, Mengyang; Rogge, Sven; Culcer, Dimitrie
2016-06-17
The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin-orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin-orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin-orbit induced dipole-dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin-orbit terms are responsible for sweet spots in the dephasing time [Formula: see text] as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin-orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.
Quantum computing with acceptor spins in silicon
NASA Astrophysics Data System (ADS)
Salfi, Joe; Tong, Mengyang; Rogge, Sven; Culcer, Dimitrie
2016-06-01
The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin-orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin-orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin-orbit induced dipole-dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin-orbit terms are responsible for sweet spots in the dephasing time {T}2* as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin-orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.
Digitized adiabatic quantum computing with a superconducting circuit
NASA Astrophysics Data System (ADS)
Barends, R.; Shabani, A.; Lamata, L.; Kelly, J.; Mezzacapo, A.; Heras, U. Las; Babbush, R.; Fowler, A. G.; Campbell, B.; Chen, Yu; Chen, Z.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J. Y.; Neeley, M.; Neill, C.; O'Malley, P. J. J.; Quintana, C.; Roushan, P.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Solano, E.; Neven, H.; Martinis, John M.
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-01
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable. PMID:27279216
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-08
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Holonomic quantum computation on microwave photons with all resonant interactions
NASA Astrophysics Data System (ADS)
Dong, Ping; Yu, Long-Bao; Zhou, Jian
2016-08-01
The intrinsic difficulties of holonomic quantum computation on superconducting circuits are originated from the use of three levels in superconducting transmon qubits and the complicated dispersive interaction between them. Due to the limited anharmonicity of transmon qubits, the experimental realization seems to be very challenging. However, with recent experimental progress, coherent control over microwave photons in superconducting circuit cavities is well achieved, and thus provides a promising platform for quantum information processing with photonic qubits. Here, with all resonant inter-cavity photon-photon interactions, we propose a scheme for implementing scalable holonomic quantum computation on a circuit QED lattice. In our proposal, three cavities, connected by a SQUID, are used to encode a logical qubit. By tuning the inter-cavity photon-photon interaction, we can construct all the holonomies needed for universal quantum computation in a non-adiabatic way. Therefore, our scheme presents a promising alternative for robust quantum computation with microwave photons.
Holonomic quantum computation on microwave photons with all resonant interactions
NASA Astrophysics Data System (ADS)
Dong, Ping; Yu, Long-Bao; Zhou, Jian
2016-08-01
The intrinsic difficulties of holonomic quantum computation on superconducting circuits are originated from the use of three levels in superconducting transmon qubits and the complicated dispersive interaction between them. Due to the limited anharmonicity of transmon qubits, the experimental realization seems to be very challenging. However, with recent experimental progress, coherent control over microwave photons in superconducting circuit cavities is well achieved, and thus provides a promising platform for quantum information processing with photonic qubits. Here, with all resonant inter-cavity photon–photon interactions, we propose a scheme for implementing scalable holonomic quantum computation on a circuit QED lattice. In our proposal, three cavities, connected by a SQUID, are used to encode a logical qubit. By tuning the inter-cavity photon–photon interaction, we can construct all the holonomies needed for universal quantum computation in a non-adiabatic way. Therefore, our scheme presents a promising alternative for robust quantum computation with microwave photons.
Universal quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
2016-05-01
We theoretically show that a nonlinear oscillator network with controllable parameters can be used for universal quantum computation. The initialization is achieved by a quantum-mechanical bifurcation based on quantum adiabatic evolution, which yields a Schrödinger cat state. All the elementary quantum gates are also achieved by quantum adiabatic evolution, in which dynamical phases accompanying the adiabatic evolutions are controlled by the system parameters. Numerical simulation results indicate that high gate fidelities can be achieved, where no dissipation is assumed.
Symbolic Quantum Computation Simulation in SymPy
NASA Astrophysics Data System (ADS)
Cugini, Addison; Curry, Matt; Granger, Brian
2010-10-01
Quantum computing is an emerging field which aims to use quantum mechanics to solve difficult computational problems with greater efficiency than on a classical computer. There is a need to create software that i) helps newcomers to learn the field, ii) enables practitioners to design and simulate quantum circuits and iii) provides an open foundation for further research in the field. Towards these ends we have created a package, in the open-source symbolic computation library SymPy, that simulates the quantum circuit model of quantum computation using Dirac notation. This framework builds on the extant powerful symbolic capabilities of SymPy to preform its simulations in a fully symbolic manner. We use object oriented design to abstract circuits as ordered collections of quantum gate and qbit objects. The gate objects can either be applied directly to the qbit objects or be represented as matrices in different bases. The package is also capable of performing the quantum Fourier transform and Shor's algorithm. A notion of measurement is made possible through the use of a non-commutative gate object. In this talk, we describe the software and show examples of quantum circuits on single and multi qbit states that involve common algorithms, gates and measurements.
Stabilizer quantum error correction with quantum bus computation
Myers, Casey R.; Silva, Marcus; Nemoto, Kae; Munro, William J.
2007-07-15
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators that generate the stabilizer group of a quantum code. First, we show how to measure a Pauli operator acting on physical qubits using a single coherent state with large average photon number, displacement operations, and photon detection. Second, we show how to measure the stabilizer operators fault-tolerantly by the deterministic preparation of coherent quantum superposition ('cat') states along with one-bit teleportations between a qubitlike encoding of coherent states and physical qubits.
Trapped Ion Quantum Computing with Microwaves
NASA Astrophysics Data System (ADS)
Randall, Joe; Weidt, Sebastian; Standing, Eamon; Webster, Simon; Lake, Kim; Murgia, David; Navickas, Tomas; Lekitsch, Bjoern; Hughes, Marcus; Sterling, Robin; de Motte, Darren; Giri, Gouri; Rodriguez, Andrea; Webb, Anna; Rattanasonti, Hwanjit; Srinivasan, Prasanna; Kraft, Michael; Maclean, Jessica; Mellor, Chris; Hensinger, Winfried
2015-03-01
To this point, entanglement operations in trapped ion qubits have been predominantly performed with lasers. However, this becomes problematic when scaling to large numbers of qubits due to the challenging engineering required. The use of stable and easily controllable microwaves to drive entanglement gates can overcome this problem. We will present our work towards implementing multi-qubit entanglement gates using microwaves in an experimental setup that produces a static magnetic field gradient of 24 T/m over an ion string. We will first present a scheme for preparing and manipulating dressed-state qubits and qutrits that are highly robust to decoherence from magnetic field fluctuations. We will also present our work experimentally demonstrating motional sideband transitions and Schrödinger cat states using microwaves in conjunction with the magnetic field gradient, as well as sideband cooling to the ground state of motion using dressed-states. Furthermore, we will show our latest results in creating microfabricated ion trap chips towards large scale quantum computing and simulation.
Consciousness and Logic in a Quantum-Computing Universe
NASA Astrophysics Data System (ADS)
Zizzi, Paola
The early inflationary universe can be described in terms of quantum information. More specifically, the inflationary universe can be viewed as a superposed state of quantum registers. Actually, during inflation, one can speak of a quantum superposition of universes. At the end of inflation, only one universe is selected, by a mechanism called self-reduction, which is consistent with Penrose's objective reduction (OR) model. The quantum gravity threshold of (OR) is reached at the end of inflation, and corresponds to a superposed state of 109 quantum registers. This is also the number of superposed tubulins — qubits in our brain, which undergo the Penrose-Hameroff orchestrated objective reduction, (Orch OR), leading to a conscious event. Then, an analogy naturally arises between the very early quantum-computing universe, and our mind. In fact, we argue that at the end of in- flation, the universe underwent a cosmic conscious event, the so-called "Big Wow", which acted as an imprinting for the future minds to come, with future modes of computation, consciousness and logic. The postinflationary universe organized itself as a cellular automaton (CA) with two computational modes: quantum and classical, like the two conformations assumed by the cellular automaton of tubulins in our brain, as in Hameroff's model. In the quantum configuration, the universe quantum-evaluates recursive functions, which are the laws of physics in their most abstract form. To do so in a very efficient way, the universe uses, as subroutines, black holes - quantum computers and quantum minds, which operate in parallel. The outcomes of the overall quantum computation are the universals, the attributes of things in themselves. These universals are partially obtained also by the quantum minds, and are endowed with subjective meaning. The units of the subjective universals are qualia, which are strictly related to the (virtual) existence of Planckian black holes. Further, we consider two aspects
Towards scalable quantum communication and computation: Novel approaches and realizations
NASA Astrophysics Data System (ADS)
Jiang, Liang
Quantum information science involves exploration of fundamental laws of quantum mechanics for information processing tasks. This thesis presents several new approaches towards scalable quantum information processing. First, we consider a hybrid approach to scalable quantum computation, based on an optically connected network of few-qubit quantum registers. Specifically, we develop a novel scheme for scalable quantum computation that is robust against various imperfections. To justify that nitrogen-vacancy (NV) color centers in diamond can be a promising realization of the few-qubit quantum register, we show how to isolate a few proximal nuclear spins from the rest of the environment and use them for the quantum register. We also demonstrate experimentally that the nuclear spin coherence is only weakly perturbed under optical illumination, which allows us to implement quantum logical operations that use the nuclear spins to assist the repetitive-readout of the electronic spin. Using this technique, we demonstrate more than two-fold improvement in signal-to-noise ratio. Apart from direct application to enhance the sensitivity of the NV-based nano-magnetometer, this experiment represents an important step towards the realization of robust quantum information processors using electronic and nuclear spin qubits. We then study realizations of quantum repeaters for long distance quantum communication. Specifically, we develop an efficient scheme for quantum repeaters based on atomic ensembles. We use dynamic programming to optimize various quantum repeater protocols. In addition, we propose a new protocol of quantum repeater with encoding, which efficiently uses local resources (about 100 qubits) to identify and correct errors, to achieve fast one-way quantum communication over long distances. Finally, we explore quantum systems with topological order. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as
Preparing Ground States of Quantum Many-Body Systems on a Quantum Computer
Poulin, David; Wocjan, Pawel
2009-04-03
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to determine the one with lowest energy, requiring a running time proportional to N. A quantum computer, if it could be built, could solve this problem in time {radical}(N). Here, we present a powerful extension of this result to the case of interacting quantum particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems.
Experimental quantum computing to solve systems of linear equations.
Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei
2013-06-01
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.
Secure Entanglement Distillation for Double-Server Blind Quantum Computation
NASA Astrophysics Data System (ADS)
Morimae, Tomoyuki; Fujii, Keisuke
2013-07-01
Blind quantum computation is a new secure quantum computing protocol where a client, who does not have enough quantum technologies at her disposal, can delegate her quantum computation to a server, who has a fully fledged quantum computer, in such a way that the server cannot learn anything about the client’s input, output, and program. If the client interacts with only a single server, the client has to have some minimum quantum power, such as the ability of emitting randomly rotated single-qubit states or the ability of measuring states. If the client interacts with two servers who share Bell pairs but cannot communicate with each other, the client can be completely classical. For such a double-server scheme, two servers have to share clean Bell pairs, and therefore the entanglement distillation is necessary in a realistic noisy environment. In this Letter, we show that it is possible to perform entanglement distillation in the double-server scheme without degrading the security of blind quantum computing.
Secure entanglement distillation for double-server blind quantum computation.
Morimae, Tomoyuki; Fujii, Keisuke
2013-07-12
Blind quantum computation is a new secure quantum computing protocol where a client, who does not have enough quantum technologies at her disposal, can delegate her quantum computation to a server, who has a fully fledged quantum computer, in such a way that the server cannot learn anything about the client's input, output, and program. If the client interacts with only a single server, the client has to have some minimum quantum power, such as the ability of emitting randomly rotated single-qubit states or the ability of measuring states. If the client interacts with two servers who share Bell pairs but cannot communicate with each other, the client can be completely classical. For such a double-server scheme, two servers have to share clean Bell pairs, and therefore the entanglement distillation is necessary in a realistic noisy environment. In this Letter, we show that it is possible to perform entanglement distillation in the double-server scheme without degrading the security of blind quantum computing.
Computing protein infrared spectroscopy with quantum chemistry.
Besley, Nicholas A
2007-12-15
Quantum chemistry is a field of science that has undergone unprecedented advances in the last 50 years. From the pioneering work of Boys in the 1950s, quantum chemistry has evolved from being regarded as a specialized and esoteric discipline to a widely used tool that underpins much of the current research in chemistry today. This achievement was recognized with the award of the 1998 Nobel Prize in Chemistry to John Pople and Walter Kohn. As the new millennium unfolds, quantum chemistry stands at the forefront of an exciting new era. Quantitative calculations on systems of the magnitude of proteins are becoming a realistic possibility, an achievement that would have been unimaginable to the early pioneers of quantum chemistry. In this article we will describe ongoing work towards this goal, focusing on the calculation of protein infrared amide bands directly with quantum chemical methods.
Time independent universal computing with spin chains: quantum plinko machine
NASA Astrophysics Data System (ADS)
Thompson, K. F.; Gokler, C.; Lloyd, S.; Shor, P. W.
2016-07-01
We present a scheme for universal quantum computing using XY Heisenberg spin chains. Information is encoded into packets propagating down these chains, and they interact with each other to perform universal quantum computation. A circuit using g gate blocks on m qubits can be encoded into chains of length O({g}3+δ {m}3+δ ) for all δ \\gt 0 with vanishingly small error.
Some generalizations of fuzzy structures in quantum computational logic
NASA Astrophysics Data System (ADS)
Giuntini, Roberto; Ledda, Antonio; Sergioli, Giuseppe; Paoli, Francesco
2011-01-01
Quantum computational logics provide a fertile common ground for a unified treatment of vagueness and uncertainty. In this paper, we describe an approach to the logic of quantum computation that has been recently taken up and developed. After reporting on the state of the art, we explore some future research perspectives in the light of some recent limitative results whose general significance will be duly assessed.
Quantum computation for large-scale image classification
NASA Astrophysics Data System (ADS)
Ruan, Yue; Chen, Hanwu; Tan, Jianing; Li, Xi
2016-10-01
Due to the lack of an effective quantum feature extraction method, there is currently no effective way to perform quantum image classification or recognition. In this paper, for the first time, a global quantum feature extraction method based on Schmidt decomposition is proposed. A revised quantum learning algorithm is also proposed that will classify images by computing the Hamming distance of these features. From the experimental results derived from the benchmark database Caltech 101, and an analysis of the algorithm, an effective approach to large-scale image classification is derived and proposed against the background of big data.
Quantum computation for large-scale image classification
NASA Astrophysics Data System (ADS)
Ruan, Yue; Chen, Hanwu; Tan, Jianing; Li, Xi
2016-07-01
Due to the lack of an effective quantum feature extraction method, there is currently no effective way to perform quantum image classification or recognition. In this paper, for the first time, a global quantum feature extraction method based on Schmidt decomposition is proposed. A revised quantum learning algorithm is also proposed that will classify images by computing the Hamming distance of these features. From the experimental results derived from the benchmark database Caltech 101, and an analysis of the algorithm, an effective approach to large-scale image classification is derived and proposed against the background of big data.
Algorithm-based analysis of collective decoherence in quantum computation
NASA Astrophysics Data System (ADS)
Utsunomiya, Shoko; Master, Cyrus P.; Yamamoto, Yoshihisa
2007-02-01
In a quantum computer, qubits are often stored in identical two-level systems separated by a distance shorter than the characteristic wavelength of the reservoirs that are responsible for decoherence. In this case the collective qubit-reservoir interaction, rather than the individual qubit-reservoir interaction, may determine the decoherence properties. We study the collective decoherence behavior in between each step in certain quantum algorithms and propose a simple alternative of implementing quantum algorithms using a quantum trajectory that is close to a decoherence-free subspace that avoids unstable Dicke's superradiant states and Schrödinger's cat state.
Universal linear Bogoliubov transformations through one-way quantum computation
Ukai, Ryuji; Yoshikawa, Jun-ichi; Iwata, Noriaki; Furusawa, Akira; Loock, Peter van
2010-03-15
We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.
ONSET OF CHAOS IN A MODEL OF QUANTUM COMPUTATION
G. BERMAN; ET AL
2001-02-01
Recently, the question of a relevance of the so-called quantum chaos has been raised in applications to quantum computation [2,3]. Indeed, according to the general approach to closed systems of finite number of interacting Fermi-particles (see, e.g. [4,5]), with an increase of an interaction between qubits a kind of chaos is expected to emerge in the energy spectra and structure of many-body states. Specifically, the fluctuations of energy levels and components of the eigenstates turn out to be very strong and described by the Random Matrix Theory. Clearly, if this happens in a quantum computer, it may lead to a destruction of the coherence of quantum computations due to internal decoherence inside many-body states. It is important to stress that quantum chaos occurs not only in the systems with random interaction, but also for purely dynamical interaction. In the latter case, the mechanism of chaos is due to a complex (non-linear) form of a two-body interaction represented in the basis of non-interacting particles. Numerical analysis [2] of a simplest model of quantum computer (2D model of 1/2-spins with a random interqubit interaction J) shows that with an increase of the number L of qubits, the chaos threshold J{sub cr} decreases as J{sub cr} {infinity} 1/L. On this ground, it was claimed that the onset of quantum chaos could be dangerous for quantum computers, since their effectiveness requires L >> 1. On the other hand, in [3] it was argued that in order to treat this problem properly, one needs to distinguish between chaotic properties of stationary states, and the dynamical process of quantum computation.
Continuous-Variable Quantum Computation of Oracle Decision Problems
NASA Astrophysics Data System (ADS)
Adcock, Mark R. A.
Quantum information processing is appealing due its ability to solve certain problems quantitatively faster than classical information processing. Most quantum algorithms have been studied in discretely parameterized systems, but many quantum systems are continuously parameterized. The field of quantum optics in particular has sophisticated techniques for manipulating continuously parameterized quantum states of light, but the lack of a code-state formalism has hindered the study of quantum algorithms in these systems. To address this situation, a code-state formalism for the solution of oracle decision problems in continuously-parameterized quantum systems is developed. Quantum information processing is appealing due its ability to solve certain problems quantitatively faster than classical information processing. Most quantum algorithms have been studied in discretely parameterized systems, but many quantum systems are continuously parameterized. The field of quantum optics in particular has sophisticated techniques for manipulating continuously parameterized quantum states of light, but the lack of a code-state formalism has hindered the study of quantum algorithms in these systems. To address this situation, a code-state formalism for the solution of oracle decision problems in continuously-parameterized quantum systems is developed. In the infinite-dimensional case, we study continuous-variable quantum algorithms for the solution of the Deutsch--Jozsa oracle decision problem implemented within a single harmonic-oscillator. Orthogonal states are used as the computational bases, and we show that, contrary to a previous claim in the literature, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform. We further demonstrate that orthogonal encoding bases are not unique, and using the coherent states of the harmonic oscillator as the computational bases, our formalism enables quantifying
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Ohzeki, Masayuki
2013-09-01
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
Exponential rise of dynamical complexity in quantum computing through projections.
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-10-10
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.
Scalable digital hardware for a trapped ion quantum computer
NASA Astrophysics Data System (ADS)
Mount, Emily; Gaultney, Daniel; Vrijsen, Geert; Adams, Michael; Baek, So-Young; Hudek, Kai; Isabella, Louis; Crain, Stephen; van Rynbach, Andre; Maunz, Peter; Kim, Jungsang
2015-09-01
Many of the challenges of scaling quantum computer hardware lie at the interface between the qubits and the classical control signals used to manipulate them. Modular ion trap quantum computer architectures address scalability by constructing individual quantum processors interconnected via a network of quantum communication channels. Successful operation of such quantum hardware requires a fully programmable classical control system capable of frequency stabilizing the continuous wave lasers necessary for loading, cooling, initialization, and detection of the ion qubits, stabilizing the optical frequency combs used to drive logic gate operations on the ion qubits, providing a large number of analog voltage sources to drive the trap electrodes, and a scheme for maintaining phase coherence among all the controllers that manipulate the qubits. In this work, we describe scalable solutions to these hardware development challenges.
Nonadiabatic holonomic quantum computation with all-resonant control
NASA Astrophysics Data System (ADS)
Xue, Zheng-Yuan; Zhou, Jian; Chu, Yao-Ming; Hu, Yong
2016-08-01
The implementation of holonomic quantum computation on superconducting quantum circuits is challenging due to the general requirement of controllable complicated coupling between multilevel systems. Here we solve this problem by proposing a scalable circuit QED lattice with simple realization of a universal set of nonadiabatic holonomic quantum gates. Compared with the existing proposals, we can achieve both the single and two logical qubit gates in a tunable and all-resonant way through a hybrid transmon-transmission-line encoding of the logical qubits in the decoherence-free subspaces. This distinct advantage thus leads to quantum gates with very fast speeds and consequently very high fidelities. Therefore, our scheme paves a promising way towards the practical realization of high-fidelity nonadiabatic holonomic quantum computation.
Exponential rise of dynamical complexity in quantum computing through projections
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-01-01
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics. PMID:25300692
Quantum perceptron over a field and neural network architecture selection in a quantum computer.
da Silva, Adenilton José; Ludermir, Teresa Bernarda; de Oliveira, Wilson Rosa
2016-04-01
In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a non-linear quantum operator. PMID:26878722
Quantum perceptron over a field and neural network architecture selection in a quantum computer.
da Silva, Adenilton José; Ludermir, Teresa Bernarda; de Oliveira, Wilson Rosa
2016-04-01
In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a non-linear quantum operator.
Unitary R-matrices for topological quantum computing
NASA Astrophysics Data System (ADS)
Burton, P. J.; Gould, M. D.
2006-02-01
The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding—the R-matrix—be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.
Quantum Computation Based on Photons with Three Degrees of Freedom.
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun
2016-01-01
Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems. PMID:27174302
Quantum Computation Based on Photons with Three Degrees of Freedom
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun
2016-01-01
Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems. PMID:27174302
Quantum Computation Based on Photons with Three Degrees of Freedom
NASA Astrophysics Data System (ADS)
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun
2016-05-01
Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems.
Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious
ERIC Educational Resources Information Center
Cirasella, Jill
2009-01-01
This article presents an annotated selection of the most important and informative Internet resources for learning about quantum computing, finding quantum computing literature, and tracking quantum computing news. All of the quantum computing resources described in this article are freely available, English-language web sites that fall into one…
Quantum Monte Carlo Endstation for Petascale Computing
David Ceperley
2011-03-02
CUDA GPU platform. We restructured the CPU algorithms to express additional parallelism, minimize GPU-CPU communication, and efficiently utilize the GPU memory hierarchy. Using mixed precision on GT200 GPUs and MPI for intercommunication and load balancing, we observe typical full-application speedups of approximately 10x to 15x relative to quad-core Xeon CPUs alone, while reproducing the double-precision CPU results within statistical error. We developed an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and used it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We computed the static contribution to the free energy with the QMC method and obtained the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We computed the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy. We compared experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron momentum density, we derived its discontinuity at the Fermi wavevector finding an accurate measure of the renormalization factor that we compared with quantum-Monte-Carlo and G0W0 calculations performed both on crystalline sodium and on the homogeneous electron gas. Our calculated results are in good agreement with the experiment. We have been studying the heat of formation for various Kubas complexes of molecular
LDRD final report on quantum computing using interacting semiconductor quantum wires.
Lyo, Sungkwun Kenneth; Dunn, Roberto G.; Lilly, Michael Patrick; Tibbetts, Denise R. ); Stephenson, Larry L.; Seamons, John Andrew; Reno, John Louis; Bielejec, Edward Salvador; Simmons, Jerry Alvon
2006-01-01
For several years now quantum computing has been viewed as a new paradigm for certain computing applications. Of particular importance to this burgeoning field is the development of an algorithm for factoring large numbers which obviously has deep implications for cryptography and national security. Implementation of these theoretical ideas faces extraordinary challenges in preparing and manipulating quantum states. The quantum transport group at Sandia has demonstrated world-leading, unique double quantum wires devices where we have unprecedented control over the coupling strength, number of 1 D channels, overlap and interaction strength in this nanoelectronic system. In this project, we study 1D-1D tunneling with the ultimate aim of preparing and detecting quantum states of the coupled wires. In a region of strong tunneling, electrons can coherently oscillate from one wire to the other. By controlling the velocity of the electrons, length of the coupling region and tunneling strength we will attempt to observe tunneling oscillations. This first step is critical for further development double quantum wires into the basic building block for a quantum computer, and indeed for other coupled nanoelectronic devices that will rely on coherent transport. If successful, this project will have important implications for nanoelectronics, quantum computing and information technology.
Blind quantum computation over a collective-noise channel
NASA Astrophysics Data System (ADS)
Takeuchi, Yuki; Fujii, Keisuke; Ikuta, Rikizo; Yamamoto, Takashi; Imoto, Nobuyuki
2016-05-01
Blind quantum computation (BQC) allows a client (Alice), who only possesses relatively poor quantum devices, to delegate universal quantum computation to a server (Bob) in such a way that Bob cannot know Alice's inputs, algorithm, and outputs. The quantum channel between Alice and Bob is noisy, and the loss over the long-distance quantum communication should also be taken into account. Here we propose to use decoherence-free subspace (DFS) to overcome the collective noise in the quantum channel for BQC, which we call DFS-BQC. We propose three variations of DFS-BQC protocols. One of them, a coherent-light-assisted DFS-BQC protocol, allows Alice to faithfully send the signal photons with a probability proportional to a transmission rate of the quantum channel. In all cases, we combine the ideas based on DFS and the Broadbent-Fitzsimons-Kashefi protocol, which is one of the BQC protocols, without degrading unconditional security. The proposed DFS-based schemes are generic and hence can be applied to other BQC protocols where Alice sends quantum states to Bob.
Slow phase relaxation as a route to quantum computing beyond the quantum chaos border
NASA Astrophysics Data System (ADS)
Flores, J.; Kun, S. Yu.; Seligman, T. H.
2005-07-01
We reveal that phase memory can be much longer than energy relaxation in systems with exponentially large dimensions of Hilbert space; this finding is documented by 50 years of nuclear experiments, though the information is somewhat hidden. For quantum computers Hilbert spaces of dimension 2100 or larger will be typical and therefore this effect may contribute significantly to reduce the problems of scaling of quantum computers to a useful number of qubits.
Ma, Buyong; Nussinov, Ruth
2004-12-01
Computations are being integrated into biological research at an increasingly fast pace. This has not only changed the way in which biological information is managed; it has also changed the way in which experiments are planned in order to obtain information from nature. Can experiments and computations be full partners? Computational chemistry has expanded over the years, proceeding from computations of a hydrogen molecule toward the challenging goal of systems biology, which attempts to handle the entire living cell. Applying theories from ab initio quantum mechanics to simplified models, the virtual worlds explored by computations provide replicas of real-world phenomena. At the same time, the virtual worlds can affect our perception of the real world. Computational biology targets a world of complex organization, for which a unified theory is unlikely to exist. A computational biology model, even if it has a clear physical or chemical basis, may not reduce to physics and chemistry. At the molecular level, computational biology and experimental biology have already been partners, mutually benefiting from each other. For the perception to become reality, computation and experiment should be united as full partners in biological research.
NASA Astrophysics Data System (ADS)
Ma, Buyong; Nussinov, Ruth
2004-12-01
Computations are being integrated into biological research at an increasingly fast pace. This has not only changed the way in which biological information is managed; it has also changed the way in which experiments are planned in order to obtain information from nature. Can experiments and computations be full partners? Computational chemistry has expanded over the years, proceeding from computations of a hydrogen molecule toward the challenging goal of systems biology, which attempts to handle the entire living cell. Applying theories from ab initio quantum mechanics to simplified models, the virtual worlds explored by computations provide replicas of real-world phenomena. At the same time, the virtual worlds can affect our perception of the real world. Computational biology targets a world of complex organization, for which a unified theory is unlikely to exist. A computational biology model, even if it has a clear physical or chemical basis, may not reduce to physics and chemistry. At the molecular level, computational biology and experimental biology have already been partners, mutually benefiting from each other. For the perception to become reality, computation and experiment should be united as full partners in biological research.
Entanglement-based machine learning on a quantum computer.
Cai, X-D; Wu, D; Su, Z-E; Chen, M-C; Wang, X-L; Li, Li; Liu, N-L; Lu, C-Y; Pan, J-W
2015-03-20
Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge is that machine learning with the rapidly growing "big data" could become intractable for classical computers. Recently, quantum machine learning algorithms [Lloyd, Mohseni, and Rebentrost, arXiv.1307.0411] were proposed which could offer an exponential speedup over classical algorithms. Here, we report the first experimental entanglement-based classification of two-, four-, and eight-dimensional vectors to different clusters using a small-scale photonic quantum computer, which are then used to implement supervised and unsupervised machine learning. The results demonstrate the working principle of using quantum computers to manipulate and classify high-dimensional vectors, the core mathematical routine in machine learning. The method can, in principle, be scaled to larger numbers of qubits, and may provide a new route to accelerate machine learning. PMID:25839250
Entanglement-based machine learning on a quantum computer.
Cai, X-D; Wu, D; Su, Z-E; Chen, M-C; Wang, X-L; Li, Li; Liu, N-L; Lu, C-Y; Pan, J-W
2015-03-20
Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge is that machine learning with the rapidly growing "big data" could become intractable for classical computers. Recently, quantum machine learning algorithms [Lloyd, Mohseni, and Rebentrost, arXiv.1307.0411] were proposed which could offer an exponential speedup over classical algorithms. Here, we report the first experimental entanglement-based classification of two-, four-, and eight-dimensional vectors to different clusters using a small-scale photonic quantum computer, which are then used to implement supervised and unsupervised machine learning. The results demonstrate the working principle of using quantum computers to manipulate and classify high-dimensional vectors, the core mathematical routine in machine learning. The method can, in principle, be scaled to larger numbers of qubits, and may provide a new route to accelerate machine learning.
Entanglement-Based Machine Learning on a Quantum Computer
NASA Astrophysics Data System (ADS)
Cai, X.-D.; Wu, D.; Su, Z.-E.; Chen, M.-C.; Wang, X.-L.; Li, Li; Liu, N.-L.; Lu, C.-Y.; Pan, J.-W.
2015-03-01
Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge is that machine learning with the rapidly growing "big data" could become intractable for classical computers. Recently, quantum machine learning algorithms [Lloyd, Mohseni, and Rebentrost, arXiv.1307.0411] were proposed which could offer an exponential speedup over classical algorithms. Here, we report the first experimental entanglement-based classification of two-, four-, and eight-dimensional vectors to different clusters using a small-scale photonic quantum computer, which are then used to implement supervised and unsupervised machine learning. The results demonstrate the working principle of using quantum computers to manipulate and classify high-dimensional vectors, the core mathematical routine in machine learning. The method can, in principle, be scaled to larger numbers of qubits, and may provide a new route to accelerate machine learning.
From transistor to trapped-ion computers for quantum chemistry.
Yung, M-H; Casanova, J; Mezzacapo, A; McClean, J; Lamata, L; Aspuru-Guzik, A; Solano, E
2014-01-01
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology. PMID:24395054
Kochen-Specker Theorem as a Precondition for Quantum Computing
NASA Astrophysics Data System (ADS)
Nagata, Koji; Nakamura, Tadao
2016-08-01
We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or -1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-01-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-01-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Optimal control, geometry, and quantum computing
NASA Astrophysics Data System (ADS)
Nielsen, Michael A.; Dowling, Mark R.; Gu, Mile; Doherty, Andrew C.
2006-06-01
We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U , to the optimal control cost associated to the synthesis of U . These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo Mauro
2010-05-01
I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational "principles of the quantumness," I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm "the universe is a huge quantum computer," reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe. Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.
D'Ariano, Giacomo Mauro
2010-05-04
I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational 'principles of the quantumness', I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm 'the universe is a huge quantum computer', reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.
a Computable Framework for Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Husain, Viqar; Pawłowski, Tomasz
2015-01-01
We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The methods of loop quantum gravity applied to this model lead to a physical Hilbert space and Hamiltonian. This provides a framework for physical calculations in the theory.
Quantum computation in the analysis of hyperspectral data
NASA Astrophysics Data System (ADS)
Gomez, Richard B.; Ghoshal, Debabrata; Jayanna, Anil
2004-08-01
Recent research on the topic of quantum computation provides us with some quantum algorithms with higher efficiency and speedup compared to their classical counterparts. In this paper, it is our intent to provide the results of our investigation of several applications of such quantum algorithms - especially the Grover's Search algorithm - in the analysis of Hyperspectral Data. We found many parallels with Grover's method in existing data processing work that make use of classical spectral matching algorithms. Our efforts also included the study of several methods dealing with hyperspectral image analysis work where classical computation methods involving large data sets could be replaced with quantum computation methods. The crux of the problem in computation involving a hyperspectral image data cube is to convert the large amount of data in high dimensional space to real information. Currently, using the classical model, different time consuming methods and steps are necessary to analyze these data including: Animation, Minimum Noise Fraction Transform, Pixel Purity Index algorithm, N-dimensional scatter plot, Identification of Endmember spectra - are such steps. If a quantum model of computation involving hyperspectral image data can be developed and formalized - it is highly likely that information retrieval from hyperspectral image data cubes would be a much easier process and the final information content would be much more meaningful and timely. In this case, dimensionality would not be a curse, but a blessing.
Combining dynamical decoupling with fault-tolerant quantum computation
Ng, Hui Khoon; Preskill, John; Lidar, Daniel A.
2011-07-15
We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise and have a lower overhead cost than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer and can be expressed either in terms of the operator norm of the bath's Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations.
Linear optical quantum computing in a single spatial mode.
Humphreys, Peter C; Metcalf, Benjamin J; Spring, Justin B; Moore, Merritt; Jin, Xian-Min; Barbieri, Marco; Kolthammer, W Steven; Walmsley, Ian A
2013-10-11
We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.
Scheme for Entering Binary Data Into a Quantum Computer
NASA Technical Reports Server (NTRS)
Williams, Colin
2005-01-01
A quantum algorithm provides for the encoding of an exponentially large number of classical data bits by use of a smaller (polynomially large) number of quantum bits (qubits). The development of this algorithm was prompted by the need, heretofore not satisfied, for a means of entering real-world binary data into a quantum computer. The data format provided by this algorithm is suitable for subsequent ultrafast quantum processing of the entered data. Potential applications lie in disciplines (e.g., genomics) in which one needs to search for matches between parts of very long sequences of data. For example, the algorithm could be used to encode the N-bit-long human genome in only log2N qubits. The resulting log2N-qubit state could then be used for subsequent quantum data processing - for example, to perform rapid comparisons of sequences.
Universal quantum computation with hybrid spin-Majorana qubits
NASA Astrophysics Data System (ADS)
Hoffman, Silas; Schrade, Constantin; Klinovaja, Jelena; Loss, Daniel
2016-07-01
We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum-dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot that is tunnel coupled to two topological superconductors. The effective spin-Majorana exchange facilitates a hybrid cnot gate for which either qubit can be the control or target. The second setup is a modular scalable network of topological superconductors and quantum dots. As a result of the exchange interaction between adjacent spin qubits, a cnot gate is implemented that acts on neighboring Majorana qubits and eliminates the necessity of interqubit braiding. In both setups, the spin-Majorana exchange interaction allows for a phase gate, acting on either the spin or the Majorana qubit, and for a swap or hybrid swap gate which is sufficient for universal quantum computation without projective measurements.
Computational studies of quantum spin systems
NASA Astrophysics Data System (ADS)
Wang, Ling
Quantum spin models are important for studying the magnetic behavior of strongly correlated electronic insulators. Specifically, the 2D S = 1/2 Heisenberg model closely captures the antiferromagnetic state of CuO2 layers of the high-Tc superconductor parent compounds at half band filling. Introducing competing interactions or disorder can drive quantum phase transitions to other new states. I use the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method and finite-size scaling to study the quantum critical points of two Heisenberg bilayers, each with intra- and inter-plane couplings J and J⊥. Tuning the inter- to intra-layer coupling constant ratio g = J⊥ /J drives a quantum phase transition between the Neel ordered state and a quantum disordered state. I discuss the ground-state finite-size scaling properties of three different quantities and extract the critical value of the coupling ratio gc. The results improve gc by more than an order of magnitude over the previous best estimates. Upon doping with static non-magnetic impurities, (e.g., substituting Cu with Zn), the cuprate layer is driven through a percolation phase transition. While the static properties are described by 2D classical percolation, the dynamical properties are quantum mechanical. I use exact diagonalization to calculate the lowest excitation gap Delta and use SSE to study an upper bound for Delta obtained from sum rules. Scaling the gap distribution with the cluster length L, a dynamic exponent z ≈ 2Df is obtained, where Df is the fractal dimensionality of the percolating cluster. I present several arguments showing that the low-energy excitations are due to weakly coupled effective moments formed owing to local imbalance in sublattice occupation. Many interesting quantum spin models lead to negative signs in the importance weight used in QMC sampling, and thus this method cannot be used. Matrix product states (MPSs) and tensor product states (TPSs) have recently been
Quantum algorithms for spin models and simulable gate sets for quantum computation
NASA Astrophysics Data System (ADS)
van den Nest, M.; Dür, W.; Raussendorf, R.; Briegel, H. J.
2009-11-01
We present simple mappings between classical lattice models and quantum circuits, which provide a systematic formalism to obtain quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. We, e.g., present an efficient quantum algorithm for the six-vertex model as well as a two-dimensional Ising-type model. We show that classically simulating these (complex-parameter) spin models is as hard as simulating universal quantum computation, i.e., BQP complete (BQP denotes bounded-error quantum polynomial time). Furthermore, our mappings provide a framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. We, e.g., show that the simulability of Valiant’s match gates can be recovered by using the solvability of the free-fermion eight-vertex model.
An Invitation to the Mathematics of Topological Quantum Computation
NASA Astrophysics Data System (ADS)
Rowell, E. C.
2016-03-01
Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials.
Individual addressing in quantum computation through spatial refocusing
NASA Astrophysics Data System (ADS)
Shen, C.; Gong, Z.-X.; Duan, L.-M.
2013-11-01
Separate addressing of individual qubits is a challenging requirement for scalable quantum computation, and crosstalk between operations on neighboring qubits remains a significant source of error for current experimental implementations of multiqubit platforms. We propose a scheme based on spatial refocusing from interference of several coherent laser beams to significantly reduce the crosstalk error for any type of quantum gate. A general framework is developed for the spatial refocusing technique, in particular with practical Gaussian beams, and we show that the crosstalk-induced infidelity of quantum gates can be reduced by several orders of magnitude with a moderate cost of a few correction laser beams under typical experimental conditions.
Topological quantum computing with Read-Rezayi states.
Hormozi, L; Bonesteel, N E; Simon, S H
2009-10-16
Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which, in principle, can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with k>2, k not equal 4. This work extends previous results which only applied to the case k=3 (Fibonacci) and clarifies why, in that case, gate constructions are simpler than for a generic Read-Rezayi state.
Computer studies of multiple-quantum spin dynamics
Murdoch, J.B.
1982-11-01
The excitation and detection of multiple-quantum (MQ) transitions in Fourier transform NMR spectroscopy is an interesting problem in the quantum mechanical dynamics of spin systems as well as an important new technique for investigation of molecular structure. In particular, multiple-quantum spectroscopy can be used to simplify overly complex spectra or to separate the various interactions between a nucleus and its environment. The emphasis of this work is on computer simulation of spin-system evolution to better relate theory and experiment.
Positive Wigner Functions Render Classical Simulation of Quantum Computation Efficient
NASA Astrophysics Data System (ADS)
Mari, A.; Eisert, J.
2012-12-01
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.
Ground-state geometric quantum computing in superconducting systems
Solinas, P.; Moettoenen, M.
2010-11-15
We present a theoretical proposal for the implementation of geometric quantum computing based on a Hamiltonian which has a doubly degenerate ground state. Thus the system which is steered adiabatically, remains in the ground-state. The proposed physical implementation relies on a superconducting circuit composed of three SQUIDs and two superconducting islands with the charge states encoding the logical states. We obtain a universal set of single-qubit gates and implement a nontrivial two-qubit gate exploiting the mutual inductance between two neighboring circuits, allowing us to realize a fully geometric ground-state quantum computing. The introduced paradigm for the implementation of geometric quantum computing is expected to be robust against environmental effects.
Exploring quantum computing application to satellite data assimilation
NASA Astrophysics Data System (ADS)
Cheung, S.; Zhang, S. Q.
2015-12-01
This is an exploring work on potential application of quantum computing to a scientific data optimization problem. On classical computational platforms, the physical domain of a satellite data assimilation problem is represented by a discrete variable transform, and classical minimization algorithms are employed to find optimal solution of the analysis cost function. The computation becomes intensive and time-consuming when the problem involves large number of variables and data. The new quantum computer opens a very different approach both in conceptual programming and in hardware architecture for solving optimization problem. In order to explore if we can utilize the quantum computing machine architecture, we formulate a satellite data assimilation experimental case in the form of quadratic programming optimization problem. We find a transformation of the problem to map it into Quadratic Unconstrained Binary Optimization (QUBO) framework. Binary Wavelet Transform (BWT) will be applied to the data assimilation variables for its invertible decomposition and all calculations in BWT are performed by Boolean operations. The transformed problem will be experimented as to solve for a solution of QUBO instances defined on Chimera graphs of the quantum computer.
Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation.
Ukai, Ryuji; Yokoyama, Shota; Yoshikawa, Jun-ichi; van Loock, Peter; Furusawa, Akira
2011-12-16
We experimentally demonstrate a controlled-phase gate for continuous variables using a cluster-state resource of four optical modes. The two independent input states of the gate are coupled with the cluster in a teleportation-based fashion. As a result, one of the entanglement links present in the initial cluster state appears in the two unmeasured output modes as the corresponding entangling gate acting on the input states. The genuine quantum character of this gate becomes manifest and is verified through the presence of entanglement at the output for a product two-mode coherent input state. By combining our gate with the recently reported module for single-mode Gaussian operations [R. Ukai et al., Phys. Rev. Lett. 106, 240504 (2011)], it is possible to implement any multimode Gaussian operation as a fully measurement-based one-way quantum computation. PMID:22243056
Robust and scalable optical one-way quantum computation
Wang Hefeng; Yang Chuiping; Nori, Franco
2010-05-15
We propose an efficient approach for deterministically generating scalable cluster states with photons. This approach involves unitary transformations performed on atoms coupled to optical cavities. Its operation cost scales linearly with the number of qubits in the cluster state, and photon qubits are encoded such that single-qubit operations can be easily implemented by using linear optics. Robust optical one-way quantum computation can be performed since cluster states can be stored in atoms and then transferred to photons that can be easily operated and measured. Therefore, this proposal could help in performing robust large-scale optical one-way quantum computation.
Efficient computations of quantum canonical Gibbs state in phase space
NASA Astrophysics Data System (ADS)
Bondar, Denys I.; Campos, Andre G.; Cabrera, Renan; Rabitz, Herschel A.
2016-06-01
The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.
Efficient computations of quantum canonical Gibbs state in phase space.
Bondar, Denys I; Campos, Andre G; Cabrera, Renan; Rabitz, Herschel A
2016-06-01
The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation. PMID:27415384
Adiabatic quantum computing with spin qubits hosted by molecules.
Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji
2015-01-28
A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.
Quantum annealing: The fastest route to quantum computation?
NASA Astrophysics Data System (ADS)
Smorra, C.; Blaum, K.; Bojtar, L.; Borchert, M.; Franke, K. A.; Higuchi, T.; Leefer, N.; Nagahama, H.; Matsuda, Y.; Mooser, A.; Niemann, M.; Ospelkaus, C.; Quint, W.; Schneider, G.; Sellner, S.; Tanaka, T.; Van Gorp, S.; Walz, J.; Yamazaki, Y.; Ulmer, S.
2015-11-01
The Baryon Antibaryon Symmetry Experiment (BASE) aims at performing a stringent test of the combined charge parity and time reversal (CPT) symmetry by comparing the magnetic moments of the proton and the antiproton with high precision. Using single particles in a Penning trap, the proton/antiproton g-factors, i.e. the magnetic moment in units of the nuclear magneton, are determined by measuring the respective ratio of the spin-precession frequency to the cyclotron frequency. The spin precession frequency is measured by non-destructive detection of spin quantum transitions using the continuous Stern-Gerlach effect, and the cyclotron frequency is determined from the particle*s motional eigenfrequencies in the Penning trap using the invariance theorem. By application of the double Penning-trap method we expect that in our measurements a fractional precision of δ g/ g 10-9 can be achieved. The successful application of this method to the antiproton will consist a factor 1000 improvement in the fractional precision of its magnetic moment. The BASE collaboration has constructed and commissioned a new experiment at the Antiproton Decelerator (AD) of CERN. This article describes and summarizes the physical and technical aspects of this new experiment.
Magnetic resonance force microscopy and a solid state quantum computer.
Pelekhov, D. V.; Martin, I.; Suter, A.; Reagor, D. W.; Hammel, P. C.
2001-01-01
A Quantum Computer (QC) is a device that utilizes the principles of Quantum Mechanics to perform computations. Such a machine would be capable of accomplishing tasks not achievable by means of any conventional digital computer, for instance factoring large numbers. Currently it appears that the QC architecture based on an array of spin quantum bits (qubits) embedded in a solid-state matrix is one of the most promising approaches to fabrication of a scalable QC. However, the fabrication and operation of a Solid State Quantum Computer (SSQC) presents very formidable challenges; primary amongst these are: (1) the characterization and control of the fabrication process of the device during its construction and (2) the readout of the computational result. Magnetic Resonance Force Microscopy (MRFM)--a novel scanning probe technique based on mechanical detection of magnetic resonance-provides an attractive means of addressing these requirements. The sensitivity of the MRFM significantly exceeds that of conventional magnetic resonance measurement methods, and it has the potential for single electron spin detection. Moreover, the MRFM is capable of true 3D subsurface imaging. These features will make MRFM an invaluable tool for the implementation of a spin-based QC. Here we present the general principles of MRFM operation, the current status of its development and indicate future directions for its improvement.
Quantum computing with an electron spin ensemble.
Wesenberg, J H; Ardavan, A; Briggs, G A D; Morton, J J L; Schoelkopf, R J; Schuster, D I; Mølmer, K
2009-08-14
We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper pair box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.
Quantum computing with collective ensembles of multilevel systems.
Brion, E; Mølmer, K; Saffman, M
2007-12-31
We propose a new physical approach for encoding and processing of quantum information in ensembles of multilevel quantum systems, where the different bits are not carried by individual particles but associated with the collective population of different internal levels. One- and two-bit gates are implemented by collective internal state transitions taking place in the presence of an excitation blockade mechanism, which restricts the population of each internal state to the values zero and unity. Quantum computers with 10-20 bits can be built via this scheme in single trapped clouds of ground state atoms subject to the Rydberg excitation blockade mechanism, and the linear dependence between register size and the number of internal quantum states in atoms offers realistic means to reach larger registers.
Computational nuclear quantum many-body problem: The UNEDF project
Fann, George I
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Philosophical and metamathematical considerations of quantum mechanical computers
NASA Astrophysics Data System (ADS)
Caulfield, H. John; Shamir, Joseph
1990-07-01
We ask and give only very preliminary answers to two questions which must arise when we consider quantum mechanical computers with significant quantunt indeterminacy. First, how does this impact our belief in Church's thesis? Second, how does this impact our belief in freedom of thought?
Adapting the traveling salesman problem to an adiabatic quantum computer
NASA Astrophysics Data System (ADS)
Warren, Richard H.
2013-04-01
We show how to guide a quantum computer to select an optimal tour for the traveling salesman. This is significant because it opens a rapid solution method for the wide range of applications of the traveling salesman problem, which include vehicle routing, job sequencing and data clustering.
Human-competitive evolution of quantum computing artefacts by Genetic Programming.
Massey, Paul; Clark, John A; Stepney, Susan
2006-01-01
We show how Genetic Programming (GP) can be used to evolve useful quantum computing artefacts of increasing sophistication and usefulness: firstly specific quantum circuits, then quantum programs, and finally system-independent quantum algorithms. We conclude the paper by presenting a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.
Interplay between computable measures of entanglement and other quantum correlations
Girolami, Davide; Adesso, Gerardo
2011-11-15
Composite quantum systems can be in generic states characterized not only by entanglement but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue, focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord D{sub G}. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship D{sub G}{>=}N{sup 2} holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner, and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, which we conjecture to be universal, between two relevant and experimentally friendly nonclassicality indicators. This ties in with the intuition that general quantum correlations should at least contain and in general exceed entanglement on mixed states of composite quantum systems.
Quantum computation mediated by ancillary qudits and spin coherent states
NASA Astrophysics Data System (ADS)
Proctor, Timothy J.; Dooley, Shane; Kendon, Viv
2015-01-01
Models of universal quantum computation in which the required interactions between register (computational) qubits are mediated by some ancillary system are highly relevant to experimental realizations of a quantum computer. We introduce such a universal model that employs a d -dimensional ancillary qudit. The ancilla-register interactions take the form of controlled displacements operators, with a displacement operator defined on the periodic and discrete lattice phase space of a qudit. We show that these interactions can implement controlled phase gates on the register by utilizing geometric phases that are created when closed loops are traversed in this phase space. The extra degrees of freedom of the ancilla can be harnessed to reduce the number of operations required for certain gate sequences. In particular, we see that the computational advantages of the quantum bus (qubus) architecture, which employs a field-mode ancilla, are also applicable to this model. We then explore an alternative ancilla-mediated model which employs a spin ensemble as the ancillary system and again the interactions with the register qubits are via controlled displacement operators, with a displacement operator defined on the Bloch sphere phase space of the spin coherent states of the ensemble. We discuss the computational advantages of this model and its relationship with the qubus architecture.
Computational complexity of nonequilibrium steady states of quantum spin chains
NASA Astrophysics Data System (ADS)
Marzolino, Ugo; Prosen, Tomaž
2016-03-01
We study nonequilibrium steady states (NESS) of spin chains with boundary Markovian dissipation from the computational complexity point of view. We focus on X X chains whose NESS are matrix product operators, i.e., with coefficients of a tensor operator basis described by transition amplitudes in an auxiliary space. Encoding quantum algorithms in the auxiliary space, we show that estimating expectations of operators, being local in the sense that each acts on disjoint sets of few spins covering all the system, provides the answers of problems at least as hard as, and believed by many computer scientists to be much harder than, those solved by quantum computers. We draw conclusions on the hardness of the above estimations.
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George
2013-10-01
Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.
Simulating Ising spin glasses on a quantum computer
NASA Astrophysics Data System (ADS)
Lidar, Daniel A.; Biham, Ofer
1997-09-01
A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum probability equal to the corresponding thermodynamic weight. The partition function is thus approximated efficiently. The algorithm neither suffers from critical slowing down nor gets stuck in local minima. The algorithm can be applied in any dimension, to a class of spin-glass Ising models with a finite portion of frustrated plaquettes, diluted Ising models, and models with a magnetic field.
Efficient quantum algorithm for computing n-time correlation functions.
Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E
2014-07-11
We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.
Quantum computation using weak nonlinearities: Robustness against decoherence
Jeong, Hyunseok
2006-05-15
We investigate decoherence effects in the recently suggested quantum-computation scheme using weak nonlinearities, strong probe coherent fields, detection, and feedforward methods. It is shown that in the weak-nonlinearity-based quantum gates, decoherence in nonlinear media can be made arbitrarily small simply by using arbitrarily strong probe fields, if photon-number-resolving detection is used. On the contrary, we find that homodyne detection with feedforward is not appropriate for this scheme because in this case decoherence rapidly increases as the probe field gets larger.
Controllable coherent population transfers in superconducting qubits for quantum computing.
Wei, L F; Johansson, J R; Cen, L X; Ashhab, S; Nori, Franco
2008-03-21
We propose an approach to coherently transfer populations between selected quantum states in one- and two-qubit systems by using controllable Stark-chirped rapid adiabatic passages. These evolution-time insensitive transfers, assisted by easily implementable single-qubit phase-shift operations, could serve as elementary logic gates for quantum computing. Specifically, this proposal could be conveniently demonstrated with existing Josephson phase qubits. Our proposal can find an immediate application in the readout of these qubits. Indeed, the broken parity symmetries of the bound states in these artificial atoms provide an efficient approach to design the required adiabatic pulses.
Wei, Hai-Rui; Deng, Fu-Guo
2013-07-29
We investigate the possibility of achieving scalable photonic quantum computing by the giant optical circular birefringence induced by a quantum-dot spin in a double-sided optical microcavity as a result of cavity quantum electrodynamics. We construct a deterministic controlled-not gate on two photonic qubits by two single-photon input-output processes and the readout on an electron-medium spin confined in an optical resonant microcavity. This idea could be applied to multi-qubit gates on photonic qubits and we give the quantum circuit for a three-photon Toffoli gate. High fidelities and high efficiencies could be achieved when the side leakage to the cavity loss rate is low. It is worth pointing out that our devices work in both the strong and the weak coupling regimes. PMID:23938640
Wei, Hai-Rui; Deng, Fu-Guo
2013-07-29
We investigate the possibility of achieving scalable photonic quantum computing by the giant optical circular birefringence induced by a quantum-dot spin in a double-sided optical microcavity as a result of cavity quantum electrodynamics. We construct a deterministic controlled-not gate on two photonic qubits by two single-photon input-output processes and the readout on an electron-medium spin confined in an optical resonant microcavity. This idea could be applied to multi-qubit gates on photonic qubits and we give the quantum circuit for a three-photon Toffoli gate. High fidelities and high efficiencies could be achieved when the side leakage to the cavity loss rate is low. It is worth pointing out that our devices work in both the strong and the weak coupling regimes.
Prediction by linear regression on a quantum computer
NASA Astrophysics Data System (ADS)
Schuld, Maria; Sinayskiy, Ilya; Petruccione, Francesco
2016-08-01
We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least-squares optimization. In contrast to related previous contributions suffering from the problem of reading out the optimal parameters of the fit, our scheme focuses on the machine-learning task of guessing the output corresponding to a new input given examples of data points. Furthermore, we adapt the algorithm to process nonsparse data matrices that can be represented by low-rank approximations, and significantly improve the dependency on its condition number. The prediction result can be accessed through a single-qubit measurement or used for further quantum information processing routines. The algorithm's runtime is logarithmic in the dimension of the input space provided the data is given as quantum information as an input to the routine.
Semiconductor-inspired design principles for superconducting quantum computing.
Shim, Yun-Pil; Tahan, Charles
2016-01-01
Superconducting circuits offer tremendous design flexibility in the quantum regime culminating most recently in the demonstration of few qubit systems supposedly approaching the threshold for fault-tolerant quantum information processing. Competition in the solid-state comes from semiconductor qubits, where nature has bestowed some very useful properties which can be utilized for spin qubit-based quantum computing. Here we begin to explore how selective design principles deduced from spin-based systems could be used to advance superconducting qubit science. We take an initial step along this path proposing an encoded qubit approach realizable with state-of-the-art tunable Josephson junction qubits. Our results show that this design philosophy holds promise, enables microwave-free control, and offers a pathway to future qubit designs with new capabilities such as with higher fidelity or, perhaps, operation at higher temperature. The approach is also especially suited to qubits on the basis of variable super-semi junctions. PMID:26983379
Semiconductor-inspired design principles for superconducting quantum computing.
Shim, Yun-Pil; Tahan, Charles
2016-03-17
Superconducting circuits offer tremendous design flexibility in the quantum regime culminating most recently in the demonstration of few qubit systems supposedly approaching the threshold for fault-tolerant quantum information processing. Competition in the solid-state comes from semiconductor qubits, where nature has bestowed some very useful properties which can be utilized for spin qubit-based quantum computing. Here we begin to explore how selective design principles deduced from spin-based systems could be used to advance superconducting qubit science. We take an initial step along this path proposing an encoded qubit approach realizable with state-of-the-art tunable Josephson junction qubits. Our results show that this design philosophy holds promise, enables microwave-free control, and offers a pathway to future qubit designs with new capabilities such as with higher fidelity or, perhaps, operation at higher temperature. The approach is also especially suited to qubits on the basis of variable super-semi junctions.
Semiconductor-inspired design principles for superconducting quantum computing
Shim, Yun-Pil; Tahan, Charles
2016-01-01
Superconducting circuits offer tremendous design flexibility in the quantum regime culminating most recently in the demonstration of few qubit systems supposedly approaching the threshold for fault-tolerant quantum information processing. Competition in the solid-state comes from semiconductor qubits, where nature has bestowed some very useful properties which can be utilized for spin qubit-based quantum computing. Here we begin to explore how selective design principles deduced from spin-based systems could be used to advance superconducting qubit science. We take an initial step along this path proposing an encoded qubit approach realizable with state-of-the-art tunable Josephson junction qubits. Our results show that this design philosophy holds promise, enables microwave-free control, and offers a pathway to future qubit designs with new capabilities such as with higher fidelity or, perhaps, operation at higher temperature. The approach is also especially suited to qubits on the basis of variable super-semi junctions. PMID:26983379
Semiconductor-inspired design principles for superconducting quantum computing
NASA Astrophysics Data System (ADS)
Shim, Yun-Pil; Tahan, Charles
2016-03-01
Superconducting circuits offer tremendous design flexibility in the quantum regime culminating most recently in the demonstration of few qubit systems supposedly approaching the threshold for fault-tolerant quantum information processing. Competition in the solid-state comes from semiconductor qubits, where nature has bestowed some very useful properties which can be utilized for spin qubit-based quantum computing. Here we begin to explore how selective design principles deduced from spin-based systems could be used to advance superconducting qubit science. We take an initial step along this path proposing an encoded qubit approach realizable with state-of-the-art tunable Josephson junction qubits. Our results show that this design philosophy holds promise, enables microwave-free control, and offers a pathway to future qubit designs with new capabilities such as with higher fidelity or, perhaps, operation at higher temperature. The approach is also especially suited to qubits on the basis of variable super-semi junctions.
Quantum computation of the electromagnetic cross section of dielectric targets
NASA Astrophysics Data System (ADS)
Lanzagorta, Marco; Uhlmann, Jeffrey; Jitrik, Oliverio; Venegas-Andraca, Salvador E.; Wiesman, Seth
2016-05-01
The Radar Cross Section (RCS) is a crucial element for assessing target visibility and target characterization, and it depends not only on the target's geometry but also on its composition. However, the calculation of the RCS is a challenging task due to the mathematical description of electromagnetic phenomena as well as the computational resources needed. In this paper, we will introduce two ideas for the use of quantum information processing techniques to calculate the RCS of dielectric targets. The first is to use toolboxes of quantum functions to determine the geometric component of the RCS. The second idea is to use quantum walks, expressed in terms of scattering processes, to model radar absorbing materials.
Is the brain a Clifford algebra quantum computer?
NASA Astrophysics Data System (ADS)
Labunets, Valeri G.; Labunets-Rundblad, Ekaterina V.; Astola, Jaakko T.
2001-11-01
We propose a novel method to calculate invariants of colour and multicolour images. It employs an idea of classical and quantum hypercomplex numbers and combines it with the idea of classical and quantum number theoretical transforms over hypercomplex algebras, which reduce the computational complexity of the global recognition algorithm for nD k-multispectral images from O(knNn+1)to O(kNn log N) and to O(kn log N), respectively. Our hypotheses are 1) the brain of primates calculates hypercomplex-valued invariants of an image during recognizing, 2) visual systems of animals with different evolutionary history use different hypercomplex algebras. The main goal of the paper is to show that quantum Clifford algebras can be used to solve pattern recognition in multispectral environment in a natural and effective manner.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via its bifurcation with a slowly varying parameter. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing. To distinguish them, we refer to the present approach as bifurcation-based adiabatic quantum computation. Our numerical simulation results suggest that quantum superposition and quantum fluctuation work effectively to find optimal solutions.
Exploring the quantum speed limit with computer games.
Sørensen, Jens Jakob W H; Pedersen, Mads Kock; Munch, Michael; Haikka, Pinja; Jensen, Jesper Halkjær; Planke, Tilo; Andreasen, Morten Ginnerup; Gajdacz, Miroslav; Mølmer, Klaus; Lieberoth, Andreas; Sherson, Jacob F
2016-04-14
Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. 'Gamification'--the application of game elements in a non-game context--is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond. PMID:27075097
Exploring the quantum speed limit with computer games
NASA Astrophysics Data System (ADS)
Sørensen, Jens Jakob W. H.; Pedersen, Mads Kock; Munch, Michael; Haikka, Pinja; Jensen, Jesper Halkjær; Planke, Tilo; Andreasen, Morten Ginnerup; Gajdacz, Miroslav; Mølmer, Klaus; Lieberoth, Andreas; Sherson, Jacob F.
2016-04-01
Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. ‘Gamification’—the application of game elements in a non-game context—is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.
Exploring the quantum speed limit with computer games.
Sørensen, Jens Jakob W H; Pedersen, Mads Kock; Munch, Michael; Haikka, Pinja; Jensen, Jesper Halkjær; Planke, Tilo; Andreasen, Morten Ginnerup; Gajdacz, Miroslav; Mølmer, Klaus; Lieberoth, Andreas; Sherson, Jacob F
2016-04-14
Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. 'Gamification'--the application of game elements in a non-game context--is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.
Promoting Conceptual Coherence in Quantum Learning through Computational Models
NASA Astrophysics Data System (ADS)
Lee, Hee-Sun
2012-02-01
In order to explain phenomena at the quantum level, scientists use multiple representations in verbal, pictorial, mathematical, and computational forms. Conceptual coherence among these multiple representations is used as an analytical framework to describe student learning trajectories in quantum physics. A series of internet-based curriculum modules are designed to address topics in quantum mechanics, semiconductor physics, and nano-scale engineering applications. In these modules, students are engaged in inquiry-based activities situated in a highly interactive computational modeling environment. This study was conducted in an introductory level solid state physics course. Based on in-depth interviews with 13 students, methods for identifying conceptual coherence as a function of students' level of understanding are presented. Pre-post test comparisons of 20 students in the course indicate a statistically significant improvement in students' conceptual coherence of understanding quantum phenomena before and after the course, Effect Size = 1.29 SD. Additional analyses indicate that students who responded to the modules more coherently improved their conceptual coherence to a greater extent than those who did less to the modules after controlling for their course grades.
Phonon-based scalable quantum computing and sensing (Presentation Video)
NASA Astrophysics Data System (ADS)
El-Kady, Ihab
2015-04-01
Quantum computing fundamentally depends on the ability to concurrently entangle and individually address/control a large number of qubits. In general, the primary inhibitors of large scale entanglement are qubit dependent; for example inhomogeneity in quantum dots, spectral crowding brought about by proximity-based entanglement in ions, weak interactions of neutral atoms, and the fabrication tolerances in the case of Si-vacancies or SQUIDs. We propose an inherently scalable solid-state qubit system with individually addressable qubits based on the coupling of a phonon with an acceptor impurity in a high-Q Phononic Crystal resonant cavity. Due to their unique nonlinear properties, phonons enable new opportunities for quantum devices and physics. We present a phononic crystal-based platform for observing the phonon analogy of cavity quantum electrodynamics, called phonodynamics, in a solid-state system. Practical schemes involve selective placement of a single acceptor atom in the peak of the strain field in a high-Q phononic crystal cavity that enables strong coupling of the phonon modes to the energy levels of the atom. A qubit is then created by entangling a phonon at the resonance frequency of the cavity with the atomic acceptor states. We show theoretical optimization of the cavity design and excitation waveguides, along with estimated performance figures of the phoniton system. Qubits based on this half-sound, half-matter quasi-particle, may outcompete other quantum architectures in terms of combined emission rate, coherence lifetime, and fabrication demands.
Universal fault-tolerant adiabatic quantum computing with quantum dots or donors
NASA Astrophysics Data System (ADS)
Landahl, Andrew
I will present a conceptual design for an adiabatic quantum computer that can achieve arbitrarily accurate universal fault-tolerant quantum computations with a constant energy gap and nearest-neighbor interactions. This machine can run any quantum algorithm known today or discovered in the future, in principle. The key theoretical idea is adiabatic deformation of degenerate ground spaces formed by topological quantum error-correcting codes. An open problem with the design is making the four-body interactions and measurements it uses more technologically accessible. I will present some partial solutions, including one in which interactions between quantum dots or donors in a two-dimensional array can emulate the desired interactions in second-order perturbation theory. I will conclude with some open problems, including the challenge of reformulating Kitaev's gadget perturbation theory technique so that it preserves fault tolerance. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
NASA Astrophysics Data System (ADS)
Wei, Hai-Rui; Deng, Fu-Guo
2014-12-01
Quantum logic gates are the key elements in quantum computing. Here we investigate the possibility of achieving a scalable and compact quantum computing based on stationary electron-spin qubits, by using the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics. We design the compact quantum circuits for implementing universal and deterministic quantum gates for electron-spin systems, including the two-qubit CNOT gate and the three-qubit Toffoli gate. They are compact and economic, and they do not require additional electron-spin qubits. Moreover, our devices have good scalability and are attractive as they both are based on solid-state quantum systems and the qubits are stationary. They are feasible with the current experimental technology, and both high fidelity and high efficiency can be achieved when the ratio of the side leakage to the cavity decay is low.
Wei, Hai-Rui; Deng, Fu-Guo
2014-12-18
Quantum logic gates are the key elements in quantum computing. Here we investigate the possibility of achieving a scalable and compact quantum computing based on stationary electron-spin qubits, by using the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics. We design the compact quantum circuits for implementing universal and deterministic quantum gates for electron-spin systems, including the two-qubit CNOT gate and the three-qubit Toffoli gate. They are compact and economic, and they do not require additional electron-spin qubits. Moreover, our devices have good scalability and are attractive as they both are based on solid-state quantum systems and the qubits are stationary. They are feasible with the current experimental technology, and both high fidelity and high efficiency can be achieved when the ratio of the side leakage to the cavity decay is low.
Wei, Hai-Rui; Deng, Fu-Guo
2014-01-01
Quantum logic gates are the key elements in quantum computing. Here we investigate the possibility of achieving a scalable and compact quantum computing based on stationary electron-spin qubits, by using the giant optical circular birefringence induced by quantum-dot spins in double-sided optical microcavities as a result of cavity quantum electrodynamics. We design the compact quantum circuits for implementing universal and deterministic quantum gates for electron-spin systems, including the two-qubit CNOT gate and the three-qubit Toffoli gate. They are compact and economic, and they do not require additional electron-spin qubits. Moreover, our devices have good scalability and are attractive as they both are based on solid-state quantum systems and the qubits are stationary. They are feasible with the current experimental technology, and both high fidelity and high efficiency can be achieved when the ratio of the side leakage to the cavity decay is low. PMID:25518899
SYMBMAT: Symbolic computation of quantum transition matrix elements
NASA Astrophysics Data System (ADS)
Ciappina, M. F.; Kirchner, T.
2012-08-01
We have developed a set of Mathematica notebooks to compute symbolically quantum transition matrices relevant for atomic ionization processes. The utilization of a symbolic language allows us to obtain analytical expressions for the transition matrix elements required in charged-particle and laser induced ionization of atoms. Additionally, by using a few simple commands, it is possible to export these symbolic expressions to standard programming languages, such as Fortran or C, for the subsequent computation of differential cross sections or other observables. One of the main drawbacks in the calculation of transition matrices is the tedious algebraic work required when initial states other than the simple hydrogenic 1s state need to be considered. Using these notebooks the work is dramatically reduced and it is possible to generate exact expressions for a large set of bound states. We present explicit examples of atomic collisions (in First Born Approximation and Distorted Wave Theory) and laser-matter interactions (within the Dipole and Strong Field Approximations and different gauges) using both hydrogenic wavefunctions and Slater-Type Orbitals with arbitrary nlm quantum numbers as initial states. Catalogue identifier: AEMI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 71 628 No. of bytes in distributed program, including test data, etc.: 444 195 Distribution format: tar.gz Programming language: Mathematica Computer: Single machines using Linux or Windows (with cores with any clock speed, cache memory and bits in a word) Operating system: Any OS that supports Mathematica. The notebooks have been tested under Windows and Linux and with versions 6.x, 7.x and 8.x Classification: 2.6 Nature of problem
Numerical simulation of NQR/NMR: Applications in quantum computing.
Possa, Denimar; Gaudio, Anderson C; Freitas, Jair C C
2011-04-01
A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php.
Secure multiparty computation with a dishonest majority via quantum means
Loukopoulos, Klearchos; Browne, Daniel E.
2010-06-15
We introduce a scheme for secure multiparty computation utilizing the quantum correlations of entangled states. First we present a scheme for two-party computation, exploiting the correlations of a Greenberger-Horne-Zeilinger state to provide, with the help of a third party, a near-private computation scheme. We then present a variation of this scheme which is passively secure with threshold t=2, in other words, remaining secure when pairs of players conspire together provided they faithfully follow the protocol. Furthermore, we show that the passively secure variant can be modified to be secure when cheating parties are allowed to deviate from the protocol. We show that this can be generalized to computations of n-party polynomials of degree 2 with a threshold of n-1. The threshold achieved is significantly higher than the best known classical threshold, which satisfies the bound t
Secure multiparty computation with a dishonest majority via quantum means
NASA Astrophysics Data System (ADS)
Loukopoulos, Klearchos; Browne, Daniel E.
2010-06-01
We introduce a scheme for secure multiparty computation utilizing the quantum correlations of entangled states. First we present a scheme for two-party computation, exploiting the correlations of a Greenberger-Horne-Zeilinger state to provide, with the help of a third party, a near-private computation scheme. We then present a variation of this scheme which is passively secure with threshold t=2, in other words, remaining secure when pairs of players conspire together provided they faithfully follow the protocol. Furthermore, we show that the passively secure variant can be modified to be secure when cheating parties are allowed to deviate from the protocol. We show that this can be generalized to computations of n-party polynomials of degree 2 with a threshold of n-1. The threshold achieved is significantly higher than the best known classical threshold, which satisfies the bound t
Experimental detection of nonclassical correlations in mixed-state quantum computation
Passante, G.; Moussa, O.; Trottier, D. A.; Laflamme, R.
2011-10-15
We report on an experiment to detect nonclassical correlations in a highly mixed state. The correlations are characterized by the quantum discord and are observed using four qubits in a liquid-state nuclear magnetic resonance quantum information processor. The state analyzed is the output of a DQC1 computation, whose input is a single quantum bit accompanied by n maximally mixed qubits. This model of computation outperforms the best known classical algorithms and, although it contains vanishing entanglement, it is known to have quantum correlations characterized by the quantum discord. This experiment detects nonvanishing quantum discord, ensuring the existence of nonclassical correlations as measured by the quantum discord.
Quantum computation in brain microtubules: Decoherence and biological feasibility
NASA Astrophysics Data System (ADS)
Hagan, S.; Hameroff, S. R.; Tuszyński, J. A.
2002-06-01
The Penrose-Hameroff orchestrated objective reduction (orch. OR) model assigns a cognitive role to quantum computations in microtubules within the neurons of the brain. Despite an apparently ``warm, wet, and noisy'' intracellular milieu, the proposal suggests that microtubules avoid environmental decoherence long enough to reach threshold for ``self-collapse'' (objective reduction) by a quantum gravity mechanism put forth by Penrose. The model has been criticized as regards the issue of environmental decoherence, and a recent report by Tegmark finds that microtubules can maintain quantum coherence for only 10-13 s, far too short to be neurophysiologically relevant. Here, we critically examine the decoherence mechanisms likely to dominate in a biological setting and find that (1) Tegmark's commentary is not aimed at an existing model in the literature but rather at a hybrid that replaces the superposed protein conformations of the orch. OR theory with a soliton in superposition along the microtubule; (2) recalculation after correcting for differences between the model on which Tegmark bases his calculations and the orch. OR model (superposition separation, charge vs dipole, dielectric constant) lengthens the decoherence time to 10-5-10-4 s (3) decoherence times on this order invalidate the assumptions of the derivation and determine the approximation regime considered by Tegmark to be inappropriate to the orch. OR superposition; (4) Tegmark's formulation yields decoherence times that increase with temperature contrary to well-established physical intuitions and the observed behavior of quantum coherent states; (5) incoherent metabolic energy supplied to the collective dynamics ordering water in the vicinity of microtubules at a rate exceeding that of decoherence can counter decoherence effects (in the same way that lasers avoid decoherence at room temperature); (6) microtubules are surrounded by a Debye layer of counterions, which can screen thermal fluctuations
SYMBMAT: Symbolic computation of quantum transition matrix elements
NASA Astrophysics Data System (ADS)
Ciappina, M. F.; Kirchner, T.
2012-08-01
We have developed a set of Mathematica notebooks to compute symbolically quantum transition matrices relevant for atomic ionization processes. The utilization of a symbolic language allows us to obtain analytical expressions for the transition matrix elements required in charged-particle and laser induced ionization of atoms. Additionally, by using a few simple commands, it is possible to export these symbolic expressions to standard programming languages, such as Fortran or C, for the subsequent computation of differential cross sections or other observables. One of the main drawbacks in the calculation of transition matrices is the tedious algebraic work required when initial states other than the simple hydrogenic 1s state need to be considered. Using these notebooks the work is dramatically reduced and it is possible to generate exact expressions for a large set of bound states. We present explicit examples of atomic collisions (in First Born Approximation and Distorted Wave Theory) and laser-matter interactions (within the Dipole and Strong Field Approximations and different gauges) using both hydrogenic wavefunctions and Slater-Type Orbitals with arbitrary nlm quantum numbers as initial states. Catalogue identifier: AEMI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 71 628 No. of bytes in distributed program, including test data, etc.: 444 195 Distribution format: tar.gz Programming language: Mathematica Computer: Single machines using Linux or Windows (with cores with any clock speed, cache memory and bits in a word) Operating system: Any OS that supports Mathematica. The notebooks have been tested under Windows and Linux and with versions 6.x, 7.x and 8.x Classification: 2.6 Nature of problem
Multilevel distillation of magic states for quantum computing
NASA Astrophysics Data System (ADS)
Jones, Cody
2013-03-01
We develop a procedure for distilling magic states used in universal quantum computing which requires substantially fewer resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes with a transversal Hadamard operation which can distill the eigenstate of the Hadamard operator. A crucial result of this design is that low-fidelity magic states can be consumed to purify high-fidelity magic states to even higher fidelity, which we call ``multilevel distillation.'' We show numerically that there exist multilevel protocols such that the average number of magic states consumed to distill from error rate ɛin = 0 . 01 to ɛout in the range 10-5 to 10-40 is about 14log10 (1 /ɛout) - 40 ; the efficiency of multilevel distillation dominates all other reported protocols when distilling Hadamard magic states from initial infidelity 0.01 to any final infidelity below 10-7. These methods are an important advance for magic-state distillation circuits in high-performance quantum computing.
Universal quantum computation with ordered spin-chain networks
NASA Astrophysics Data System (ADS)
Tserkovnyak, Yaroslav; Loss, Daniel
2011-09-01
It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently developed topological Majorana-based proposals. We show how to realize the single-qubit Hadamard, phase, and π/8 gates as well as the two-qubit controlled-not (cnot) gate, which together form a fault-tolerant universal set of quantum gates. The gates are implemented by judiciously controlling Ising exchange and magnetic fields along a network of spin chains, with each individual qubit furnished by a spin-chain segment. A subset of single-qubit operations is geometric in nature, relying on control of anisotropy of spin interactions rather than their strength. We contrast topological aspects of the anisotropic spin-chain networks to those of p-wave superconducting wires discussed in the literature.
Fast and robust quantum computation with ionic Wigner crystals
Baltrusch, J. D.; Negretti, A.; Taylor, J. M.; Calarco, T.
2011-04-15
We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze the situation in which the cyclotron ({omega}{sub c}) and the crystal rotation ({omega}{sub r}) frequencies do not fulfill the condition {omega}{sub c}=2{omega}{sub r}. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme.
Quantum computer networks with the orbital angular momentum of light
NASA Astrophysics Data System (ADS)
Garcia-Escartin, Juan Carlos; Chamorro-Posada, Pedro
2012-09-01
Inside computer networks, different information processing tasks are necessary to deliver the user data efficiently. This processing can also be done in the quantum domain. We present simple optical quantum networks where the orbital angular momentum (OAM) of a single photon is used as an ancillary degree of freedom which controls decisions at the network level. Linear optical elements are enough to provide important network primitives such as multiplexing and routing. First we show how to build a simple multiplexer and demultiplexer which combine photonic qubits and separate them again at the receiver. We also give two different self-routing networks where the OAM of an input photon is enough to make it find its desired destination.
Majorana Fermion Surface Code for Universal Quantum Computation
NASA Astrophysics Data System (ADS)
Vijay, Sagar; Hsieh, Tim; Fu, Liang
We introduce an exactly solvable model of interacting Majorana fermions realizing Z2 topological order with a Z2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid state systems, including topological insulators, nanowires or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.
Majorana Fermion Surface Code for Universal Quantum Computation
NASA Astrophysics Data System (ADS)
Vijay, Sagar; Hsieh, Timothy H.; Fu, Liang
2015-10-01
We introduce an exactly solvable model of interacting Majorana fermions realizing Z2 topological order with a Z2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s -wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.
Percolation, renormalization, and quantum computing with nondeterministic gates.
Kieling, K; Rudolph, T; Eisert, J
2007-09-28
We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of nondeterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single-qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.
Multilevel distillation of magic states for quantum computing
NASA Astrophysics Data System (ADS)
Jones, Cody
2013-04-01
We develop a procedure for distilling magic states used in universal quantum computing that requires substantially fewer initial resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes that possess a transversal Hadamard operation, enabling each of these codes to distill the eigenstate of the Hadamard operator. A crucial result of this design is that low-fidelity magic states can be consumed to purify other high-fidelity magic states to even higher fidelity, which we call multilevel distillation. When distilling in the asymptotic regime of infidelity ɛ→0 for each input magic state, the number of input magic states consumed on average to yield an output state with infidelity O(ɛ2r) approaches 2r+1, which comes close to saturating the conjectured bound in another investigation [Bravyi and Haah, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.86.052329 86, 052329 (2012)]. We show numerically that there exist multilevel protocols such that the average number of magic states consumed to distill from error rate ɛin=0.01 to ɛout in the range 10-5-10-40 is about 14log10(1/ɛout)-40; the efficiency of multilevel distillation dominates all other reported protocols when distilling Hadamard magic states from initial infidelity 0.01 to any final infidelity below 10-7. These methods are an important advance for magic-state distillation circuits in high-performance quantum computing and provide insight into the limitations of nearly resource-optimal quantum error correction.
An Atomic Abacus: Trapped ion quantum computing experiments at NIST
NASA Astrophysics Data System (ADS)
Demarco, Brian
2003-03-01
Trapped atomic ions are an ideal system for exploring quantum information science because deterministic state preparation and efficient state detection are possible and coherent manipulation of atomic systems is relatively advanced. In our experiment, a few singly charged Be ions are confined by static and radio-frequency electric fields in a micro-machined linear Paul trap. The internal and motional states of the ions are coherently manipulated using applied laser light. Our current work focuses on demonstrating the necessary ingredients to produce a scalable quantum computing scheme and on simplifying and improving quantum logic gates. I will speak about a new set of experiments that was made possible by recent improvements in trap technology. A novel trap with multiple trapping regions was used to demonstrate the first steps towards a fully scalable quantum computing scheme. Single ions were ``shuttled" between trapping regions without disturbing the ion's motional and internal state, and two ions were separated from a single to two different trapping zones. Improvements in the trap manufacturing process has led to a reduction of nearly two orders of magnitude in the ion's motional heating rate, making possible two new improved logic gates. The first gate utilizes the wave-packet nature of the ions to tune the laser-atom interaction and achieve a controlled-NOT gate between a single ion's spin and motional states. The second, a two-ion phase gate, uses phase-space dynamics to produce a state-sensitive geometric phase. I will end with a quick look at experiments using a Mg ion to sympathetically cool a simultaneously trapped Be ion and a glimpse of the next generation of ions traps currently under construction.
Two results in topology, motivated by quantum computation
NASA Astrophysics Data System (ADS)
Alagic, Gorjan
2015-03-01
The field of quantum computation is built on the foundation of physics, mathematics, and computer science. While it has taken much from these fields, there are also interesting examples where it has given back. I will discuss two new results of this kind. In both cases, we use very basic ideas from quantum computation to prove an interesting fact about low-dimensional topology. First, we use the Solovay-Kitaev universality theorem with exponential precision to give a simple proof of the #P-hardness of certain 3-manifold invariants. We then apply this result to show the existence of rather exotic 3-manifold diagrams. Second, we show a relationship between the distinguishing power of a link invariant, and the entangling power of the linear operator associated to braiding. More precisely, we show that link invariants derived from non-entangling solutions to the Yang-Baxter equation are trivial. The former is joint work with Catharine Lo (Caltech), and the latter is joint work with Stephen Jordan and Michael Jarett (UMD).
Schedule path optimization for adiabatic quantum computing and optimization
NASA Astrophysics Data System (ADS)
Zeng, Lishan; Zhang, Jun; Sarovar, Mohan
2016-04-01
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are probabilistic in nature and the minimum gap between the ground state and first excited state of the system during evolution is a major factor in determining the success probability. In this work we investigate a strategy for increasing the minimum gap and success probability by introducing intermediate Hamiltonians that modify the evolution path between initial and final Hamiltonians. We focus on an optimization problem relevant to recent hardware implementations and present numerical evidence for the existence of a purely local intermediate Hamiltonian that achieve the optimum performance in terms of pushing the minimum gap to one of the end points of the evolution. As a part of this study we develop a convex optimization formulation of the search for optimal adiabatic schedules that makes this computation more tractable, and which may be of independent interest. We further study the effectiveness of random intermediate Hamiltonians on the minimum gap and success probability, and empirically find that random Hamiltonians have a significant probability of increasing the success probability, but only by a modest amount.
Holism, ambiguity and approximation in the logics of quantum computation: a survey
NASA Astrophysics Data System (ADS)
Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto
2011-01-01
Quantum computation has suggested some new forms of quantum logic (called quantum computational logics), where meanings of sentences are identified with quantum information quantities. This provides a mathematical formalism for an abstract theory of meanings that can be applied to investigate different kinds of semantic phenomena (in social sciences, in medicine, in natural languages and in the languages of art), where both ambiguity and holism play an essential role.
Arbitrary precision composite pulses for NMR quantum computing.
Alway, William G; Jones, Jonathan A
2007-11-01
We discuss the implementation of arbitrary precision composite pulses developed using the methods of Brown et al. [K.R. Brown, A.W. Harrow, I.L. Chuang, Arbitrarily accurate composite pulse sequences, Phys. Rev. A 70 (2004) 052318]. We give explicit results for pulse sequences designed to tackle both the simple case of pulse length errors and the more complex case of off-resonance errors. The results are developed in the context of NMR quantum computation, but could be applied more widely.
Repeat-until-success linear optics distributed quantum computing.
Lim, Yuan Liang; Beige, Almut; Kwek, Leong Chuan
2005-07-15
We demonstrate the possibility to perform distributed quantum computing using only single-photon sources (atom-cavity-like systems), linear optics, and photon detectors. The qubits are encoded in stable ground states of the sources. To implement a universal two-qubit gate, two photons should be generated simultaneously and pass through a linear optics network, where a measurement is performed on them. Gate operations can be repeated until a success is heralded without destroying the qubits at any stage of the operation. In contrast with other schemes, this does not require explicit qubit-qubit interactions, a priori entangled ancillas, nor the feeding of photons into photon sources.
Topological quantum computation of the Dold-Thom functor
NASA Astrophysics Data System (ADS)
Ospina, Juan
2014-05-01
A possible topological quantum computation of the Dold-Thom functor is presented. The method that will be used is the following: a) Certain 1+1-topological quantum field theories valued in symmetric bimonoidal categories are converted into stable homotopical data, using a machinery recently introduced by Elmendorf and Mandell; b) we exploit, in this framework, two recent results (independent of each other) on refinements of Khovanov homology: our refinement into a module over the connective k-theory spectrum and a stronger result by Lipshitz and Sarkar refining Khovanov homology into a stable homotopy type; c) starting from the Khovanov homotopy the Dold-Thom functor is constructed; d) the full construction is formulated as a topological quantum algorithm. It is conjectured that the Jones polynomial can be described as the analytical index of certain Dirac operator defined in the context of the Khovanov homotopy using the Dold-Thom functor. As a line for future research is interesting to study the corresponding supersymmetric model for which the Khovanov-Dirac operator plays the role of a supercharge.
Quantum transport modelling of silicon nanobeams using heterogeneous computing scheme
NASA Astrophysics Data System (ADS)
Harb, M.; Michaud-Rioux, V.; Zhu, Y.; Liu, L.; Zhang, L.; Guo, H.
2016-03-01
We report the development of a powerful method for quantum transport calculations of nanowire/nanobeam structures with large cross sectional area. Our approach to quantum transport is based on Green's functions and tight-binding potentials. A linear algebraic formulation allows us to harness the massively parallel nature of Graphics Processing Units (GPUs) and our implementation is based on a heterogeneous parallel computing scheme with traditional processors and GPUs working together. Using our software tool, the electronic and quantum transport properties of silicon nanobeams with a realistic cross sectional area of ˜22.7 nm2 and a length of ˜81.5 nm—comprising 105 000 Si atoms and 24 000 passivating H atoms in the scattering region—are investigated. The method also allows us to perform significant averaging over impurity configurations—all possible configurations were considered in the case of single impurities. Finally, the effect of the position and number of vacancy defects on the transport properties was considered. It is found that the configurations with the vacancies lying closer to the local density of states (LDOS) maxima have lower transmission functions than the configurations with the vacancies located at LDOS minima or far away from LDOS maxima, suggesting both a qualitative method to tune or estimate optimal impurity configurations as well as a physical picture that accounts for device variability. Finally, we provide performance benchmarks for structures as large as ˜42.5 nm2 cross section and ˜81.5 nm length.
Computing the rates of measurement-induced quantum jumps
NASA Astrophysics Data System (ADS)
Bauer, Michel; Bernard, Denis; Tilloy, Antoine
2015-06-01
Small quantum systems can now be continuously monitored experimentally which allows for the reconstruction of quantum trajectories. A peculiar feature of these trajectories is the emergence of jumps between the eigenstates of the observable which is measured. Using the stochastic master equation (SME) formalism for continuous quantum measurements, we show that the density matrix of a system indeed shows a jumpy behaviour when it is subjected to a tight measurement (even if the noise in the SME is Gaussian). We are able to compute the jump rates analytically for any system evolution, i.e. any Lindbladian, and we illustrate how our general recipe can be applied to two simple examples. We then discuss the mathematical, foundational and practical applications of our results. The analysis we present is based on a study of the strong noise limit of a class of stochastic differential equations (the SME) and as such the method may be applicable to other physical situations in which a strong noise limit plays a role.
P/NP, and the quantum field computer.
Freedman, M H
1998-01-01
The central problem in computer science is the conjecture that two complexity classes, P (polynomial time) and NP (nondeterministic polynomial time-roughly those decision problems for which a proposed solution can be checked in polynomial time), are distinct in the standard Turing model of computation: P not equal NP. As a generality, we propose that each physical theory supports computational models whose power is limited by the physical theory. It is well known that classical physics supports a multitude of implementation of the Turing machine. Non-Abelian topological quantum field theories exhibit the mathematical features necessary to support a model capable of solving all #P problems, a computationally intractable class, in polynomial time. Specifically, Witten [Witten, E. (1989) Commun. Math. Phys. 121, 351-391] has identified expectation values in a certain SU(2)-field theory with values of the Jones polynomial [Jones, V. (1985) Bull. Am. Math. Soc. 12, 103-111] that are #P-hard [Jaeger, F., Vertigen, D. & Welsh, D. (1990) Math. Proc. Comb. Philos. Soc. 108, 35-53]. This suggests that some physical system whose effective Lagrangian contains a non-Abelian topological term might be manipulated to serve as an analog computer capable of solving NP or even #P-hard problems in polynomial time. Defining such a system and addressing the accuracy issues inherent in preparation and measurement is a major unsolved problem.
P/NP, and the quantum field computer
Freedman, Michael H.
1998-01-01
The central problem in computer science is the conjecture that two complexity classes, P (polynomial time) and NP (nondeterministic polynomial time—roughly those decision problems for which a proposed solution can be checked in polynomial time), are distinct in the standard Turing model of computation: P ≠ NP. As a generality, we propose that each physical theory supports computational models whose power is limited by the physical theory. It is well known that classical physics supports a multitude of implementation of the Turing machine. Non-Abelian topological quantum field theories exhibit the mathematical features necessary to support a model capable of solving all ⧣P problems, a computationally intractable class, in polynomial time. Specifically, Witten [Witten, E. (1989) Commun. Math. Phys. 121, 351–391] has identified expectation values in a certain SU(2)-field theory with values of the Jones polynomial [Jones, V. (1985) Bull. Am. Math. Soc. 12, 103–111] that are ⧣P-hard [Jaeger, F., Vertigen, D. & Welsh, D. (1990) Math. Proc. Comb. Philos. Soc. 108, 35–53]. This suggests that some physical system whose effective Lagrangian contains a non-Abelian topological term might be manipulated to serve as an analog computer capable of solving NP or even ⧣P-hard problems in polynomial time. Defining such a system and addressing the accuracy issues inherent in preparation and measurement is a major unsolved problem. PMID:9419335
NASA Astrophysics Data System (ADS)
Song, Xue-Ke; Zhang, Hao; Ai, Qing; Qiu, Jing; Deng, Fu-Guo
2016-02-01
By using transitionless quantum driving algorithm (TQDA), we present an efficient scheme for the shortcuts to the holonomic quantum computation (HQC). It works in decoherence-free subspace (DFS) and the adiabatic process can be speeded up in the shortest possible time. More interestingly, we give a physical implementation for our shortcuts to HQC with nitrogen-vacancy centers in diamonds dispersively coupled to a whispering-gallery mode microsphere cavity. It can be efficiently realized by controlling appropriately the frequencies of the external laser pulses. Also, our scheme has good scalability with more qubits. Different from previous works, we first use TQDA to realize a universal HQC in DFS, including not only two noncommuting accelerated single-qubit holonomic gates but also a accelerated two-qubit holonomic controlled-phase gate, which provides the necessary shortcuts for the complete set of gates required for universal quantum computation. Moreover, our experimentally realizable shortcuts require only two-body interactions, not four-body ones, and they work in the dispersive regime, which relax greatly the difficulty of their physical implementation in experiment. Our numerical calculations show that the present scheme is robust against decoherence with current experimental parameters.
Communication: Spin-free quantum computational simulations and symmetry adapted states.
Whitfield, James Daniel
2013-07-14
The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point, many techniques from classical simulations must be imported into the quantum domain. In this article, we consider the applications of symmetry in the context of quantum simulation. Building upon well established machinery, we propose a form of first quantized simulation that only requires the spatial part of the wave function, thereby allowing spin-free quantum computational simulations. We go further and discuss the preparation of N-body states with specified symmetries based on projection techniques. We consider two simple examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas. The methods here are the first to explicitly deal with preparing N-body symmetry-adapted states and open the door for future investigations into group theory, chemistry, and quantum simulation. PMID:23862919
Communication: Spin-free quantum computational simulations and symmetry adapted states.
Whitfield, James Daniel
2013-07-14
The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point, many techniques from classical simulations must be imported into the quantum domain. In this article, we consider the applications of symmetry in the context of quantum simulation. Building upon well established machinery, we propose a form of first quantized simulation that only requires the spatial part of the wave function, thereby allowing spin-free quantum computational simulations. We go further and discuss the preparation of N-body states with specified symmetries based on projection techniques. We consider two simple examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas. The methods here are the first to explicitly deal with preparing N-body symmetry-adapted states and open the door for future investigations into group theory, chemistry, and quantum simulation.
Quantum Error Correction and the Future of Solid State Quantum Computing
NASA Astrophysics Data System (ADS)
Divincenzo, David
Quantum error correction (QEC) theory has provided a very challenging but well defined goal for the further development of solid state qubit systems: achieve high enough fidelity so that fault-tolerant, error-corrected quantum computation in networks of these qubits becomes possible. I will begin by touching on some historical points: initial work on QEC is actually more than 20 years old, and the landmark work of Kitaev in 1996 which established 2D lattice structures as a suitable host for effective error correction, has its roots in theoretical work in many-body theory from Wegner in the 1970s. I will give some perspective on current developments in the implementation of small fragments of the surface code. The surface-code concept has driven a number of distinct requirements, beyond the reduction of error rates below the 1% range, that are actively considered as experiments are scaled beyond the 10-qubit level. Support of JARA FIT is acknolwedged.
Universal Quantum Computation From 2/3 Bilayer Quantum Hall States
NASA Astrophysics Data System (ADS)
Vaezi, Abolhassan; Barkeshli, Maissam
2015-03-01
In this talk, I consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer, in the presence of interlayer tunneling. I show that interlayer tunneling can drive a continuous phase transition to an exotic non-Abelian state that contains the famous ``Fibonacci anyon,'' whose non-Abelian statistics is powerful enough for universal topological quantum computation. The analysis that I will present towards this result rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. The charge gap remains open at the phase transition while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν = 2 / 3 in bilayers, as past experiments may not have definitively ruled them out.
NASA Astrophysics Data System (ADS)
Lidar, Daniel A.; Brun, Todd A.
2013-09-01
Prologue; Preface; Part I. Background: 1. Introduction to decoherence and noise in open quantum systems Daniel Lidar and Todd Brun; 2. Introduction to quantum error correction Dave Bacon; 3. Introduction to decoherence-free subspaces and noiseless subsystems Daniel Lidar; 4. Introduction to quantum dynamical decoupling Lorenza Viola; 5. Introduction to quantum fault tolerance Panos Aliferis; Part II. Generalized Approaches to Quantum Error Correction: 6. Operator quantum error correction David Kribs and David Poulin; 7. Entanglement-assisted quantum error-correcting codes Todd Brun and Min-Hsiu Hsieh; 8. Continuous-time quantum error correction Ognyan Oreshkov; Part III. Advanced Quantum Codes: 9. Quantum convolutional codes Mark Wilde; 10. Non-additive quantum codes Markus Grassl and Martin Rötteler; 11. Iterative quantum coding systems David Poulin; 12. Algebraic quantum coding theory Andreas Klappenecker; 13. Optimization-based quantum error correction Andrew Fletcher; Part IV. Advanced Dynamical Decoupling: 14. High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu; 15. Combinatorial approaches to dynamical decoupling Martin Rötteler and Pawel Wocjan; Part V. Alternative Quantum Computation Approaches: 16. Holonomic quantum computation Paolo Zanardi; 17. Fault tolerance for holonomic quantum computation Ognyan Oreshkov, Todd Brun and Daniel Lidar; 18. Fault tolerant measurement-based quantum computing Debbie Leung; Part VI. Topological Methods: 19. Topological codes Héctor Bombín; 20. Fault tolerant topological cluster state quantum computing Austin Fowler and Kovid Goyal; Part VII. Applications and Implementations: 21. Experimental quantum error correction Dave Bacon; 22. Experimental dynamical decoupling Lorenza Viola; 23. Architectures Jacob Taylor; 24. Error correction in quantum communication Mark Wilde; Part VIII. Critical Evaluation of Fault Tolerance: 25. Hamiltonian methods in QEC and fault tolerance Eduardo Novais, Eduardo Mucciolo and
Topological and geometrical quantum computation in cohesive Khovanov homotopy type theory
NASA Astrophysics Data System (ADS)
Ospina, Juan
2015-05-01
The recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called "open-closed stringy topological quantum computer" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided.
Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability
NASA Astrophysics Data System (ADS)
Nearing, G. S.; Halem, M.; Chapman, D. R.; Pelissier, C. S.
2014-12-01
Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixed-precision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC's solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.
Adame, J.; Warzel, S.
2015-11-15
In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.
Computer-automated tuning of semiconductor double quantum dots into the single-electron regime
NASA Astrophysics Data System (ADS)
Baart, T. A.; Eendebak, P. T.; Reichl, C.; Wegscheider, W.; Vandersypen, L. M. K.
2016-05-01
We report the computer-automated tuning of gate-defined semiconductor double quantum dots in GaAs heterostructures. We benchmark the algorithm by creating three double quantum dots inside a linear array of four quantum dots. The algorithm sets the correct gate voltages for all the gates to tune the double quantum dots into the single-electron regime. The algorithm only requires (1) prior knowledge of the gate design and (2) the pinch-off value of the single gate T that is shared by all the quantum dots. This work significantly alleviates the user effort required to tune multiple quantum dot devices.
An architecture for quantum computation with magnetically trapped Holmium atoms
NASA Astrophysics Data System (ADS)
Saffman, Mark; Hostetter, James; Booth, Donald; Collett, Jeffrey
2016-05-01
Outstanding challenges for scalable neutral atom quantum computation include correction of atom loss due to collisions with untrapped background gas, reduction of crosstalk during state preparation and measurement due to scattering of near resonant light, and the need to improve quantum gate fidelity. We present a scalable architecture based on loading single Holmium atoms into an array of Ioffe-Pritchard traps. The traps are formed by grids of superconducting wires giving a trap array with 40 μm period, suitable for entanglement via long range Rydberg gates. The states | F = 5 , M = 5 > and | F = 7 , M = 7 > provide a magic trapping condition at a low field of 3.5 G for long coherence time qubit encoding. The F = 11 level will be used for state preparation and measurement. The availability of different states for encoding, gate operations, and measurement, spectroscopically isolates the different operations and will prevent crosstalk to neighboring qubits. Operation in a cryogenic environment with ultra low pressure will increase atom lifetime and Rydberg gate fidelity by reduction of blackbody induced Rydberg decay. We will present a complete description of the architecture including estimates of achievable performance metrics. Work supported by NSF award PHY-1404357.
Estimating Turaev-Viro three-manifold invariants is universal for quantum computation
Alagic, Gorjan; Reichardt, Ben W.; Jordan, Stephen P.; Koenig, Robert
2010-10-15
The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-dimensional topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a relation between the task of distinguishing nonhomeomorphic 3-manifolds and the power of a general quantum computer.
Sumner, Isaiah; Iyengar, Srinivasan S
2007-10-18
We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.
Enhanced fault-tolerant quantum computing in d-level systems.
Campbell, Earl T
2014-12-01
Error-correcting codes protect quantum information and form the basis of fault-tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transversal non-Clifford gate. Codes with the desired property are presented for d-level qudit systems with prime d. The codes use n=d-1 qudits and can detect up to ∼d/3 errors. We quantify the performance of these codes for one approach to quantum computation known as magic-state distillation. Unlike prior work, we find performance is always enhanced by increasing d.
Differential geometric treewidth estimation in adiabatic quantum computation
NASA Astrophysics Data System (ADS)
Wang, Chi; Jonckheere, Edmond; Brun, Todd
2016-07-01
The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.
Spin-bus concept of spin quantum computing
Mehring, Michael; Mende, Jens
2006-05-15
We present a spin-bus concept of quantum computing where an electron spin S=1/2 acts as a bus qubit connected to a finite number N of nuclear spins I=1/2 serving as client qubits. Spin-bus clusters are considered as local processing units and may be interconnected with other spin-bus clusters via electron-electron coupling in a scaled up version. Here we lay the ground for the basic functional unit with long qubit registers, provide the theory and experimental verification of correlated qubit states, and demonstrate the Deutsch algorithm. Experiments were performed on a qubyte plus one nuclear spin in a solid state system.
Fault tolerance in parity-state linear optical quantum computing
Hayes, A. J. F.; Ralph, T. C.; Haselgrove, H. L.; Gilchrist, Alexei
2010-08-15
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest level of code concatenation in order to efficiently correct errors arising from the inherent nondeterminism of two-qubit linear-optical gates. When combined with teleported error-correction (using either a Steane or Golay code) at higher levels of concatenation, the parity-state scheme is found to achieve a saving of approximately three orders of magnitude in resources when compared to the cluster state scheme, at a cost of a somewhat reduced noise threshold.
High-fidelity linear optical quantum computing with polarization encoding
Spedalieri, Federico M.; Lee, Hwang; Dowling, Jonathan P.
2006-01-15
We show that the KLM scheme [Knill, Laflamme, and Milburn, Nature 409, 46 (2001)] can be implemented using polarization encoding, thus reducing the number of path modes required by half. One of the main advantages of this new implementation is that it naturally incorporates a loss detection mechanism that makes the probability of a gate introducing a non-detected error, when non-ideal detectors are considered, dependent only on the detector dark-count rate and independent of its efficiency. Since very low dark-count rate detectors are currently available, a high-fidelity gate (probability of error of order 10{sup -6} conditional on the gate being successful) can be implemented using polarization encoding. The detector efficiency determines the overall success probability of the gate but does not affect its fidelity. This can be applied to the efficient construction of optical cluster states with very high fidelity for quantum computing.
Differential geometric treewidth estimation in adiabatic quantum computation
NASA Astrophysics Data System (ADS)
Wang, Chi; Jonckheere, Edmond; Brun, Todd
2016-10-01
The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.
Single ion implantation for solid state quantum computer development
Schenkel, Thomas; Meijers, Jan; Persaud, Arun; McDonald, Joseph W.; Holder, Joseph P.; Schneider, Dieter H.
2001-12-18
Several solid state quantum computer schemes are based on the manipulation of electron and nuclear spins of single donor atoms in a solid matrix. The fabrication of qubit arrays requires the placement of individual atoms with nanometer precision and high efficiency. In this article we describe first results from low dose, low energy implantations and our development of a low energy (<10 keV), single ion implantation scheme for {sup 31}P{sup q+} ions. When {sup 31}P{sup q+} ions impinge on a wafer surface, their potential energy (9.3 keV for P{sup 15+}) is released, and about 20 secondary electrons are emitted. The emission of multiple secondary electrons allows detection of each ion impact with 100% efficiency. The beam spot on target is controlled by beam focusing and collimation. Exactly one ion is implanted into a selected area avoiding a Poissonian distribution of implanted ions.
Universal holonomic quantum computing with cat-codes
NASA Astrophysics Data System (ADS)
Albert, Victor V.; Shu, Chi; Krastanov, Stefan; Shen, Chao; Liu, Ren-Bao; Yang, Zhen-Biao; Schoelkopf, Robert J.; Mirrahimi, Mazyar; Devoret, Michel H.; Jiang, Liang
2016-05-01
Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of ``colliding'' two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems which support tunable nonlinearities, such as trapped ions and circuit QED.
Distillation of nonstabilizer states for universal quantum computation
NASA Astrophysics Data System (ADS)
Duclos-Cianci, Guillaume; Svore, Krysta M.
2013-10-01
Magic-state distillation is a fundamental technique for realizing fault-tolerant universal quantum computing and produces high-fidelity Clifford eigenstates, called magic states, which can be used to implement the non-Clifford π/8 gate. We propose an efficient protocol for distilling other nonstabilizer states that requires only Clifford operations, measurement, and magic states. One critical application of our protocol is efficiently and fault-tolerantly implementing arbitrary, non-Clifford, single-qubit rotations in, on average, constant online circuit depth and polylogarithmic (in precision) offline resource cost, resulting in significant improvements over state-of-the-art decomposition techniques. Finally, we show that our protocol is robust to noise in the resource states.
Two dimensional electron systems for solid state quantum computation
NASA Astrophysics Data System (ADS)
Mondal, Sumit
Two dimensional electron systems based on GaAs/AlGaAs heterostructures are extremely useful in various scientific investigations of recent times including the search for quantum computational schemes. Although significant strides have been made over the past few years to realize solid state qubits on GaAs/AlGaAs 2DEGs, there are numerous factors limiting the progress. We attempt to identify factors that have material and design-specific origin and develop ways to overcome them. The thesis is divided in two broad segments. In the first segment we describe the realization of a new field-effect induced two dimensional electron system on GaAs/AlGaAs heterostructure where the novel device-design is expected to suppress the level of charge noise present in the device. Modulation-doped GaAs/AlGaAs heterostructures are utilized extensively in the study of quantum transport in nanostructures, but charge fluctuations associated with remote ionized dopants often produce deleterious effects. Electric field-induced carrier systems offer an attractive alternative if certain challenges can be overcome. We demonstrate a field-effect transistor in which the active channel is locally devoid of modulation-doping, but silicon dopant atoms are retained in the ohmic contact region to facilitate low-resistance contacts. A high quality two-dimensional electron gas is induced by a field-effect that is tunable over a density range of 6.5x10 10cm-2 to 2.6x1011cm-2 . Device design, fabrication, and low temperature (T=0.3K) characterization results are discussed. The demonstrated device-design overcomes several existing limitations in the fabrication of field-induced 2DEGs and might find utility in hosting nanostructures required for making spin qubits. The second broad segment describes our effort to correlate transport parameters measured at T=0.3K to the strength of the fractional quantum Hall state observed at nu=5/2 in the second Landau level of high-mobility GaAs/AlGaAs two dimensional
Adiabatic pipelining: a key to ternary computing with quantum dots.
Pečar, P; Ramšak, A; Zimic, N; Mraz, M; Lebar Bajec, I
2008-12-10
The quantum-dot cellular automaton (QCA), a processing platform based on interacting quantum dots, was introduced by Lent in the mid-1990s. What followed was an exhilarating period with the development of the line, the functionally complete set of logic functions, as well as more complex processing structures, however all in the realm of binary logic. Regardless of these achievements, it has to be acknowledged that the use of binary logic is in computing systems mainly the end result of the technological limitations, which the designers had to cope with in the early days of their design. The first advancement of QCAs to multi-valued (ternary) processing was performed by Lebar Bajec et al, with the argument that processing platforms of the future should not disregard the clear advantages of multi-valued logic. Some of the elementary ternary QCAs, necessary for the construction of more complex processing entities, however, lead to a remarkable increase in size when compared to their binary counterparts. This somewhat negates the advantages gained by entering the ternary computing domain. As it turned out, even the binary QCA had its initial hiccups, which have been solved by the introduction of adiabatic switching and the application of adiabatic pipeline approaches. We present here a study that introduces adiabatic switching into the ternary QCA and employs the adiabatic pipeline approach to successfully solve the issues of elementary ternary QCAs. What is more, the ternary QCAs presented here are sizewise comparable to binary QCAs. This in our view might serve towards their faster adoption.
Introduction: From Efficient Quantum Computation to Nonextensive Statistical Mechanics
NASA Astrophysics Data System (ADS)
Prosen, Tomaz
These few pages will attempt to make a short comprehensive overview of several contributions to this volume which concern rather diverse topics. I shall review the following works, essentially reversing the sequence indicated in my title: • First, by C. Tsallis on the relation of nonextensive statistics to the stability of quantum motion on the edge of quantum chaos. • Second, the contribution by P. Jizba on information theoretic foundations of generalized (nonextensive) statistics. • Third, the contribution by J. Rafelski on a possible generalization of Boltzmann kinetics, again, formulated in terms of nonextensive statistics. • Fourth, the contribution by D.L. Stein on the state-of-the-art open problems in spin glasses and on the notion of complexity there. • Fifth, the contribution by F.T. Arecchi on the quantum-like uncertainty relations and decoherence appearing in the description of perceptual tasks of the brain. • Sixth, the contribution by G. Casati on the measurement and information extraction in the simulation of complex dynamics by a quantum computer. Immediately, the following question arises: What do the topics of these talks have in common? Apart from the variety of questions they address, it is quite obvious that the common denominator of these contributions is an approach to describe and control "the complexity" by simple means. One of the very useful tools to handle such problems, also often used or at least referred to in several of the works presented here, is the concept of Tsallis entropy and nonextensive statistics.
Quantum computations with atoms in optical lattices: Marker qubits and molecular interactions
Calarco, T.; Dorner, U.; Zoller, P.; Julienne, P.S.; Williams, C.J.
2004-07-01
We develop a scheme for quantum computation with neutral atoms, based on the concept of 'marker' atoms, i.e., auxiliary atoms that can be efficiently transported in state-independent periodic external traps to operate quantum gates between physically distant qubits. This allows for relaxing a number of experimental constraints for quantum computation with neutral atoms in microscopic potential, including single-atom laser addressability. We discuss the advantages of this approach in a concrete physical scenario involving molecular interactions.
High-speed linear optics quantum computing using active feed-forward.
Prevedel, Robert; Walther, Philip; Tiefenbacher, Felix; Böhi, Pascal; Kaltenbaek, Rainer; Jennewein, Thomas; Zeilinger, Anton
2007-01-01
As information carriers in quantum computing, photonic qubits have the advantage of undergoing negligible decoherence. However, the absence of any significant photon-photon interaction is problematic for the realization of non-trivial two-qubit gates. One solution is to introduce an effective nonlinearity by measurements resulting in probabilistic gate operations. In one-way quantum computation, the random quantum measurement error can be overcome by applying a feed-forward technique, such that the future measurement basis depends on earlier measurement results. This technique is crucial for achieving deterministic quantum computation once a cluster state (the highly entangled multiparticle state on which one-way quantum computation is based) is prepared. Here we realize a concatenated scheme of measurement and active feed-forward in a one-way quantum computing experiment. We demonstrate that, for a perfect cluster state and no photon loss, our quantum computation scheme would operate with good fidelity and that our feed-forward components function with very high speed and low error for detected photons. With present technology, the individual computational step (in our case the individual feed-forward cycle) can be operated in less than 150 ns using electro-optical modulators. This is an important result for the future development of one-way quantum computers, whose large-scale implementation will depend on advances in the production and detection of the required highly entangled cluster states.
A Compact Code for Simulations of Quantum Error Correction in Classical Computers
Nyman, Peter
2009-03-10
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
NASA Astrophysics Data System (ADS)
Dong, Yumin; Xiao, Shufen; Ma, Hongyang; Chen, Libo
2016-08-01
Cloud computing and big data have become the developing engine of current information technology (IT) as a result of the rapid development of IT. However, security protection has become increasingly important for cloud computing and big data, and has become a problem that must be solved to develop cloud computing. The theft of identity authentication information remains a serious threat to the security of cloud computing. In this process, attackers intrude into cloud computing services through identity authentication information, thereby threatening the security of data from multiple perspectives. Therefore, this study proposes a model for cloud computing protection and management based on quantum authentication, introduces the principle of quantum authentication, and deduces the quantum authentication process. In theory, quantum authentication technology can be applied in cloud computing for security protection. This technology cannot be cloned; thus, it is more secure and reliable than classical methods.
Fundamental studies of quantum codes and gates for building a reliable quantum computer
NASA Astrophysics Data System (ADS)
Siddiqui, Shabnam
In this dissertation we have studied various methods that have been proposed to overcome the problem of decoherence in a quantum computer. These methods are: (1) Quantum-error correcting codes (QECC's); (2) Decoherence-free subsystem/subspace (DFS); (3) Adiabatic gate operation. In the first two methods, information is encoded in the form of a code that provides protection against certain noise and hence protect the qubit from losing information to the environment. In the third method, the gate operation is performed in such a way that the qubit is made to evolve adiabatically because of which it acquires a phase which is insensitive to the certain form of noise. Thus, because of the insensivity of the phase to the noise, the qubit is prevented from losing information to the environment. All these methods have limitations and in this work we studied these limitations. This work is divided into two parts. In the first part, we studied the performance of a 3-qubit QECC in the presence of quantized partially correlated noise, as well as 3 and 4-qubit DFS in the presence of partially correlated noise. We derived the relationship between the fidelity of the code, the initial state, coherence length of the noise and the spatial distance between the qubits. For the case of, 3-qubit QECC we found that the quantum nature of the noise enhances the infidelity of the code. For the case of, 3 and 4-qubit DFS we found that under certain conditions 3-qubit DFS code is a better code over 4-qubit code. Nonetheless, these studies provide us insights of the influence of the environment on the performance of quantum codes. In the second part, we studied the problem of the entanglement of the coherent field (that is used to turn on/off the gate) with the qubit on which gate operation is performed. The gate operation is made adiabatic by making the coherent field to change very slowly in time. The entanglement arises due to the quantum nature of the coherent field and causes faulty gate
Automatic computation of quantum-mechanical bound states and wavefunctions
NASA Astrophysics Data System (ADS)
Ledoux, V.; Van Daele, M.
2013-04-01
We discuss the automatic solution of the multichannel Schrödinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Prüfer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index. Catalogue identifier: AEON_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEON_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/license/license.html No. of lines in distributed program, including test data, etc.: 3822 No. of bytes in distributed program, including test data, etc.: 119814 Distribution format: tar.gz Programming language: Matlab. Computer: Personal computer architectures. Operating system: Windows, Linux, Mac (all systems on which Matlab can be installed). RAM: Depends on the problem size. Classification: 4.3. Nature of problem: Computation of eigenvalues and eigenfunctions of multichannel Schrödinger equations appearing in quantum mechanics. Solution method: A CP-based propagation scheme is used to advance the R-matrix in a shooting process. The shooting algorithm is supplemented by a Prüfer type mechanism which allows the eigenvalues to be computed according to index: the user specifies an integer k≥0, and the code computes an approximation to the kth eigenvalue. Eigenfunctions are also available through an auxiliary routine, called after the eigenvalue has been determined. Restrictions: The program can only deal with non-singular problems. Additional
All-optical quantum computing with a hybrid solid-state processing unit
Pei Pei; Zhang Fengyang; Li Chong; Song Heshan
2011-10-15
We develop an architecture of a hybrid quantum solid-state processing unit for universal quantum computing. The architecture allows distant and nonidentical solid-state qubits in distinct physical systems to interact and work collaboratively. All the quantum computing procedures are controlled by optical methods using classical fields and cavity QED. Our methods have a prominent advantage of the insensitivity to dissipation process benefiting from the virtual excitation of subsystems. Moreover, the quantum nondemolition measurements and state transfer for the solid-state qubits are proposed. The architecture opens promising perspectives for implementing scalable quantum computation in a broader sense that different solid-state systems can merge and be integrated into one quantum processor afterward.
NASA Astrophysics Data System (ADS)
Zhang, Yong; Zhang, Kun; Pang, Jinglong
2016-01-01
This paper focuses on the study of topological features in teleportation-based quantum computation and aims at presenting a detailed review on teleportation-based quantum computation (Gottesman and Chuang in Nature 402: 390, 1999). In the extended Temperley-Lieb diagrammatical approach, we clearly show that such topological features bring about the fault-tolerant construction of both universal quantum gates and four-partite entangled states more intuitive and simpler. Furthermore, we describe the Yang-Baxter gate by its extended Temperley-Lieb configuration and then study teleportation-based quantum circuit models using the Yang-Baxter gate. Moreover, we discuss the relationship between the extended Temperley-Lieb diagrammatical approach and the Yang-Baxter gate approach. With these research results, we propose a worthwhile subject, the extended Temperley-Lieb diagrammatical approach, for physicists in quantum information and quantum computation.
Quantum And Relativistic Protocols For Secure Multi-Party Computation
NASA Astrophysics Data System (ADS)
Colbeck, Roger
2009-11-01
After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner, but, also, to introduce a new protocol for non-relativistic strong coin tossing. This protocol matches the security of the best protocol known to date while using a conceptually different approach to achieve the task. In the second part variable bias coin tossing is introduced. This is a variant of coin tossing in which one party secretly chooses one of two biased coins to toss. It is shown that this can be achieved with unconditional security for a specified range of biases, and with cheat-evident security for any bias. We also discuss two further protocols which are conjectured to be unconditionally secure for any bias. The third section looks at other two-party secure computations for which, prior to our work, protocols and no-go theorems were unknown. We introduce a general model for such computations, and show that, within this model, a wide range of functions are impossible to compute securely. We give explicit cheating attacks for such functions. In the final chapter we discuss the task of expanding a private random string, while dropping the usual assumption that the protocol's user trusts her devices. Instead we assume that all quantum devices are supplied by an arbitrarily malicious adversary. We give two protocols that we conjecture securely perform this task. The first allows a private random string to be expanded by a finite amount, while the second generates an arbitrarily large expansion of such a string.
No-go theorem for passive single-rail linear optical quantum computing.
Wu, Lian-Ao; Walther, Philip; Lidar, Daniel A
2013-01-01
Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.
Quantum computing with atomic qubits and Rydberg interactions: progress and challenges
NASA Astrophysics Data System (ADS)
Saffman, M.
2016-10-01
We present a review of quantum computation with neutral atom qubits. After an overview of architectural options and approaches to preparing large qubit arrays we examine Rydberg mediated gate protocols and fidelity for two- and multi-qubit interactions. Quantum simulation and Rydberg dressing are alternatives to circuit based quantum computing for exploring many body quantum dynamics. We review the properties of the dressing interaction and provide a quantitative figure of merit for the complexity of the coherent dynamics that can be accessed with dressing. We conclude with a summary of the current status and an outlook for future progress.
Holographic description of a quantum black hole on a computer.
Hanada, Masanori; Hyakutake, Yoshifumi; Ishiki, Goro; Nishimura, Jun
2014-05-23
Black holes have been predicted to radiate particles and eventually evaporate, which has led to the information loss paradox and implies that the fundamental laws of quantum mechanics may be violated. Superstring theory, a consistent theory of quantum gravity, provides a possible solution to the paradox if evaporating black holes can actually be described in terms of standard quantum mechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantum mechanical system numerically. Our results agree well with the prediction from gravity theory, including the leading quantum gravity correction. Our ability to simulate black holes offers the potential to further explore the yet mysterious nature of quantum gravity through well-established quantum mechanics. PMID:24790030
Holographic description of a quantum black hole on a computer.
Hanada, Masanori; Hyakutake, Yoshifumi; Ishiki, Goro; Nishimura, Jun
2014-05-23
Black holes have been predicted to radiate particles and eventually evaporate, which has led to the information loss paradox and implies that the fundamental laws of quantum mechanics may be violated. Superstring theory, a consistent theory of quantum gravity, provides a possible solution to the paradox if evaporating black holes can actually be described in terms of standard quantum mechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantum mechanical system numerically. Our results agree well with the prediction from gravity theory, including the leading quantum gravity correction. Our ability to simulate black holes offers the potential to further explore the yet mysterious nature of quantum gravity through well-established quantum mechanics.
High threshold distributed quantum computing with three-qubit nodes
NASA Astrophysics Data System (ADS)
Li, Ying; Benjamin, Simon C.
2012-09-01
In the distributed quantum computing paradigm, well-controlled few-qubit ‘nodes’ are networked together by connections which are relatively noisy and failure prone. A practical scheme must offer high tolerance to errors while requiring only simple (i.e. few-qubit) nodes. Here we show that relatively modest, three-qubit nodes can support advanced purification techniques and so offer robust scalability: the infidelity in the entanglement channel may be permitted to approach 10% if the infidelity in local operations is of order 0.1%. Our tolerance of network noise is therefore an order of magnitude beyond prior schemes, and our architecture remains robust even in the presence of considerable decoherence rates (memory errors). We compare the performance with that of schemes involving nodes of lower and higher complexity. Ion traps, and NV-centres in diamond, are two highly relevant emerging technologies: they possess the requisite properties of good local control, rapid and reliable readout, and methods for entanglement-at-a-distance.
Enabling Technologies for Scalable Trapped Ion Quantum Computing
NASA Astrophysics Data System (ADS)
Crain, Stephen; Gaultney, Daniel; Mount, Emily; Knoernschild, Caleb; Baek, Soyoung; Maunz, Peter; Kim, Jungsang
2013-05-01
Scalability is one of the main challenges of trapped ion based quantum computation, mainly limited by the lack of enabling technologies needed to trap, manipulate and process the increasing number of qubits. Microelectromechanical systems (MEMS) technology allows one to design movable micromirrors to focus laser beams on individual ions in a chain and steer the focal point in two dimensions. Our current MEMS system is designed to steer 355 nm pulsed laser beams to carry out logic gates on a chain of Yb ions with a waist of 1.5 μm across a 20 μm range. In order to read the state of the qubit chain we developed a 32-channel PMT with a custom read-out circuit operating near the thermal noise limit of the readout amplifier which increases state detection fidelity. We also developed a set of digital to analog converters (DACs) used to supply analog DC voltages to the electrodes of an ion trap. We designed asynchronous DACs to avoid added noise injection at the update rate commonly found in synchronous DACs. Effective noise filtering is expected to reduce the heating rate of a surface trap, thus improving multi-qubit logic gate fidelities. Our DAC system features 96 channels and an integrated FPGA that allows the system to be controlled in real time. This work was supported by IARPA/ARO.
Aspects of Quantum Computing with Polar Paramagnetic Molecules
NASA Astrophysics Data System (ADS)
Karra, Mallikarjun; Friedrich, Bretislav
2015-05-01
Since the original proposal by DeMille, arrays of optically trapped ultracold polar molecules have been considered among the most promising prototype platforms for the implementation of a quantum computer. The qubit of a molecular array is realized by a single dipolar molecule entangled via its dipole-dipole interaction with the rest of the array's molecules. A superimposed inhomogeneous electric field precludes the quenching of the body-fixed dipole moments by rotation and a time dependent external field controls the qubits to perform gate operations. Much like our previous work in which we considered the simplest cases of a polar 1 Σ and a symmetric top molecule, here we consider a X2Π3 / 2 polar molecule (exemplified by the OH radical) which, by virtue of its nonzero electronic spin and orbital angular momenta, is, in addition, paramagnetic. We demonstrate entanglement tuning by evaluating the concurrence (and the requisite frequencies needed for gate operations) between two such molecules in the presence of varying electric and magnetic fields. Finally, we discuss the conditions required for achieving qubit addressability (transition frequency difference, Δω , as compared with the concomitant Stark and Zeeman broadening) and high fidelity. International Max Planck Research School - Functional Interfaces in Physics and Chemistry.
NMR quantum computing: applying theoretical methods to designing enhanced systems.
Mawhinney, Robert C; Schreckenbach, Georg
2004-10-01
Density functional theory results for chemical shifts and spin-spin coupling constants are presented for compounds currently used in NMR quantum computing experiments. Specific design criteria were examined and numerical guidelines were assessed. Using a field strength of 7.0 T, protons require a coupling constant of 4 Hz with a chemical shift separation of 0.3 ppm, whereas carbon needs a coupling constant of 25 Hz for a chemical shift difference of 10 ppm, based on the minimal coupling approximation. Using these guidelines, it was determined that 2,3-dibromothiophene is limited to only two qubits; the three qubit system bromotrifluoroethene could be expanded to five qubits and the three qubit system 2,3-dibromopropanoic acid could also be used as a six qubit system. An examination of substituent effects showed that judiciously choosing specific groups could increase the number of available qubits by removing rotational degeneracies in addition to introducing specific conformational preferences that could increase (or decrease) the magnitude of the couplings. The introduction of one site of unsaturation can lead to a marked improvement in spectroscopic properties, even increasing the number of active nuclei.
Fault-tolerant linear optical quantum computing with small-amplitude coherent States.
Lund, A P; Ralph, T C; Haselgrove, H L
2008-01-25
Quantum computing using two coherent states as a qubit basis is a proposed alternative architecture with lower overheads but has been questioned as a practical way of performing quantum computing due to the fragility of diagonal states with large coherent amplitudes. We show that using error correction only small amplitudes (alpha>1.2) are required for fault-tolerant quantum computing. We study fault tolerance under the effects of small amplitudes and loss using a Monte Carlo simulation. The first encoding level resources are orders of magnitude lower than the best single photon scheme.
Gates for the Kane quantum computer in the presence of dephasing
Hill, Charles D.; Goan Hsisheng
2004-08-01
In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is 8.3x10{sup -5}. We also compute the fidelities of Z, X, swap, and controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.
NASA Astrophysics Data System (ADS)
Gómez Muñoz, J. L.; Delgado, F.
2016-03-01
This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics.
Step-by-step magic state encoding for efficient fault-tolerant quantum computation.
Goto, Hayato
2014-12-16
Quantum error correction allows one to make quantum computers fault-tolerant against unavoidable errors due to decoherence and imperfect physical gate operations. However, the fault-tolerant quantum computation requires impractically large computational resources for useful applications. This is a current major obstacle to the realization of a quantum computer. In particular, magic state distillation, which is a standard approach to universality, consumes the most resources in fault-tolerant quantum computation. For the resource problem, here we propose step-by-step magic state encoding for concatenated quantum codes, where magic states are encoded step by step from the physical level to the logical one. To manage errors during the encoding, we carefully use error detection. Since the sizes of intermediate codes are small, it is expected that the resource overheads will become lower than previous approaches based on the distillation at the logical level. Our simulation results suggest that the resource requirements for a logical magic state will become comparable to those for a single logical controlled-NOT gate. Thus, the present method opens a new possibility for efficient fault-tolerant quantum computation.
NASA Astrophysics Data System (ADS)
Pfister, Olivier; Wang, Pei; Alexander, Rafael; Chen, Moran; Sridhar, Niranjan; Menicucci, Nicolas
2015-05-01
On the heels of the experimental demonstrations of record-scale one-dimensional cluster-state entanglement--suitable for implementing single-qumode quantum computing gates--in the time domain and the frequency domain, we show here that both degrees of freedom can be combined to generate a two-dimensional square-grid cluster-state--suitable for universal quantum computing--from a single optical parametric oscillator. This method, the most compact yet, has the potential to reach 109 entangled qumodes, based on the current state of the art.
Experimental test of Mermin inequalities on a five-qubit quantum computer
NASA Astrophysics Data System (ADS)
Alsina, Daniel; Latorre, José Ignacio
2016-07-01
Violation of Mermin inequalities is tested on the five-qubit IBM quantum computer. For three, four, and five parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits. Measurements on different bases are included as additional final gates in the circuits. The experimental results obtained using the quantum computer show violation of all Mermin inequalities, with a clear degradation of the results in the five-qubit case. Though this quantum computer is not competitive to test Mermin inequalities as compared to other techniques when applied to a few qubits, it does offer the opportunity to explore multipartite entanglement for four and five qubits beyond the reach of other alternative technologies.
Protected quantum computing: interleaving gate operations with dynamical decoupling sequences.
Zhang, Jingfu; Souza, Alexandre M; Brandao, Frederico Dias; Suter, Dieter
2014-02-01
Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling attenuates the destructive effect of the environmental noise, but so far, it has been used primarily in the context of quantum memories. Here, we experimentally demonstrate a general scheme for combining dynamical decoupling with quantum logical gate operations using the example of an electron-spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than the unprotected dephasing time T2.
Black hole based quantum computing in labs and in the sky
NASA Astrophysics Data System (ADS)
Dvali, Gia; Panchenko, Mischa
2016-08-01
Analyzing some well established facts, we give a model-independent parameterization of black hole quantum computing in terms of a set of macro and micro quantities and their relations. These include the relations between the extraordinarily-small energy gap of black hole qubits and important time-scales of information-processing, such as, scrambling time and Page's time. We then show, confirming and extending previous results, that other systems of nature with identical quantum informatics features are attractive Bose-Einstein systems at the critical point of quantum phase transition. Here we establish a complete isomorphy between the quantum computational properties of these two systems. In particular, we show that the quantum hair of a critical condensate is strikingly similar to the quantum hair of a black hole. Irrespectively whether one takes the similarity between the two systems as a remarkable coincidence or as a sign of a deeper underlying connection, the following is evident. Black holes are not unique in their way of quantum information processing and we can manufacture black hole based quantum computers in labs by taking advantage of quantum criticality.
Demonstration of Deutsch's algorithm on a stable linear optical quantum computer
Zhang Pei; Liu Ruifeng; Gao Hong; Li Fuli; Huang Yunfeng
2010-12-15
We report an experimental demonstration of quantum Deutsch's algorithm using a linear-optical system. By employing photon polarization and spatial modes, we implement all balanced and constant functions for a quantum computer. The experimental system is very stable, and the experimental data are in excellent accordance with the theoretical results.
Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2016-08-18
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.
Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2016-08-18
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations. PMID:27499026
Introduction: From Efficient Quantum Computation to Nonextensive Statistical Mechanics
NASA Astrophysics Data System (ADS)
Prosen, Tomaz
These few pages will attempt to make a short comprehensive overview of several contributions to this volume which concern rather diverse topics. I shall review the following works, essentially reversing the sequence indicated in my title: First, by C. Tsallis on the relation of nonextensive statistics to the stability of quantum motion "on the edge of quantum chaos".
Adiabatic quantum computing with phase modulated laser pulses
Goswami, Debabrata
2005-01-01
Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language. PMID:17195865
Magnetic polyoxometalates: from molecular magnetism to molecular spintronics and quantum computing.
Clemente-Juan, Juan M; Coronado, Eugenio; Gaita-Ariño, Alejandro
2012-11-21
In this review we discuss the relevance of polyoxometalate (POM) chemistry to provide model objects in molecular magnetism. We present several potential applications in nanomagnetism, in particular, in molecular spintronics and quantum computing.
NASA Astrophysics Data System (ADS)
Bienert, M.; Flores, J.; Kun, S. Yu.; Seligman, T. H.
2006-02-01
Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits n ≈ 100-1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90° c.m. of evaporating proton yield in the Bi(γ,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).
Computational and Mathematical Modeling of Coupled Superconducting Quantum Interference Devices
NASA Astrophysics Data System (ADS)
Berggren, Susan Anne Elizabeth
This research focuses on conducting an extensive computational investigation and mathematical analysis into the average voltage response of arrays of Superconducting Quantum Interference Devices (SQUIDs). These arrays will serve as the basis for the development of a sensitive, low noise, significantly lower Size, Weight and Power (SWaP) antenna integrated with Low-Noise Amplifier (LNA) using the SQUID technology. The goal for this antenna is to be capable of meeting all requirements for Guided Missile Destroyers (DDG) 1000 class ships for Information Operations/Signals Intelligence (IO/SIGINT) applications in Very High Frequency/Ultra High Frequency (V/UHF) bands. The device will increase the listening capability of receivers by moving technology into a new regime of energy detection allowing wider band, smaller size, more sensitive, stealthier systems. The smaller size and greater sensitivity will allow for ships to be “de-cluttered” of their current large dishes and devices, replacing everything with fewer and smaller SQUID antenna devices. The fewer devices present on the deck of a ship, the more invisible the ship will be to enemy forces. We invent new arrays of SQUIDs, optimized for signal detection with very high dynamic range and excellent spur-free dynamic range, while maintaining extreme small size (and low radar cross section), wide bandwidth, and environmentally noise limited sensitivity, effectively shifting the bottle neck of receiver systems forever away from the antenna itself deeper into the receiver chain. To accomplish these goals we develop and validate mathematical models for different designs of SQUID arrays and use them to invent a new device and systems design. This design is capable of significantly exceeding, per size weight and power, state-of-the-art receiver system measures of performance, such as bandwidth, sensitivity, dynamic range, and spurious-free dynamic range.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor. PMID:26234709
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate
NASA Astrophysics Data System (ADS)
Dridi, G.; Julien, R.; Hliwa, M.; Joachim, C.
2015-08-01
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
Cluster-state quantum computing enhanced by high-fidelity generalized measurements.
Biggerstaff, D N; Kaltenbaek, R; Hamel, D R; Weihs, G; Rudolph, T; Resch, K J
2009-12-11
We introduce and implement a technique to extend the quantum computational power of cluster states by replacing some projective measurements with generalized quantum measurements (POVMs). As an experimental demonstration we fully realize an arbitrary three-qubit cluster computation by implementing a tunable linear-optical POVM, as well as fast active feedforward, on a two-qubit photonic cluster state. Over 206 different computations, the average output fidelity is 0.9832+/-0.0002; furthermore the error contribution from our POVM device and feedforward is only of O(10(-3)), less than some recent thresholds for fault-tolerant cluster computing.
Entanglement, discord, and the power of quantum computation
Brodutch, Aharon; Terno, Daniel R.
2011-01-15
We show that the ability to create entanglement is necessary for execution of bipartite quantum gates even when they are applied to unentangled states and create no entanglement. Starting with a simple example we demonstrate that to execute such a gate bilocally the local operations and classical communications (LOCC) should be supplemented by shared entanglement. Our results point to the changes in quantum discord, which is a measure of quantumness of correlations even in the absence of entanglement, as the indicator of failure of a LOCC implementation of the gates.
NASA Astrophysics Data System (ADS)
Dattani, Nike; Tanburn, Richard; Lunt, Oliver
We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonian's density of states away from the ground state, so that fewer states occupy the low-lying energies near the minimum, hence allowing for faster adiabatic passages to find the ground state with less risk of getting caught in an undesired low-lying excited state during the passage. Even more generally, our methods can be used to transform a discrete optimization problem into a new one whose unique minimum still encodes the desired answer, but with the objective function's values forming a different landscape. Aspects of the landscape such as the objective function's range, or the values of certain coefficients, or how many different inputs lead to a given output value, can be decreased *or* increased. One of the many examples for which these methods are useful is in finding the ground state of a Hamiltonian using NMR. We apply our methods to an AQC algorithm for integer factorization, and the first method reduces the maximum runtime in our example by up to 754%, and the second method reduces the maximum runtime of another example by up to 250%.
Weapons of Mass Simulation: Smashing down the barriers to building a robust quantum computer
NASA Astrophysics Data System (ADS)
Crosswhite, Gregory Milton
Quantum computation holds the potential to bring forth a new age of science and engineering when currently intractable problems can be routinely solved on a quantum computer. Unfortunately, it is very difficult to design a quantum computer that is robust to noise. In this thesis, we present two tools that leverage classical computational power to attack this problem. The first tool, CodeQuest, is an algorithm that computes the optimal quantum subsystem code that can be implemented using an input choice of Pauli measurement; it proves particularly useful for searching through large sets of choices of measurements to see if any of them result in a useful code. The second tool, Matrix Product States, is an ansatz that one can use to compute the lowest-lying eigenspectra of a Hamiltonian by employing the variational method. For each of these tools we describe both the theory behind them and the practice of using them to advance the science of designing robust quantum computers.
Poulin, David; Wocjan, Pawel
2009-11-27
We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound D{sup {alpha}} on the thermalization time of a quantum system, where D is the system's Hilbert space dimension and {alpha}<=(1/2) is proportional to the Helmholtz free energy density. We also derive an algorithm to evaluate the partition function of a quantum system in a time proportional to the system's thermalization time and inversely proportional to the targeted accuracy squared.
Holonomic quantum computation in the ultrastrong-coupling regime of circuit QED
NASA Astrophysics Data System (ADS)
Wang, Yimin; Zhang, Jiang; Wu, Chunfeng; You, J. Q.; Romero, G.
2016-07-01
We present an experimentally feasible scheme to implement holonomic quantum computation in the ultrastrong-coupling regime of light-matter interaction. The large anharmonicity and the Z2 symmetry of the quantum Rabi model allow us to build an effective three-level Λ -structured artificial atom for quantum computation. The proposed physical implementation includes two gradiometric flux qubits and two microwave resonators where single-qubit gates are realized by a two-tone driving on one physical qubit, and a two-qubit gate is achieved with a time-dependent coupling between the field quadratures of both resonators. Our work paves the way for scalable holonomic quantum computation in ultrastrongly coupled systems.
Tesch, Carmen M; de Vivie-Riedle, Regina
2004-12-22
The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.
Gillen-Christandl, Katharina; Copsey, Bert D.
2011-02-15
The neutral-atom quantum computing community has successfully implemented almost all necessary steps for constructing a neutral-atom quantum computer. We present computational results of a study aimed at solving the remaining problem of creating a quantum memory with individually addressable sites for quantum computing. The basis of this quantum memory is the diffraction pattern formed by laser light incident on a circular aperture. Very close to the aperture, the diffraction pattern has localized bright and dark spots that can serve as red-detuned or blue-detuned atomic dipole traps. These traps are suitable for quantum computing even for moderate laser powers. In particular, for moderate laser intensities ({approx}100 W/cm{sup 2}) and comparatively small detunings ({approx}1000-10 000 linewidths), trap depths of {approx}1 mK and trap frequencies of several to tens of kilohertz are achieved. Our results indicate that these dipole traps can be moved by tilting the incident laser beams without significantly changing the trap properties. We also explored the polarization dependence of these dipole traps. We developed a code that calculates the trapping potential energy for any magnetic substate of any hyperfine ground state of any alkali-metal atom for any laser detuning much smaller than the fine-structure splitting for any given electric field distribution. We describe details of our calculations and include a summary of different notations and conventions for the reduced matrix element and how to convert it to SI units. We applied this code to these traps and found a method for bringing two traps together and apart controllably without expelling the atoms from the trap and without significant tunneling probability between the traps. This approach can be scaled up to a two-dimensional array of many pinholes, forming a quantum memory with single-site addressability, in which pairs of atoms can be brought together and apart for two-qubit gates for quantum computing.
Sesé, Luis M
2012-06-28
A systematic study of the direct computation of the isothermal compressibility of normal quantum fluids is presented by analyzing the solving of the Ornstein-Zernike integral (OZ2) equation for the pair correlations between the path-integral necklace centroids. A number of issues related to the accuracy that can be achieved via this sort of procedure have been addressed, paying particular attention to the finite-N effects and to the definition of significant error bars for the estimates of isothermal compressibilities. Extensive path-integral Monte Carlo computations for the quantum hard-sphere fluid (QHS) have been performed in the (N, V, T) ensemble under temperature and density conditions for which dispersion effects dominate the quantum behavior. These computations have served to obtain the centroid correlations, which have been processed further via the numerical solving of the OZ2 equation. To do so, Baxter-Dixon-Hutchinson's variational procedure, complemented with Baumketner-Hiwatari's grand-canonical corrections, has been used. The virial equation of state has also been obtained and several comparisons between different versions of the QHS equation of state have been made. The results show the reliability of the procedure based on isothermal compressibilities discussed herein, which can then be regarded as a useful and quick means of obtaining the equation of state for fluids under quantum conditions involving strong repulsive interactions.
ERIC Educational Resources Information Center
Orenha, Renato P.; Galembeck, Sérgio E.
2014-01-01
This computational experiment presents qualitative molecular orbital (QMO) and computational quantum chemistry exercises of NO, NO[superscript+], and NO[superscript-]. Initially students explore several properties of the target molecules by Lewis diagrams and the QMO theory. Then, they compare qualitative conclusions with EHT and DFT calculations…
Dicke simulators with emergent collective quantum computational abilities.
Rotondo, Pietro; Cosentino Lagomarsino, Marco; Viola, Giovanni
2015-04-10
Using an approach inspired from spin glasses, we show that the multimode disordered Dicke model is equivalent to a quantum Hopfield network. We propose variational ground states for the system at zero temperature, which we conjecture to be exact in the thermodynamic limit. These ground states contain the information on the disordered qubit-photon couplings. These results lead to two intriguing physical implications. First, once the qubit-photon couplings can be engineered, it should be possible to build scalable pattern-storing systems whose dynamics is governed by quantum laws. Second, we argue with an example of how such Dicke quantum simulators might be used as a solver of "hard" combinatorial optimization problems. PMID:25910121
Regression relation for pure quantum states and its implications for efficient computing.
Elsayed, Tarek A; Fine, Boris V
2013-02-15
We obtain a modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many-body quantum systems. We use the insights gained from this relation to show that high-temperature time correlation functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians, using instead the direct integration of the Schrödinger equation for randomly sampled pure states. This method is also applicable to quantum quenches and other situations describable by time-dependent many-body Hamiltonians. The method implies exponential reduction of the computer memory requirement in comparison with the complete diagonalization. We illustrate the method by numerically computing infinite-temperature correlation functions for translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we also test the spin diffusion hypothesis and find it in a satisfactory agreement with the numerical results. Both the derivation of the modified regression relation and the justification of the computational method are based on the notion of quantum typicality.
Goto, Hayato; Uchikawa, Hironori
2013-01-01
Fault-tolerant quantum computation with quantum error-correcting codes has been considerably developed over the past decade. However, there are still difficult issues, particularly on the resource requirement. For further improvement of fault-tolerant quantum computation, here we propose a soft-decision decoder for quantum error correction and detection by teleportation. This decoder can achieve almost optimal performance for the depolarizing channel. Applying this decoder to Knill's C4/C6 scheme for fault-tolerant quantum computation, which is one of the best schemes so far and relies heavily on error correction and detection by teleportation, we dramatically improve its performance. This leads to substantial reduction of resources.
Decoherence-free manipulation of photonic memories for quantum computation
Sangouard, N.
2006-02-15
We present a protocol to construct an arbitrary quantum circuit. The quantum bits (qubits) are encoded in polarization states of single photons. They are stored in spatially separated dense media deposed in an optical cavity. Specific sequences of pulses address individually the storage media to encode the qubits and to implement a universal set of gates. The proposed protocol is decoherence-free in the sense that spontaneous emission and cavity damping are avoided. We discuss a coupling scheme for experimental implementation in neon atoms.
Computational approach for calculating bound states in quantum field theory
NASA Astrophysics Data System (ADS)
Lv, Q. Z.; Norris, S.; Brennan, R.; Stefanovich, E.; Su, Q.; Grobe, R.
2016-09-01
We propose a nonperturbative approach to calculate bound-state energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively discretized and truncated Hilbert space. We illustrate this approach for a Yukawa-like interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlung-induced widening.
Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
NASA Astrophysics Data System (ADS)
Xu, Haitan; Taylor, J. M.
2011-07-01
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasiparticle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multiqubit gates, for all anyon models from Chern-Simons-Witten SU(2)k theory that support universal quantum computation by braiding (k⩾3,k≠4). In the process, we show how the constructions of topological quantum memory and gates for k=2,4 connect naturally to those for k⩾3,k≠4, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory.
Simulation of Si:P spin-based quantum computer architecture
Chang Yiachung; Fang Angbo
2008-11-07
We present realistic simulation for single and double phosphorous donors in a silicon-based quantum computer design by solving a valley-orbit coupled effective-mass equation for describing phosphorous donors in strained silicon quantum well (QW). Using a generalized unrestricted Hartree-Fock method, we solve the two-electron effective-mass equation with quantum well confinement and realistic gate potentials. The effects of QW width, gate voltages, donor separation, and donor position shift on the lowest singlet and triplet energies and their charge distributions for a neighboring donor pair in the quantum computer(QC) architecture are analyzed. The gate tunability are defined and evaluated for a typical QC design. Estimates are obtained for the duration of spin half-swap gate operation.
Non-adiabatic holonomic quantum computation in linear system-bath coupling.
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-02-05
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
Non-adiabatic holonomic quantum computation in linear system-bath coupling
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-01-01
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities. PMID:26846444
NASA Astrophysics Data System (ADS)
Li, Tao; Long, Gui-Lu
2016-08-01
We propose an effective, scalable, hyperparallel photonic quantum computation scheme in which photonic qubits are hyperencoded both in the spatial degrees of freedom (DOF) and the polarization DOF of each photon. The deterministic hyper-controlled-not (hyper-cnot) gate on a two-photon system is attainable with our interesting interface between the polarized photon and the collective spin wave (magnon) of an atomic ensemble embedded in a double-sided optical cavity, and it doubles the operations in the conventional quantum cnot gate. Moreover, we present a compact hyper-cnotN gate on N +1 hyperencoded photons with only two auxiliary cavity-magnon systems, not more, and it can be faithfully constituted with current experimental techniques. Our proposal enables various applications with the hyperencoded photons in quantum computing and quantum networks.
Non-adiabatic holonomic quantum computation in linear system-bath coupling
NASA Astrophysics Data System (ADS)
Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang
2016-02-01
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
pyCTQW: A continuous-time quantum walk simulator on distributed memory computers
NASA Astrophysics Data System (ADS)
Izaac, Josh A.; Wang, Jingbo B.
2015-01-01
In the general field of quantum information and computation, quantum walks are playing an increasingly important role in constructing physical models and quantum algorithms. We have recently developed a distributed memory software package pyCTQW, with an object-oriented Python interface, that allows efficient simulation of large multi-particle CTQW (continuous-time quantum walk)-based systems. In this paper, we present an introduction to the Python and Fortran interfaces of pyCTQW, discuss various numerical methods of calculating the matrix exponential, and demonstrate the performance behavior of pyCTQW on a distributed memory cluster. In particular, the Chebyshev and Krylov-subspace methods for calculating the quantum walk propagation are provided, as well as methods for visualization and data analysis.
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer.
Martinez, Esteban A; Muschik, Christine A; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-23
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman's idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments-the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories. PMID:27337339
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
NASA Astrophysics Data System (ADS)
Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-01
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron–positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle–antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
NASA Astrophysics Data System (ADS)
Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-01
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer.
Martinez, Esteban A; Muschik, Christine A; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-22
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman's idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments-the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.