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.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
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.
Adiabatic cluster-state quantum computing
Bacon, Dave; Flammia, Steven T.
2010-09-15
Models of quantum computation (QC) are important because they change the physical requirements for achieving universal QC. For example, one-way QC requires the preparation of an entangled ''cluster'' state, followed by adaptive measurement on this state, a set of requirements which is different from the standard quantum-circuit model. Here we introduce a model based on one-way QC but without measurements (except for the final readout), instead using adiabatic deformation of a Hamiltonian whose initial ground state is the cluster state. Our results could help increase the feasibility of adiabatic schemes by using tools from one-way QC.
Adiabatic graph-state quantum computation
NASA Astrophysics Data System (ADS)
Antonio, B.; Markham, D.; Anders, J.
2014-11-01
Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any MBQC on a graph state with generalized flow (gflow) can be converted into an adiabatically driven holonomic computation, which we call adiabatic graph-state quantum computation (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of \\dot{H} as well as the degree of H, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated.
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.
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.
Decoherence in a scalable adiabatic quantum computer
Ashhab, S.; Johansson, J. R.; Nori, Franco
2006-11-15
We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability--i.e., the probability for the system to end up in its new ground state--on the noise amplitude and correlation time. We determine the optimal sweep rate that is required to maximize the success probability. We then discuss the scaling of decoherence effects with increasing system size. We find that those effects can be important for large systems, even if they are small for each of the small building blocks.
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.
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.
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
2016-06-09
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
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.
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.
Adiabatically implementing quantum gates
Sun, Jie; Lu, Songfeng Liu, Fang
2014-06-14
We show that, through the approach of quantum adiabatic evolution, all of the usual quantum gates can be implemented efficiently, yielding running time of order O(1). This may be considered as a useful alternative to the standard quantum computing approach, which involves quantum gates transforming quantum states during the computing process.
Simple proof of equivalence between adiabatic quantum computation and the circuit model.
Mizel, Ari; Lidar, Daniel A; Mitchell, Morgan
2007-08-17
We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.
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.
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.
Towards robust dynamical decoupling and high fidelity adiabatic quantum computation
NASA Astrophysics Data System (ADS)
Quiroz, Gregory
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum
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.
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.
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.
Adiabatic Quantum Computing and Quantum Walks: Algorithms and Architectures
2011-02-15
0807.0929 Title: Environment-Assisted Quantum Transport Authors: Patrick Rebentrost, Masoud Mohseni, Ivan Kassal, Seth Lloyd, Alán Aspuru-Guzik...this effect, Environment Assisted Quantum Transport (ENAQT).The use of environmental effects to enhance transport rates appears to be ubiquitous in
Digitized adiabatic quantum computing with a superconducting circuit, part II: Experiment
NASA Astrophysics Data System (ADS)
Barends, R.; Shabani, A.; Lamata, L.; Kelly, J.; Mezzacapo, A.; Las Heras, U.; Babbush, R.; Fowler, A. G.; Campbell, B.; Chen, Y.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Jeffrey, E.; Lucero, E.; Megrant, A.; Mutus, J.; Neeley, M.; Neill, C.; O'Malley, P.; Quintana, C.; Roushan, P.; Solano, E.; Neven, H.; Martinis, J.
A major challenge in quantum computing is to solve general problems with limited physical hardware. We implement digitized adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the digital approach, using a superconducting circuit with nine qubits. We probe the adiabatic evolutions, explore the scaling of errors with system size, and quantify the success of the algorithm for random spin problems. We find that the system can approximate the solutions to both frustrated Ising problems and non-stoquastic problem Hamiltonians with a performance that is comparable.
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.
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
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.
Digitized adiabatic quantum computing with a superconducting circuit, part I: Theory
NASA Astrophysics Data System (ADS)
Lamata, L.; Barends, R.; Shabani, A.; 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.; Solano, E.; Neven, H.; Martinis, John M.
Adiabatic quantum computing (AQC) is a general-purpose optimization algorithm that in contrast to circuit-model quantum algorithms can be applied to a large set of computational problems. An analog physical realization of AQC has certain limitations that we propose can be overcome by a gate-model equivalence of the AQC. In this talk we discuss the hardware advantages of digitized AQC in particular arbitrary interactions, precision, and coherence. We could experimentally realize the principles of digitized AQC on a chain of nine qubits, and highlight the physics of adiabatic evolutions as well as the Kibble-Zurek mechanism.
Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.
Gosset, David; Terhal, Barbara M; Vershynina, Anna
2015-04-10
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.
Quantum adiabatic machine learning
NASA Astrophysics Data System (ADS)
Pudenz, Kristen L.; Lidar, Daniel A.
2013-05-01
We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. This approach consists of two quantum phases, with some amount of classical preprocessing to set up the quantum problems. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. All quantum processing is strictly limited to two-qubit interactions so as to ensure physical feasibility. We apply and illustrate this approach in detail to the problem of software verification and validation, with a specific example of the learning phase applied to a problem of interest in flight control systems. Beyond this example, the algorithm can be used to attack a broad class of anomaly detection problems.
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.
Comment on ``Adiabatic quantum computation with a one-dimensional projector Hamiltonian''
NASA Astrophysics Data System (ADS)
Kay, Alastair
2013-10-01
The partial adiabatic search algorithm was introduced in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] as a modification of the usual adiabatic algorithm for a quantum search with the idea that most of the interesting computation only happens over a very short range of the adiabatic path. By focusing on that restricted range, one can potentially gain an advantage by reducing the control requirements on the system, enabling a uniform rate of evolution. In this Comment, we point out an oversight in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] that invalidates its proof. However, the argument can be corrected, and the calculations in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] are then sufficient to show that the scheme still works. Nevertheless, subsequent works [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.034304 82, 034304 (2010), Chin. Phys. BCPBHAJ1674-105610.1088/1674-1056/20/4/040309 20, 040309 (2011), Chin. Phys. BCPBHAJ1674-105610.1088/1674-1056/21/1/010306 21, 010306 (2012), AASRI Procedia 1, 5862 (2012), and Quantum Inf. Process.10.1007/s11128-013-0557-1 12, 2689 (2013)] cannot all be recovered in the same way.
Adiabatic Quantum Search in Open Systems.
Wild, Dominik S; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y; Lukin, Mikhail D
2016-10-07
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Adiabatic Quantum Search in Open Systems
NASA Astrophysics Data System (ADS)
Wild, Dominik S.; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y.; Lukin, Mikhail D.
2016-10-01
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Complexity of the Quantum Adiabatic Algorithm
NASA Technical Reports Server (NTRS)
Hen, Itay
2013-01-01
The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.
Adiabatic Quantum Simulation of Quantum Chemistry
NASA Astrophysics Data System (ADS)
Babbush, Ryan; Love, Peter J.; Aspuru-Guzik, Alán
2014-10-01
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
Adiabatic quantum simulation of quantum chemistry.
Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán
2014-10-13
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.
Adiabatic Quantum Simulation of Quantum Chemistry
Babbush, Ryan; Love, Peter J.; Aspuru-Guzik, Alán
2014-01-01
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions. PMID:25308187
An Integrated Development Environment for Adiabatic Quantum Programming
Humble, Travis S; McCaskey, Alex; Bennink, Ryan S; Billings, Jay Jay; D'Azevedo, Eduardo; Sullivan, Blair D; Klymko, Christine F; Seddiqi, Hadayat
2014-01-01
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware raises the question of how well quantum programs perform. Benchmarking behavior is challenging since the multiple steps to synthesize an adiabatic quantum program are highly tunable. We present an adiabatic quantum programming environment called JADE that provides control over all the steps taken during program development. JADE captures the workflow needed to rigorously benchmark performance while also allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation engine that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its use for benchmarking adiabatic quantum programs.
An integrated programming and development environment for adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Humble, T. S.; McCaskey, A. J.; Bennink, R. S.; Billings, J. J.; DʼAzevedo, E. F.; Sullivan, B. D.; Klymko, C. F.; Seddiqi, H.
2014-01-01
Adiabatic quantum computing is a promising route to the computational power afforded by quantum information processing. The recent availability of adiabatic hardware has raised challenging questions about how to evaluate adiabatic quantum optimization (AQO) programs. Processor behavior depends on multiple steps to synthesize an adiabatic quantum program, which are each highly tunable. We present an integrated programming and development environment for AQO called Jade Adiabatic Development Environment (JADE) that provides control over all the steps taken during program synthesis. JADE captures the workflow needed to rigorously specify the AQO algorithm while allowing a variety of problem types, programming techniques, and processor configurations. We have also integrated JADE with a quantum simulation engine that enables program profiling using numerical calculation. The computational engine supports plug-ins for simulation methodologies tailored to various metrics and computing resources. We present the design, integration, and deployment of JADE and discuss its potential use for benchmarking AQO programs by the quantum computer science community.
Determining the Complexity of the Quantum Adiabatic Algorithm using Quantum Monte Carlo Simulations
2012-12-18
efficiently a quantum computer could solve optimization problems using the quantum adiabatic algorithm (QAA). Comparisons were made with a classical...Park, NC 27709-2211 15. SUBJECT TERMS Quantum Adiabatic Algorithm , Optimization, Monte Carlo, quantum computer, satisfiability problems, spin glass... quantum adiabatic algorithm (QAA). Comparisons were made with a classical heuristic algorithm , WalkSAT. A preliminary study was also made to see if the
Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
Fixed-point adiabatic quantum search
NASA Astrophysics Data System (ADS)
Dalzell, Alexander M.; Yoder, Theodore J.; Chuang, Isaac L.
2017-01-01
Fixed-point quantum search algorithms succeed at finding one of M target items among N total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property—the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014), 10.1103/PhysRevLett.113.210501] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002), 10.1103/PhysRevA.65.042308] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.
A Modified Adiabatic Quantum Algorithm for Evaluation of Boolean Functions
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Songfeng; Liu, Fang
2015-09-01
In this paper, we propose a modified construction of the quantum adiabatic algorithm for Boolean functions studied by M. Andrecut et al. [13, 14]. Our algorithm has the time complexity O(1) for the evaluation of Boolean functions, without additional computational cost of implementing the driving Hamiltonian, which is required by the adiabatic evolution described in [13, 14].
Xu, Kebiao; Xie, Tianyu; Li, Zhaokai; Xu, Xiangkun; Wang, Mengqi; Ye, Xiangyu; Kong, Fei; Geng, Jianpei; Duan, Changkui; Shi, Fazhan; Du, Jiangfeng
2017-03-31
The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian S_{z}I_{z} on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.
An interacting adiabatic quantum motor
NASA Astrophysics Data System (ADS)
Viola Kusminskiy, Silvia; Bruch, Anton; von Oppen, Felix
We consider the effect of electron-electron interactions on the performance of an adiabatic quantum motor based on a Thouless pump operating in reverse. We model such a device by electrons in a 1d wire coupled to a slowly moving periodic potential associated with the classical mechanical degree of freedom of the motor. This periodic degree of freedom is set into motion by a bias voltage applied to the 1d electron channel. We investigate the Thouless motor with interacting leads modeled as Luttinger liquids. We show that interactions enhance the energy gap opened by the periodic potential and thus the robustness of the Thouless motor against variations in the chemical potential. We show that the motor degree of freedom can be described as a mobile impurity in a Luttinger liquid obeying Langevin dynamics with renormalized coefficients due to interactions, for which we give explicit expressions.
Accurate Variational Description of Adiabatic Quantum Optimization
NASA Astrophysics Data System (ADS)
Carleo, Giuseppe; Bauer, Bela; Troyer, Matthias
Adiabatic quantum optimization (AQO) is a quantum computing protocol where a system is driven by a time-dependent Hamiltonian. The initial Hamiltonian has an easily prepared ground-state and the final Hamiltonian encodes some desired optimization problem. An adiabatic time evolution then yields a solution to the optimization problem. Several challenges emerge in the theoretical description of this protocol: on one hand, the exact simulation of quantum dynamics is exponentially complex in the size of the optimization problem. On the other hand, approximate approaches such as tensor network states (TNS) are limited to small instances by the amount of entanglement that can be encoded. I will present here an extension of the time-dependent Variational Monte Carlo approach to problems in AQO. This approach is based on a general class of (Jastrow-Feenberg) entangled states, whose parameters are evolved in time according to a stochastic variational principle. We demonstrate this approach for optimization problems of the Ising spin-glass type. A very good accuracy is achieved when compared to exact time-dependent TNS on small instances. We then apply this approach to larger problems, and discuss the efficiency of the quantum annealing scheme in comparison with its classical counterpart.
New Dynamical Scaling Universality for Quantum Networks Across Adiabatic Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Acevedo, O. L.; Quiroga, L.; Rodríguez, F. J.; Johnson, N. F.
2014-01-01
We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.
New Dynamical Scaling Universality for Quantum Networks Across Adiabatic Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Acevedo, Oscar L.; Rodriguez, Ferney J.; Quiroga, Luis; Johnson, Neil F.; Rey, Ana M.
2014-05-01
We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.
Markovian quantum master equation beyond adiabatic regime.
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τ_{A}(t) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τ_{A}(t) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
Markovian quantum master equation beyond adiabatic regime
NASA Astrophysics Data System (ADS)
Yamaguchi, Makoto; Yuge, Tatsuro; Ogawa, Tetsuo
2017-01-01
By introducing a temporal change time scale τA(t ) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τA(t ) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.
General conditions for quantum adiabatic evolution
Comparat, Daniel
2009-07-15
Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution [H({epsilon}t),{epsilon}{yields}0], are insufficient to describe an evolution driven by the Hamiltonian H(t) itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian H(t). As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions)
Non-Adiabatic Holonomic Quantum Gates in an atomic system
NASA Astrophysics Data System (ADS)
Azimi Mousolou, Vahid; Canali, Carlo M.; Sjoqvist, Erik
2012-02-01
Quantum computation is essentially the implementation of a universal set of quantum gate operations on a set of qubits, which is reliable in the presence of noise. We propose a scheme to perform robust gates in an atomic four-level system using the idea of non-adiabatic holonomic quantum computation proposed in [1]. The gates are realized by applying sequences of short laser pulses that drive transitions between the four energy levels in such a way that the dynamical phases vanish. [4pt] [1] E. Sjoqvist, D.M. Tong, B. Hessmo, M. Johansson, K. Singh, arXiv:1107.5127v2 [quant-ph
Adiabatic quantum optimization for associative memory recall
Seddiqi, Hadayat; Humble, Travis S.
2014-12-22
Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO). Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are storedmore » in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.« less
Adiabatic quantum optimization for associative memory recall
Seddiqi, Hadayat; Humble, Travis S.
2014-12-22
Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO). Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
NASA Technical Reports Server (NTRS)
Smelyanskiy, V. N.; Toussaint, U. V.; Timucin, D. A.
2002-01-01
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
On optimal methods for adiabatic quantum state transformations
NASA Astrophysics Data System (ADS)
Somma, Rolando
2013-03-01
Many problems in science could be solved by preparing the low-energy quantum state (or any eigenstate) of a Hamiltonian. A common example is the Boolean satisfiability problem, where each clause can be mapped to the energy of an interacting many-body system, and the problem reduces to minimizing the energy. In quantum computing, adiabatic quantum state transformations (ASTs) provide a tool for preparing the quantum state. ASTs are conventionally implemented via slow or adiabatic perturbations to the Hamiltonian, relying on the quantum adiabatic theorem. Nevertheless, more efficient implementations of ASTs exist. In this talk I will review recently developed methods for ASTs that are more efficient and require less assumptions on the Hamiltonians than the conventional implementation. Such methods involve measurements of the states along the evolution path and have a best-case implementation cost of L/G, where L is the length of the (evolved) state path and G is a lower bound to the spectral gap of the Hamiltonians. I will show that this cost is optimal and comment on results of the gap amplification problem, where the goal is to reduce the cost by increasing G. We acknowledge support from NSF through the CCF program and the LDRD programs at Los Alamos National Laboratory and Sandia National Laboratories.
Shortcuts to adiabaticity for quantum annealing
NASA Astrophysics Data System (ADS)
Takahashi, Kazutaka
2017-01-01
We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz, and the Hamiltonian is designed by the inverse engineering. We show that the time dependence of physical quantities such as the magnetization is independent of the speed of the Hamiltonian variation in the infinite-range model. We also show that rotating transverse magnetic fields are useful to achieve the ideal time evolution.
Adiabatic quantum algorithm for search engine ranking.
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A
2012-06-08
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
Adiabatic Quantum Algorithm for Search Engine Ranking
NASA Astrophysics Data System (ADS)
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A.
2012-06-01
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in “q-sampling” protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
Quantum-Classical Correspondence of Shortcuts to Adiabaticity
NASA Astrophysics Data System (ADS)
Okuyama, Manaka; Takahashi, Kazutaka
2017-04-01
We formulate the theory of shortcuts to adiabaticity in classical mechanics. For a reference Hamiltonian, the counterdiabatic term is constructed from the dispersionless Korteweg-de Vries (KdV) hierarchy. Then the adiabatic theorem holds exactly for an arbitrary choice of time-dependent parameters. We use the Hamilton-Jacobi theory to define the generalized action. The action is independent of the history of the parameters and is directly related to the adiabatic invariant. The dispersionless KdV hierarchy is obtained from the classical limit of the KdV hierarchy for the quantum shortcuts to adiabaticity. This correspondence suggests some relation between the quantum and classical adiabatic theorems.
NASA Astrophysics Data System (ADS)
O'Hare, Anthony; Kusmartsev, F. V.; Kugel, K. I.
2010-12-01
We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state. We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane. The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.
NASA Astrophysics Data System (ADS)
O'Hare, Anthony; Kusmartsev, F. V.; Kugel, K. I.
We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state. We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane. The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.
Quantum Adiabatic Algorithms and Large Spin Tunnelling
NASA Technical Reports Server (NTRS)
Boulatov, A.; Smelyanskiy, V. N.
2003-01-01
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
Fidelity of adiabatic holonomic quantum gates
NASA Astrophysics Data System (ADS)
Malinovsky, Vladimir; Rudin, Sergey
2016-05-01
During last few years non-Abelian geometric phases are attracting increasing interest due to possible experimental applications in quantum computation. Here we discuss universal set of holonomic quantum gates using the geometric phase that the qubit wave function acquires after a cyclic evolution. The proposed scheme utilizes ultrafast pulses and provides a possibility to substantially suppress transient population of the ancillary states. Fidelity of the holonomic quantum gates in the presence of dephasing and dissipation is discussed. Example of electron spin qubit system in the InGaN/GaN, GaN/AlN quantum dot is considered in details.
Quantum Adiabatic Optimization and Combinatorial Landscapes
NASA Technical Reports Server (NTRS)
Smelyanskiy, V. N.; Knysh, S.; Morris, R. D.
2003-01-01
In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.
On the Role of Prior Probability in Adiabatic Quantum Algorithms
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Songfeng; Yang, Liping
2016-03-01
In this paper, we study the role of prior probability on the efficiency of quantum local adiabatic search algorithm. The following aspects for prior probability are found here: firstly, only the probabilities of marked states affect the running time of the adiabatic evolution; secondly, the prior probability can be used for improving the efficiency of the adiabatic algorithm; thirdly, like the usual quantum adiabatic evolution, the running time for the case of multiple solution states where the number of marked elements are smaller enough than the size of the set assigned that contains them can be significantly bigger than that of the case where the assigned set only contains all the marked states.
Adiabatic following for a three-state quantum system
NASA Astrophysics Data System (ADS)
Huang, Wei; Shore, Bruce W.; Rangelov, Andon; Kyoseva, Elica
2017-01-01
Adiabatic time-evolution - found in various forms of adiabatic following and adiabatic passage - is often advantageous for controlled manipulation of quantum systems due to its insensitivity to deviations in the pulse shapes and timings. In this paper we discuss controlled adiabatic evolution of a three-state quantum system, a natural advance to the widespread use of two-state systems in numerous contemporary applications. We discuss, and illustrate, not only possibilities for population transfer but also for creating, with prescribed relative phase, 50:50 superpositions of two Zeeman sublevels in a letter-vee coupling linkage.
Adiabatic Spin Pumping with Quantum Dots
NASA Astrophysics Data System (ADS)
Mucciolo, Eduardo R.
Electronic transport in mesoscopic systems has been intensively studied for more the last three decades. While there is a substantial understanding of the stationary regime, much less is know about phase-coherent nonequilibrium transport when pulses or ac perturbations are used to drive electrons at low temperatures and at small length scales. However, about 20 years ago Thouless proposed to drive nondissipative currents in quantum systems by applying simultaneously two phase-locked external perturbations. The so-called adiabatic pumping mechanism has been revived in the last few years, both theoretically and experimentally, in part because of the development of lateral semiconductor quantum dots. Here we will explain how open dots can be used to create spin-polarized currents with little or no net charge transfer. The pure spin pump we propose is the analog of a charge battery in conventional electronics and may provide a needed circuit element for spin-based electronics. We will also discuss other relevant issues such as rectification and decoherence and point out possible extensions of the mechanism to closed dots.
Generating shortcuts to adiabaticity in quantum and classical dynamics
NASA Astrophysics Data System (ADS)
Jarzynski, Christopher
2013-10-01
Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counterdiabatic Hamiltonian to stifle nonadiabatic transitions. Here this shortcut to adiabaticity is cast in terms of a generator of adiabatic transport. This yields a classical analog of transitionless driving, and provides a strategy for constructing quantal counterdiabatic Hamiltonians. As an application of this framework, exact classical and quantal counterdiabatic terms are obtained for a particle in a box and for even-power-law potentials in one degree of freedom.
Computer Code For Turbocompounded Adiabatic Diesel Engine
NASA Technical Reports Server (NTRS)
Assanis, D. N.; Heywood, J. B.
1988-01-01
Computer simulation developed to study advantages of increased exhaust enthalpy in adiabatic turbocompounded diesel engine. Subsytems of conceptual engine include compressor, reciprocator, turbocharger turbine, compounded turbine, ducting, and heat exchangers. Focus of simulation of total system is to define transfers of mass and energy, including release and transfer of heat and transfer of work in each subsystem, and relationship among subsystems. Written in FORTRAN IV.
Quantum adiabatic optimization and combinatorial landscapes
NASA Astrophysics Data System (ADS)
Smelyanskiy, V. N.; Knysh, S.; Morris, R. D.
2004-09-01
In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of the satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, γ=M/N . We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (instead of only energy) is used, and are able to show the existence of a dynamic threshold γ=γd starting with some value of K —the number of variables in each clause. Beyond the dynamic threshold, the algorithm should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz. We have been able to map the ensemble of random graphs onto another ensemble with fluctuations significantly reduced. This enabled us to obtain tight upper bounds on the satisfiability transition and to recompute the dynamical transition using the extended set of landscapes.
Acceleration of adiabatic quantum dynamics in electromagnetic fields
Masuda, Shumpei; Nakamura, Katsuhiro
2011-10-15
We show a method to accelerate quantum adiabatic dynamics of wave functions under electromagnetic field (EMF) by developing the preceding theory [Masuda and Nakamura, Proc. R. Soc. London Ser. A 466, 1135 (2010)]. Treating the orbital dynamics of a charged particle in EMF, we derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states in any desired short time. The scheme is consolidated by describing a way to overcome possible singularities in both the additional phase and driving potential due to nodes proper to wave functions under EMF. As explicit examples, we exhibit the fast forward of adiabatic squeezing and transport of excited Landau states with nonzero angular momentum, obtaining the result consistent with the transitionless quantum driving applied to the orbital dynamics in EMF.
TOPICAL REVIEW: Optimization using quantum mechanics: quantum annealing through adiabatic evolution
NASA Astrophysics Data System (ADS)
Santoro, Giuseppe E.; Tosatti, Erio
2006-09-01
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable time-dependent Hamiltonian, where 'planck' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toy-models—double-well potentials and other one-dimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schrödinger's evolutions, for the toy models, or path-integral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated non-trivial Landau-Zener tunnelling phenomena is discussed and emphasized.
Geometric Phase for Adiabatic Evolutions of General Quantum States
Wu, Biao; Liu, Jie; Niu, Qian; Singh, David J
2005-01-01
The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.
Ladd, T D; Jelezko, F; Laflamme, R; Nakamura, Y; Monroe, C; O'Brien, J L
2010-03-04
Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.
2010-03-04
1227–1230 (2009). 31. Olmschenk, S. et al. Quantum teleportation between distant matter qubits. Science 323, 486–489 (2009). 32. Dür, W., Briegel, H...REVIEWS Quantum computers T. D. Ladd1{, F. Jelezko2, R. Laflamme3,4,5, Y. Nakamura6,7, C. Monroe8,9 & J. L. O’Brien10 Over the past several decades... quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing
Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation
Zamstein, Noa; Tannor, David J.
2012-12-14
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schroedinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
1998-04-01
information representation and processing technology, although faster than the wheels and gears of the Charles Babbage computation machine, is still in...the same computational complexity class as the Babbage machine, with bits of information represented by entities which obey classical (non-quantum...nuclear double resonances Charles M Bowden and Jonathan P. Dowling Weapons Sciences Directorate, AMSMI-RD-WS-ST Missile Research, Development, and
Fluctuations of work in nearly adiabatically driven open quantum systems.
Suomela, S; Salmilehto, J; Savenko, I G; Ala-Nissila, T; Möttönen, M
2015-02-01
We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving, such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions.
Quantum state engineering with flux-biased Josephson phase qubits by rapid adiabatic passages
NASA Astrophysics Data System (ADS)
Nie, W.; Huang, J. S.; Shi, X.; Wei, L. F.
2010-09-01
In this article, the scheme of quantum computing based on the Stark-chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei, J. R. Johansson, L. X. Cen, S. Ashhab, and F. Nori, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.100.113601 100, 113601 (2008)] is extensively applied to implement quantum state manipulations in flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark shifts. Then, assisted by various transition pulses, universal quantum logic gates as well as arbitrary quantum state preparations can be implemented. Compared with the usual π-pulse operations widely used in experiments, the adiabatic population passages proposed here are insensitive to the details of the applied pulses and thus the desirable population transfers can be satisfyingly implemented. The experimental feasibility of the proposal is also discussed.
A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems
NASA Astrophysics Data System (ADS)
Tamascelli, Dario; Zanetti, Luca
2014-08-01
We present a quantum algorithm for solving graph isomorphism problems that is based on an adiabatic protocol. We use a collection of continuous time quantum walks, each one generated by an XY Hamiltonian, to visit the configuration space. In this way we avoid a diffusion over all the possible configurations and significantly reduce the dimensionality of the accessible Hilbert space. Within this restricted space, the graph isomorphism problem can be translated into searching for a satisfying assignment to a 2-SAT (satisfiable) formula and mapped onto a 2-local Hamiltonian without resorting to perturbation gadgets or projective techniques. We present an analysis of the time for execution of the algorithm on small graph isomorphism problem instances and discuss the issue of an implementation of the proposed adiabatic scheme on current quantum computing hardware.
More bang for your buck: Super-adiabatic quantum engines
Campo, A. del; Goold, J.; Paternostro, M.
2014-01-01
The practical untenability of the quasi-static assumption makes any realistic engine intrinsically irreversible and its operating time finite, thus implying friction effects at short cycle times. An important technological goal is thus the design of maximally efficient engines working at the maximum possible power. We show that, by utilising shortcuts to adiabaticity in a quantum engine cycle, one can engineer a thermodynamic cycle working at finite power and zero friction. Our findings are illustrated using a harmonic oscillator undergoing a quantum Otto cycle. PMID:25163421
Quantum computation for quantum chemistry
NASA Astrophysics Data System (ADS)
Aspuru-Guzik, Alan
2010-03-01
Numerically exact simulation of quantum systems on classical computers is in general, an intractable computational problem. Computational chemists have made progress in the development of approximate methods to tackle complex chemical problems. The downside of these approximate methods is that their failure for certain important cases such as long-range charge transfer states in the case of traditional density functional theory. In 1982, Richard Feynman suggested that a quantum device should be able to simulate quantum systems (in our case, molecules) exactly using quantum computers in a tractable fashion. Our group has been working in the development of quantum chemistry algorithms for quantum devices. In this talk, I will describe how quantum computers can be employed to carry out numerically exact quantum chemistry and chemical reaction dynamics calculations, as well as molecular properties. Finally, I will describe our recent experimental quantum computation of the energy of the hydrogen molecule using an optical quantum computer.
Experimental implementation of an adiabatic quantum optimization algorithm
NASA Astrophysics Data System (ADS)
Steffen, Matthias; van Dam, Wim; Hogg, Tad; Breyta, Greg; Chuang, Isaac
2003-03-01
A novel quantum algorithm using adiabatic evolution was recently presented by Ed Farhi [1] and Tad Hogg [2]. This algorithm represents a remarkable discovery because it offers new insights into the usefulness of quantum resources. An experimental demonstration of an adiabatic algorithm has remained beyond reach because it requires an experimentally accessible Hamiltonian which encodes the problem and which must also be smoothly varied over time. We present tools to overcome these difficulties by discretizing the algorithm and extending average Hamiltonian techniques [3]. We used these techniques in the first experimental demonstration of an adiabatic optimization algorithm: solving an instance of the MAXCUT problem using three qubits and nuclear magnetic resonance techniques. We show that there exists an optimal run-time of the algorithm which can be predicted using a previously developed decoherence model. [1] E. Farhi et al., quant-ph/0001106 (2000) [2] T. Hogg, PRA, 61, 052311 (2000) [3] W. Rhim, A. Pines, J. Waugh, PRL, 24,218 (1970)
Random matrix approach to quantum adiabatic evolution algorithms
Boulatov, A.; Smelyanskiy, V.N.
2005-05-15
We analyze the power of the quantum adiabatic evolution algorithm (QAA) for solving random computationally hard optimization problems within a theoretical framework based on random matrix theory (RMT). We present two types of driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that nonadiabatic corrections in the QAA are due to the interaction of the ground state with the 'cloud' formed by most of the excited states, confirming that in driven RMT models, the Landau-Zener scenario of pairwise level repulsions is not relevant for the description of nonadiabatic corrections. We show that the QAA has a finite probability of success in a certain range of parameters, implying a polynomial complexity of the algorithm. The second model corresponds to the standard QAA with the problem Hamiltonian taken from the RMT Gaussian unitary ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. For this reason, the driven GUE model can also lead to polynomial complexity of the QAA. The main contribution to the failure probability of the QAA comes from the nonadiabatic corrections to the eigenstates, which only depend on the absolute values of the transition amplitudes. Due to the mapping between the two models, these absolute values are the same in both cases. Our results indicate that this 'phase irrelevance' is the leading effect that can make both the Markovian- and GUE-type QAAs successful.
Crossover from adiabatic to antiadiabatic quantum pumping with dissipation.
Pellegrini, Franco; Negri, C; Pistolesi, F; Manini, Nicola; Santoro, Giuseppe E; Tosatti, Erio
2011-08-05
Quantum pumping, in its different forms, is attracting attention from different fields, from fundamental quantum mechanics, to nanotechnology, to superconductivity. We investigate the crossover of quantum pumping from the adiabatic to the antiadiabatic regime in the presence of dissipation, and find general and explicit analytical expressions for the pumped current in a minimal model describing a system with the topology of a ring forced by a periodic modulation of frequency ω. The solution allows following in a transparent way the evolution of pumped dc current from much smaller to much larger ω values than the other relevant energy scale, the energy splitting introduced by the modulation. We find and characterize a temperature-dependent optimal value of the frequency for which the pumped current is maximal.
Adiabatic response and quantum thermoelectrics for ac-driven quantum systems
NASA Astrophysics Data System (ADS)
Ludovico, María Florencia; Battista, Francesca; von Oppen, Felix; Arrachea, Liliana
2016-02-01
We generalize the theory of thermoelectrics to include coherent electron systems under adiabatic ac driving, accounting for quantum pumping of charge and heat, as well as for the work exchanged between the electron system and driving potentials. We derive the relevant response coefficients in the adiabatic regime and show that they obey generalized Onsager reciprocity relations. We analyze the consequences of our generalized thermoelectric framework for quantum motors, generators, heat engines, and heat pumps, characterizing them in terms of efficiencies and figures of merit. We illustrate these concepts in a model for a quantum pump.
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.
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.
Shortcut to Adiabaticity for an Anisotropic Gas Containing Quantum Defects.
Papoular, D J; Stringari, S
2015-07-10
We present a shortcut to adiabaticity (STA) protocol applicable to 3D unitary Fermi gases and 2D weakly interacting Bose gases containing defects such as vortices or solitons. Our protocol relies on a new class of exact scaling solutions in the presence of anisotropic time-dependent harmonic traps. It connects stationary states in initial and final traps having the same frequency ratios. The resulting scaling laws exhibit a universal form and also apply to the classical Boltzmann gas. The duration of the STA can be made very short so as to realize a quantum quench from one stationary state to another. When applied to an anisotropically trapped superfluid gas, the STA conserves the shape of the quantum defects hosted by the cloud, thereby acting like a perfect microscope, which sharply contrasts with their strong distortion occurring during the free expansion of the cloud.
Novel latch for adiabatic quantum-flux-parametron logic
Takeuchi, Naoki Yamanashi, Yuki; Yoshikawa, Nobuyuki; Ortlepp, Thomas
2014-03-14
We herein propose the quantum-flux-latch (QFL) as a novel latch for adiabatic quantum-flux-parametron (AQFP) logic. A QFL is very compact and compatible with AQFP logic gates and can be read out in one clock cycle. Simulation results revealed that the QFL operates at 5 GHz with wide parameter margins of more than ±22%. The calculated energy dissipation was only ∼0.1 aJ/bit, which yields a small energy delay product of 20 aJ·ps. We also designed shift registers using QFLs to demonstrate more complex circuits with QFLs. Finally, we experimentally demonstrated correct operations of the QFL and a 1-bit shift register (a D flip-flop)
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…
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.
Quantum robots and quantum computers
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Applications and error correction for adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Pudenz, Kristen
Adiabatic quantum optimization (AQO) is a fast-developing subfield of quantum information processing which holds great promise in the relatively near future. Here we develop an application, quantum anomaly detection, and an error correction code, Quantum Annealing Correction (QAC), for use with AQO. The motivation for the anomaly detection algorithm is the problematic nature of classical software verification and validation (V&V). The number of lines of code written for safety-critical applications such as cars and aircraft increases each year, and with it the cost of finding errors grows exponentially (the cost of overlooking errors, which can be measured in human safety, is arguably even higher). We approach the V&V problem by using a quantum machine learning algorithm to identify charateristics of software operations that are implemented outside of specifications, then define an AQO to return these anomalous operations as its result. Our error correction work is the first large-scale experimental demonstration of quantum error correcting codes. We develop QAC and apply it to USC's equipment, the first and second generation of commercially available D-Wave AQO processors. We first show comprehensive experimental results for the code's performance on antiferromagnetic chains, scaling the problem size up to 86 logical qubits (344 physical qubits) and recovering significant encoded success rates even when the unencoded success rates drop to almost nothing. A broader set of randomized benchmarking problems is then introduced, for which we observe similar behavior to the antiferromagnetic chain, specifically that the use of QAC is almost always advantageous for problems of sufficient size and difficulty. Along the way, we develop problem-specific optimizations for the code and gain insight into the various on-chip error mechanisms (most prominently thermal noise, since the hardware operates at finite temperature) and the ways QAC counteracts them. We finish by showing
Effect of Poisson noise on adiabatic quantum control
NASA Astrophysics Data System (ADS)
Kiely, A.; Muga, J. G.; Ruschhaupt, A.
2017-01-01
We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and provide approximations for the different noise strength regimes. We show that using the eigenstates of the noise superoperator as a basis can be a useful way of expressing the master equation. Using this, we simulate various settings to illustrate different effects of Poisson noise. In particular, we show a dip in the fidelity as a function of noise strength where high fidelity can occur in the strong-noise regime for some cases. We also investigate recent claims [J. Jing et al., Phys. Rev. A 89, 032110 (2014), 10.1103/PhysRevA.89.032110] that this type of noise may improve rather than destroy adiabaticity.
Adiabatic quantum-flux-parametron cell library adopting minimalist design
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-05-07
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits.
Decoherence in current induced forces: Application to adiabatic quantum motors
NASA Astrophysics Data System (ADS)
Fernández-Alcázar, Lucas J.; Bustos-Marún, Raúl A.; Pastawski, Horacio M.
2015-08-01
Current induced forces are not only related with the discrete nature of electrons but also with its quantum character. It is natural then to wonder about the effect of decoherence. Here, we develop the theory of current induced forces including dephasing processes and we apply it to study adiabatic quantum motors (AQMs). The theory is based on Büttiker's fictitious probe model, which here is reformulated for this particular case. We prove that it accomplishes the fluctuation-dissipation theorem. We also show that, in spite of decoherence, the total work performed by the current induced forces remains equal to the pumped charge per cycle times the voltage. We find that decoherence affects not only the current induced forces of the system but also its intrinsic friction and noise, modifying in a nontrivial way the efficiency of AQMs. We apply the theory to study an AQM inspired by a classical peristaltic pump where we surprisingly find that decoherence can play a crucial role by triggering its operation. Our results can help to understand how environmentally induced dephasing affects the quantum behavior of nanomechanical devices.
Wu, Jin-Lei; Ji, Xin; Zhang, Shou
2017-01-01
We propose a dressed-state scheme to achieve shortcuts to adiabaticity in atom-cavity quantum electrodynamics for speeding up adiabatic two-atom quantum state transfer and maximum entanglement generation. Compared with stimulated Raman adiabatic passage, the dressed-state scheme greatly shortens the operation time in a non-adiabatic way. By means of some numerical simulations, we determine the parameters which can guarantee the feasibility and efficiency both in theory and experiment. Besides, numerical simulations also show the scheme is robust against the variations in the parameters, atomic spontaneous emissions and the photon leakages from the cavity.
Optimal Blind Quantum Computation
NASA Astrophysics Data System (ADS)
Mantri, Atul; Pérez-Delgado, Carlos A.; Fitzsimons, Joseph F.
2013-12-01
Blind quantum computation allows a client with limited quantum capabilities to interact with a remote quantum computer to perform an arbitrary quantum computation, while keeping the description of that computation hidden from the remote quantum computer. While a number of protocols have been proposed in recent years, little is currently understood about the resources necessary to accomplish the task. Here, we present general techniques for upper and lower bounding the quantum communication necessary to perform blind quantum computation, and use these techniques to establish concrete bounds for common choices of the client’s quantum capabilities. Our results show that the universal blind quantum computation protocol of Broadbent, Fitzsimons, and Kashefi, comes within a factor of (8)/(3) of optimal when the client is restricted to preparing single qubits. However, we describe a generalization of this protocol which requires exponentially less quantum communication when the client has a more sophisticated device.
Quantum and classical non-adiabatic dynamics of Li_{2}^{+}Ne photodissociation
NASA Astrophysics Data System (ADS)
Pouilly, Brigitte; Monnerville, Maurice; Zanuttini, David; Gervais, Benoît
2015-01-01
The 3D photodissociation dynamics of Li2+Ne system is investigated by quantum calculations using the multi-configuration time-dependent Hartree (MCTDH) method and by classical simulations with the trajectory surface hopping (TSH) approach. Six electronic states of A’ symmetry and two states of A” symmetry are involved in the process. Couplings in the excitation region and two conical intersections in the vicinity of the Franck-Condon zone control the non-adiabatic nuclear dynamics. A diabatic representation including all the states and the couplings is determined. Diabatic and adiabatic populations calculated for initial excitation to pure diabatic and adiabatic states lead to a clear understanding of the mechanisms governing the non-adiabatic photodissociation process. The classical and quantum photodissociation cross-sections for absorption in two adiabatic states of the A’ symmetry are calculated. A remarkable agreement between quantum and classical results is obtained regarding the populations and the absorption cross-sections.
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.
Random Matrix Approach to Quantum Adiabatic Evolution Algorithms
NASA Technical Reports Server (NTRS)
Boulatov, Alexei; Smelyanskiy, Vadier N.
2004-01-01
We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.
Resource efficient gadgets for compiling adiabatic quantum optimization problems
NASA Astrophysics Data System (ADS)
Babbush, Ryan; O'Gorman, Bryan; Aspuru-Guzik, Alán
2013-11-01
We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic quantum algorithms are often most easily formulated using many-body interactions but experimentally available interactions are generally 2-body. In this context, the efficiency of a reduction gadget is measured by the number of ancilla qubits required as well as the amount of control precision needed to implement the resulting Hamiltonian. First, we optimize methods of applying these gadgets to obtain 2-local Hamiltonians using the least possible number of ancilla qubits. Next, we show a novel reduction gadget which minimizes control precision and a heuristic which uses this gadget to compile 3-local problems with a significant reduction in control precision. Finally, we present numerics which indicate a substantial decrease in the resources required to implement randomly generated, 3-body optimization Hamiltonians when compared to other methods in the literature.
Effects of dissipation on an adiabatic quantum search algorithm
NASA Astrophysics Data System (ADS)
de Vega, Inés; Bañuls, Mari Carmen; Pérez, A.
2010-12-01
According to recent studies (Amin et al 2008 Phys. Rev. Lett. 100 060503), the effect of a thermal bath may improve the performance of a quantum adiabatic search algorithm. In this paper, we compare the effects of such a thermal environment on the algorithm performance with those of a structured environment similar to the one encountered in systems coupled to an electromagnetic field that exists within a photonic crystal. Whereas for all the parameter regimes explored here, the algorithm performance is worsened by contact with a thermal environment, the picture appears to be different when one considers a structured environment. In this case we show that by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More specifically, we find that the imaginary part of the rates cannot be neglected with the usual argument that it simply amounts to an energy shift and in fact influences crucially the system dynamics.
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)
Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions.
Laumann, C R; Moessner, R; Scardicchio, A; Sondhi, S L
2012-07-20
Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first-order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibit a first-order transition with only an algebraically small gap. In addition, we construct a simple classical translationally invariant one-dimensional Hamiltonian containing nearest-neighbor interactions only, which exhibits an exponential gap at a thermodynamic quantum first-order transition of essentially topological origin. This establishes that (i) the QAA can be successful even across first-order transitions but also that (ii) it can fail on exceedingly simple problems readily solved by inspection, or by classical annealing.
NASA Astrophysics Data System (ADS)
Farhi, Edward; Gosset, David; Hen, Itay; Sandvik, A. W.; Shor, Peter; Young, A. P.; Zamponi, Francesco
2012-11-01
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular max-cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular max-cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.
Ultrafast adiabatic quantum algorithm for the NP-complete exact cover problem.
Wang, Hefeng; Wu, Lian-Ao
2016-02-29
An adiabatic quantum algorithm may lose quantumness such as quantum coherence entirely in its long runtime, and consequently the expected quantum speedup of the algorithm does not show up. Here we present a general ultrafast adiabatic quantum algorithm. We show that by applying a sequence of fast random or regular signals during evolution, the runtime can be reduced substantially, whereas advantages of the adiabatic algorithm remain intact. We also propose a randomized Trotter formula and show that the driving Hamiltonian and the proposed sequence of fast signals can be implemented simultaneously. We illustrate the algorithm by solving the NP-complete 3-bit exact cover problem (EC3), where NP stands for nondeterministic polynomial time, and put forward an approach to implementing the problem with trapped ions.
Ultrafast adiabatic quantum algorithm for the NP-complete exact cover problem
Wang, Hefeng; Wu, Lian-Ao
2016-01-01
An adiabatic quantum algorithm may lose quantumness such as quantum coherence entirely in its long runtime, and consequently the expected quantum speedup of the algorithm does not show up. Here we present a general ultrafast adiabatic quantum algorithm. We show that by applying a sequence of fast random or regular signals during evolution, the runtime can be reduced substantially, whereas advantages of the adiabatic algorithm remain intact. We also propose a randomized Trotter formula and show that the driving Hamiltonian and the proposed sequence of fast signals can be implemented simultaneously. We illustrate the algorithm by solving the NP-complete 3-bit exact cover problem (EC3), where NP stands for nondeterministic polynomial time, and put forward an approach to implementing the problem with trapped ions. PMID:26923834
Quantum Computing since Democritus
NASA Astrophysics Data System (ADS)
Aaronson, Scott
2013-03-01
1. Atoms and the void; 2. Sets; 3. Gödel, Turing, and friends; 4. Minds and machines; 5. Paleocomplexity; 6. P, NP, and friends; 7. Randomness; 8. Crypto; 9. Quantum; 10. Quantum computing; 11. Penrose; 12. Decoherence and hidden variables; 13. Proofs; 14. How big are quantum states?; 15. Skepticism of quantum computing; 16. Learning; 17. Interactive proofs and more; 18. Fun with the Anthropic Principle; 19. Free will; 20. Time travel; 21. Cosmology and complexity; 22. Ask me anything.
NASA Astrophysics Data System (ADS)
Dziarmaga, Jacek; Rams, Marek M.
2010-10-01
We consider an inhomogeneous quantum phase transition across a multicritical point of the XY quantum spin chain. This is an example of a Lifshitz transition with a dynamical exponent z=2. Just like in the case z=1 considered by Dziarmaga and Rams (2010 New J. Phys. 12 055007), when a critical front propagates much faster than the maximal group velocity of quasiparticles vq, then the transition is effectively homogeneous: the density of excitations obeys a generalized Kibble-Zurek mechanism and scales with the sixth root of the transition rate. However, unlike for the case z=1, the inhomogeneous transition becomes adiabatic not below vq but at a lower threshold velocity \\hat{v} , proportional to the inhomogeneity of the transition, where the excitations are suppressed exponentially. Interestingly, the adiabatic threshold \\hat{v} is nonzero despite the vanishing minimal group velocity of low-energy quasiparticles. In the adiabatic regime below \\hat{v} , the inhomogeneous transition can be used for efficient adiabatic quantum state preparation in a quantum simulator: the time required for the critical front to sweep across a chain of N spins adiabatically is merely linear in N, while the corresponding time for a homogeneous transition across the multicritical point scales with the sixth power of N. What is more, excitations after the adiabatic inhomogeneous transition, if any, are brushed away by the critical front to the end of the spin chain.
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.
Cluster State Quantum Computing
2012-12-01
implementation of quantum computation,” Fortschr. Phys. 48, 771 (2000). [Dragoman01] D. Dragoman, “Proposal for a three-qubit teleportation experiment”, Phys...CLUSTER STATE QUANTUM COMPUTING DECEMBER 2012 INTERIM TECHNICAL REPORT APPROVED FOR PUBLIC RELEASE; DISTRIBUTION...From - To) NOV 2010 – OCT 2012 4. TITLE AND SUBTITLE CLUSTER STATE QUANTUM COMPUTING 5a. CONTRACT NUMBER IN-HOUSE 5b. GRANT NUMBER N/A 5c
2001-04-01
example that other students learn to make quantum computers does not quite meet the RQC specification, consider useful in many fields . I also want to...UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADP010869 TITLE: The Rabi Quantum Computer DISTRIBUTION: Approved for...comprise the compilation report: ADP010865 thru ADP010894 UNCLASSIFIED 5-1 The Rabi Quantum Computer Rudolph A. Krutar Advanced Information Technology’ U.S
Cluster State Quantum Computation
2014-02-01
nearest neighbor cluster state has been shown to be a universal resource for MBQC thus we can say our quantum computer is universal. We note that...CLUSTER STATE QUANTUM COMPUTATION FEBRUARY 2014 FINAL TECHNICAL REPORT APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED STINFO COPY AIR FORCE...TITLE AND SUBTITLE CLUSTER STATE QUANTUM COMPUTATION 5a. CONTRACT NUMBER IN-HOUSE 5b. GRANT NUMBER N/A 5c. PROGRAM ELEMENT NUMBER 62788F 6
NASA Astrophysics Data System (ADS)
Inoue, Jun-Ichi
2011-03-01
We analytically derive deterministic equations of order parameters such as spontaneous magnetization in infinite-range quantum spin systems obeying quantum Monte Carlo dynamics. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. We discuss several possible applications of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we argue the ground state searching for infinite-range random spin systems via quantum adiabatic evolution. We were financially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science, No. 22500195.
Temperature-Driven and Electrochemical-Potential-Driven Adiabatic Pumping via a Quantum Dot
NASA Astrophysics Data System (ADS)
Hasegawa, Masahiro; Kato, Takeo
2017-02-01
We investigate adiabatic pumping via a single level quantum dot induced by periodic modulation of thermodynamic variables of reservoirs, i.e., temperatures and electrochemical potentials. We consider the impurity Anderson model and derive analytical formulas for coherent adiabatic charge pumping applicable to the strong dot-reservoir coupling within the first-order perturbation with respect to Coulomb interaction. We show that charge pumping is induced by rectification effect due to delayed response of the quantum dot to time-dependent reservoir parameters. The presence of interaction is necessary because this delayed response rectifies charge current via Coulomb interaction. For temperature-driven charge pumping, one-way pumping is realized regardless of reservoir temperatures when an energy level of the quantum dot locates near the Fermi level. We clarify that this new feature of adiabatic pumping is caused by level broadening effect of the quantum dot due to strong dot-reservoir coupling.
Di Lisi, Antonio; De Siena, Silvio; Illuminati, Fabrizio; Vitali, David
2005-09-15
We introduce an efficient, quasideterministic scheme to generate maximally entangled states of two atomic ensembles. The scheme is based on quantum nondemolition measurements of total atomic populations and on adiabatic quantum feedback conditioned by the measurements outputs. The high efficiency of the scheme is tested and confirmed numerically for ideal photodetection as well as in the presence of losses.
Bacon, Dave; Flammia, Steven T
2009-09-18
The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation, which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space. This construction allows for geometric robustness based upon the control of two independent qubit interactions. Further, our piecewise adiabatic evolution easily relates to the quantum circuit model, enabling the use of standard methods from fault-tolerance theory for establishing thresholds.
Adiabatic many-body state preparation and information transfer in quantum dot arrays
NASA Astrophysics Data System (ADS)
Farooq, Umer; Bayat, Abolfazl; Mancini, Stefano; Bose, Sougato
2015-04-01
Quantum simulation of many-body systems are one of the most interesting tasks of quantum technology. Among them is the preparation of a many-body system in its ground state when the vanishing energy gap makes the cooling mechanisms ineffective. Adiabatic theorem, as an alternative to cooling, can be exploited for driving the many-body system to its ground state. In this paper, we study two most common disorders in quantum dot arrays, namely exchange coupling fluctuations and hyperfine interaction, in adiabatic preparation of ground state in such systems. We show that the adiabatic ground-state preparation is highly robust against those disorder effects making it a good analog simulator. Moreover, we also study the adiabatic quantum information transfer, using singlet-triplet states, across a spin chain. In contrast to ground-state preparation the transfer mechanism is highly affected by disorder and in particular, the hyperfine interaction is very destructive for the performance. This suggests that for communication tasks across such arrays adiabatic evolution is not as effective and quantum quenches could be preferable.
Blind Quantum Signature with Blind Quantum Computation
NASA Astrophysics Data System (ADS)
Li, Wei; Shi, Ronghua; Guo, Ying
2017-04-01
Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.
Blind Quantum Signature with Blind Quantum Computation
NASA Astrophysics Data System (ADS)
Li, Wei; Shi, Ronghua; Guo, Ying
2016-12-01
Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation 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 Computational Cryptography
NASA Astrophysics Data System (ADS)
Kawachi, Akinori; Koshiba, Takeshi
As computational approaches to classical cryptography have succeeded in the establishment of the foundation of the network security, computational approaches even to quantum cryptography are promising, since quantum computational cryptography could offer richer applications than the quantum key distribution. Our project focused especially on the quantum one-wayness and quantum public-key cryptosystems. The one-wayness of functions (or permutations) is one of the most important notions in computational cryptography. First, we give an algorithmic characterization of quantum one-way permutations. In other words, we show a necessary and sufficient condition for quantum one-way permutations in terms of reflection operators. Second, we introduce a problem of distinguishing between two quantum states as a new underlying problem that is harder to solve than the graph automorphism problem. The new problem is a natural generalization of the distinguishability problem between two probability distributions, which are commonly used in computational cryptography. We show that the problem has several cryptographic properties and they enable us to construct a quantum publickey cryptosystem, which is likely to withstand any attack of a quantum adversary.
Quantum dynamics by the constrained adiabatic trajectory method
Leclerc, A.; Jolicard, G.; Guerin, S.; Killingbeck, J. P.
2011-03-15
We develop the constrained adiabatic trajectory method (CATM), which allows one to solve the time-dependent Schroedinger equation constraining the dynamics to a single Floquet eigenstate, as if it were adiabatic. This constrained Floquet state (CFS) is determined from the Hamiltonian modified by an artificial time-dependent absorbing potential whose forms are derived according to the initial conditions. The main advantage of this technique for practical implementation is that the CFS is easy to determine even for large systems since its corresponding eigenvalue is well isolated from the others through its imaginary part. The properties and limitations of the CATM are explored through simple examples.
Zhou, Jian; Yu, Wei-Can; Gao, Yu-Mei; Xue, Zheng-Yuan
2015-06-01
A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-vacancy centers, can be used to construct a universal set of quantum gates on the encoded logical qubits. Therefore, our scheme opens up the possibility of realizing universal holonomic quantum computation with cavity assisted interaction on solid-state spins characterized by long coherence times.
Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
NASA Astrophysics Data System (ADS)
Arrachea, Liliana; von Oppen, Felix
2015-11-01
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
Reprint of : Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor
NASA Astrophysics Data System (ADS)
Arrachea, Liliana; von Oppen, Felix
2016-08-01
The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.
Wei, Yu-Jia; He, Yu-Ming; Chen, Ming-Cheng; Hu, Yi-Nan; He, Yu; Wu, Dian; Schneider, Christian; Kamp, Martin; Höfling, Sven; Lu, Chao-Yang; Pan, Jian-Wei
2014-11-12
Single photons are attractive candidates of quantum bits (qubits) for quantum computation and are the best messengers in quantum networks. Future scalable, fault-tolerant photonic quantum technologies demand both stringently high levels of photon indistinguishability and generation efficiency. Here, we demonstrate deterministic and robust generation of pulsed resonance fluorescence single photons from a single semiconductor quantum dot using adiabatic rapid passage, a method robust against fluctuation of driving pulse area and dipole moments of solid-state emitters. The emitted photons are background-free, have a vanishing two-photon emission probability of 0.3% and a raw (corrected) two-photon Hong-Ou-Mandel interference visibility of 97.9% (99.5%), reaching a precision that places single photons at the threshold for fault-tolerant surface-code quantum computing. This single-photon source can be readily scaled up to multiphoton entanglement and used for quantum metrology, boson sampling, and linear optical quantum computing.
Tian, Si-Cong; Wan, Ren-Gang; Wang, Chun-Liang; Shu, Shi-Li; Wang, Li-Jie; Tong, Chun-Zhu
2016-12-01
We propose a scheme for creation and transfer of coherence among ground state and indirect exciton states of triple quantum dots via the technique of stimulated Raman adiabatic passage. Compared with the traditional stimulated Raman adiabatic passage, the Stokes laser pulse is replaced by the tunneling pulse, which can be controlled by the externally applied voltages. By varying the amplitudes and sequences of the pump and tunneling pulses, a complete coherence transfer or an equal coherence distribution among multiple states can be obtained. The investigations can provide further insight for the experimental development of controllable coherence transfer in semiconductor structure and may have potential applications in quantum information processing.
How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?
NASA Astrophysics Data System (ADS)
Yarman, T.; L. Kholmetskii, A.
2011-10-01
We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3 = Constant, where P is the pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al. 2010 Int. J. Phys. Sci. 5 1524). We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.
NASA Astrophysics Data System (ADS)
Kang, Yi-Hao; Wu, Qi-Cheng; Chen, Ye-Hong; Shi, Zhi-Cheng; Song, Jie; Xia, Yan
2017-04-01
In this paper, we investigate the quantum transfer for the system with three-level Λ-type structure, and construct a shortcut to the adiabatic passage via picture transformation to speed up the evolution. We can design the pulses directly without any additional couplings. Moreover, by choosing suitable control parameters, the Rabi frequencies of pulses can be expressed by the linear superpositions of Gaussian functions, which could be easily realized in experiments. Compared with the previous works using the stimulated Raman adiabatic passage, the quantum transfer can be significantly accelerated with the present scheme.
Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Terhal, Barbara M.
2016-02-01
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent two-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.
Quantum Information, Computation and Communication
NASA Astrophysics Data System (ADS)
Jones, Jonathan A.; Jaksch, Dieter
2012-07-01
Part I. Quantum Information: 1. Quantum bits and quantum gates; 2. An atom in a laser field; 3. Spins in magnetic fields; 4. Photon techniques; 5. Two qubits and beyond; 6. Measurement and entanglement; Part II. Quantum Computation: 7. Principles of quantum computing; 8. Elementary quantum algorithms; 9. More advanced quantum algorithms; 10. Trapped atoms and ions; 11. Nuclear magnetic resonance; 12. Large scale quantum computers; Part III. Quantum Communication: 13. Basics of information theory; 14. Quantum information; 15. Quantum communication; 16. Testing EPR; 17. Quantum cryptography; Appendixes; References; Index.
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.
The performance of the quantum adiabatic algorithm on spike Hamiltonians
NASA Astrophysics Data System (ADS)
Kong, Linghang; Crosson, Elizabeth
Spike Hamiltonians arise from optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work, we study the efficiency of the adiabatic algorithm for solving the “the Hamming weight with a spike” problem by analyzing the scaling of the spectral gap at the critical point for various sizes of the barrier. Our main result is a rigorous lower bound on the minimum spectral gap for the adiabatic evolution when the bit-symmetric cost function has a thin but polynomially high barrier, which is based on a comparison argument and an improved variational ansatz for the ground state. We also adapt the discrete WKB method for the case of abruptly changing potentials and compare it with the predictions of the spin coherent instanton method which was previously used by Farhi, Goldstone and Gutmann. Finally, our improved ansatz for the ground state leads to a method for predicting the location of avoided crossings in the excited energy states of the thin spike Hamiltonian, and we use a recursion relation to understand the ordering of some of these avoided crossings as a step towards analyzing the previously observed diabatic cascade phenomenon.
2011-12-01
an inspiring speech at the MIT Physics of Computation 1st Conference in 1981, Feynman proposed the development of a computer that would obey the...on ion trap based 36 quantum computing for physics and computer science students would include lecture notes, slides, lesson plans, a syllabus...reading lists, videos, demonstrations, and laboratories. 37 LIST OF REFERENCES [1] R. P. Feynman , “Simulating physics with computers,” Int. J
Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains
NASA Astrophysics Data System (ADS)
Rams, Marek M.; Mohseni, Masoud; del Campo, Adolfo
2016-12-01
We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The dependence of the residual energy on this length scale and the velocity at which the magnetic field sweeps out the chain is shown to be nonmonotonic. We determine the conditions for an optimal suppression of the residual energy of the final state and show that inhomogeneous driving can outperform conventional adiabatic schemes based on homogeneous control fields by several orders of magnitude.
Quantum computing: towards reality
NASA Astrophysics Data System (ADS)
Trabesinger, Andreas
2017-03-01
The concept of computers that harness the laws of quantum mechanics has transformed our thinking about how information can be processed. Now the environment exists to make prototype devices a reality.
Shortcuts to adiabaticity in classical and quantum processes for scale-invariant driving
NASA Astrophysics Data System (ADS)
Deffner, Sebastian; Jarzynski, Christopher; Del Campo, Adolfo
2014-03-01
All real physical processes in classical as well as in quantum devices operate in finite-time. For most applications, however, adiabatic, i.e. infinitely-slow processes, are more favorable, as these do not cause unwanted, parasitic excitations. A shortcut to adiabaticity is a driving protocol which reproduces in a short time the same final state that would result from an adiabatic process. A particular powerful technique to engineer such shortcuts is transitionless quantum driving by means of counterdiabatic fields. However, determining closed form expressions for the counterdiabatic field has generally proven to be a daunting task. In this paper, we introduce a novel approach, with which we find the explicit form of the counterdiabatic driving field in arbitrary scale-invariant dynamical processes, encompassing expansions and transport. Our approach originates in the formalism of generating functions, and unifies previous approaches independently developed for classical and quantum systems. We show how this new approach allows to design shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems. SD and CJ acknowledge support from the National Science Foundation (USA) under grant DMR-1206971. This research is further supported by the U.S Department of Energy through the LANL/LDRD Program and a LANL J. Robert Oppenheimer fellowship (AdC).
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
NASA Astrophysics Data System (ADS)
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
He, Shuang; Su, Shi-Lei; Wang, Dong-Yang; Sun, Wen-Mei; Bai, Cheng-Hua; Zhu, Ai-Dong; Wang, Hong-Fu; Zhang, Shou
2016-01-01
We propose an effective scheme of shortcuts to adiabaticity for generating a three-dimensional entanglement of two atoms trapped in a cavity using the transitionless quantum driving (TQD) approach. The key point of this approach is to construct an effective Hamiltonian that drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final state as that of an adiabatic process within a much shorter time. In this paper, the shortcuts to adiabatic passage are constructed by introducing two auxiliary excited levels in each atom and applying extra cavity modes and classical fields to drive the relevant transitions. Thereby, the three-dimensional entanglement is obtained with a faster rate than that in the adiabatic passage. Moreover, the influences of atomic spontaneous emission and photon loss on the fidelity are discussed by numerical simulation. The results show that the speed of entanglement implementation is greatly improved by the use of adiabatic shortcuts and that this entanglement implementation is robust against decoherence. This will be beneficial to the preparation of high-dimensional entanglement in experiment and provides the necessary conditions for the application of high-dimensional entangled states in quantum information processing. PMID:27499169
Robust quantum logic in neutral atoms via adiabatic Rydberg dressing
Keating, Tyler; Cook, Robert L.; Hankin, Aaron M.; Jau, Yuan -Yu; Biedermann, Grant W.; Deutsch, Ivan H.
2015-01-28
We study a scheme for implementing a controlled-Z (CZ) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a σ_{+}/σ_{-} orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces acting on doubly-excited Rydberg atoms when the blockade is imperfect. As a result, for reasonable parameters, with qubits encoded into the clock states of ^{133}Cs, we predict that our protocol could produce a CZ gate in < 10 μs with error probability on the order of 10^{-3}.
Robust quantum logic in neutral atoms via adiabatic Rydberg dressing
Keating, Tyler; Cook, Robert L.; Hankin, Aaron M.; ...
2015-01-28
We study a scheme for implementing a controlled-Z (CZ) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a σ+/σ- orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces actingmore » on doubly-excited Rydberg atoms when the blockade is imperfect. As a result, for reasonable parameters, with qubits encoded into the clock states of 133Cs, we predict that our protocol could produce a CZ gate in < 10 μs with error probability on the order of 10-3.« less
Adiabatic holonomic quantum gates for a single qubit
NASA Astrophysics Data System (ADS)
Malinovsky, Vladimir S.; Rudin, Sergey
2014-04-01
A universal set of single qubit holonomic quantum gates using the geometric phase that the qubit wave function acquires after a cyclic evolution is discussed. The proposed scheme utilizes ultrafast linearly chirped pulses and provides a possibility to substantially suppress transient population of the ancillary state in a generic three-level system. That provides a possibility to reduce the decoherence effect and achieve a higher fidelity of the quantum gates.
Quantum Computational Geodesics
2010-01-01
equation, a well-known nonlinear differential matrix equation, and L and iF (L) are Lax pairs (30–32). Some solutions to the geodesic equation...D2J j Dt2 +Rjikl ∂xi ∂t ∂xl ∂t Jk + Cj = 0, (91) the so-called “lifted Jacobi equation” (1). Nielsen and Dowling used the lifted Jacobi equation...quantum circuits (1, 28, 2). 27 6. References 1. Dowling , M. R.; Nielsen, M. A. The Geometry of Quantum Computation. Quantum Information and
REVIEWS OF TOPICAL PROBLEMS: Quantum computers and quantum computations
NASA Astrophysics Data System (ADS)
Valiev, Kamil'A.
2005-01-01
This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review.
Non-adiabatic effect in quantum pumping for a spin-boson system
NASA Astrophysics Data System (ADS)
Watanabe, Kota L.; Hayakawa, Hisao
2014-11-01
We clarify the role of non-adiabatic effects in quantum pumping for a spin-boson system. When we sinusoidally control the temperatures of two reservoirs with π /2 phase difference, we find that the pumping current strongly depends on the initial condition, and thus, the current deviates from that predicted by the adiabatic treatment. We also analytically obtain the contribution of non-adiabatic effects in the pumping current proportional to Ω ^3, where Ω is the angular frequency of the temperature control. The validity of the analytic expression is verified by our numerical calculation. Moreover, we extend the steady heat fluctuation theorem to the case for slowly modulated temperatures and large transferred energies.
O'Brien, Jeremy L
2007-12-07
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.
Algorithms Bridging Quantum Computation and Chemistry
NASA Astrophysics Data System (ADS)
McClean, Jarrod Ryan
The design of new materials and chemicals derived entirely from computation has long been a goal of computational chemistry, and the governing equation whose solution would permit this dream is known. Unfortunately, the exact solution to this equation has been far too expensive and clever approximations fail in critical situations. Quantum computers offer a novel solution to this problem. In this work, we develop not only new algorithms to use quantum computers to study hard problems in chemistry, but also explore how such algorithms can help us to better understand and improve our traditional approaches. In particular, we first introduce a new method, the variational quantum eigensolver, which is designed to maximally utilize the quantum resources available in a device to solve chemical problems. We apply this method in a real quantum photonic device in the lab to study the dissociation of the helium hydride (HeH+) molecule. We also enhance this methodology with architecture specific optimizations on ion trap computers and show how linear-scaling techniques from traditional quantum chemistry can be used to improve the outlook of similar algorithms on quantum computers. We then show how studying quantum algorithms such as these can be used to understand and enhance the development of classical algorithms. In particular we use a tool from adiabatic quantum computation, Feynman's Clock, to develop a new discrete time variational principle and further establish a connection between real-time quantum dynamics and ground state eigenvalue problems. We use these tools to develop two novel parallel-in-time quantum algorithms that outperform competitive algorithms as well as offer new insights into the connection between the fermion sign problem of ground states and the dynamical sign problem of quantum dynamics. Finally we use insights gained in the study of quantum circuits to explore a general notion of sparsity in many-body quantum systems. In particular we use
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.
Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.
Zamstein, Noa; Tannor, David J
2012-12-14
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.
Adiabatic elimination of Gaussian subsystems from quantum dynamics under continuous measurement
NASA Astrophysics Data System (ADS)
Černotík, Ondřej; Vasilyev, Denis V.; Hammerer, Klemens
2015-07-01
An ever broader range of physical platforms provides the possibility to study and engineer quantum dynamics under continuous measurements. In many experimental arrangements the system of interest is monitored by means of an ancillary device, whose sole purpose is to transduce the signal from the system to the measurement apparatus. Here we present a method of adiabatic elimination when the transducer consists of an arbitrary number of bosonic modes with Gaussian dynamics while the measured object can be any quantum system. Crucially, our approach can cope with the highly relevant case of finite temperature of the transducer, which is not easily achieved with other methods. We show that this approach provides a significant improvement in the readout of superconducting qubits in circuit QED already for a few thermal excitations and makes it possible to adiabatically eliminate optomechanical transducers relevant for frequency conversion between microwave and optical fields.
Undergraduate computational physics projects on quantum computing
NASA Astrophysics Data System (ADS)
Candela, D.
2015-08-01
Computational projects on quantum computing suitable for students in a junior-level quantum mechanics course are described. In these projects students write their own programs to simulate quantum computers. Knowledge is assumed of introductory quantum mechanics through the properties of spin 1/2. Initial, more easily programmed projects treat the basics of quantum computation, quantum gates, and Grover's quantum search algorithm. These are followed by more advanced projects to increase the number of qubits and implement Shor's quantum factoring algorithm. The projects can be run on a typical laptop or desktop computer, using most programming languages. Supplementing resources available elsewhere, the projects are presented here in a self-contained format especially suitable for a short computational module for physics students.
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.
Layered Architecture for Quantum Computing
NASA Astrophysics Data System (ADS)
Jones, N. Cody; Van Meter, Rodney; Fowler, Austin G.; McMahon, Peter L.; Kim, Jungsang; Ladd, Thaddeus D.; Yamamoto, Yoshihisa
2012-07-01
We develop a layered quantum-computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface-code quantum error correction. In doing so, we propose a new quantum-computer architecture based on optical control of quantum dots. The time scales of physical-hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum-dot architecture we study could solve such problems on the time scale of days.
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
NASA Astrophysics Data System (ADS)
Li, Yi-Chao; Chen, Xi
2016-12-01
Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.
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 for Quantum Chemistry
2010-09-01
random walks as the decoherence became strong. Recent experiments on photosynthetic light -harvesting complexes observed long-lived excitonic coherences...by the light -harvesting complex. In Environment-assisted quantum walks in energy transfer of photosynthetic complexes, J. Chem. Phys. 129 (2008...a decohered quantum walk. Motivated by the experiments on the Fenna-Matthews-Olson (FMO) light -harvesting complex of green sulfur bacteria, we
Quantum computing on encrypted data
NASA Astrophysics Data System (ADS)
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 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.
Fluxon-controlled quantum computer
NASA Astrophysics Data System (ADS)
Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki
2016-11-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e. joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
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.
NASA Astrophysics Data System (ADS)
Huo, Pengfei; Coker, David F.
2011-11-01
An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.
Quantum computing: Efficient fault tolerance
NASA Astrophysics Data System (ADS)
Gottesman, Daniel
2016-12-01
Dealing with errors in a quantum computer typically requires complex programming and many additional quantum bits. A technique for controlling errors has been proposed that alleviates both of these problems.
Open Quantum Walks and Dissipative Quantum Computing
NASA Astrophysics Data System (ADS)
Petruccione, Francesco
2012-02-01
Open Quantum Walks (OQWs) have been recently introduced as quantum Markov chains on graphs [S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy, E-print: http://hal.archives-ouvertes.fr/hal-00581553/fr/]. The formulation of the OQWs is exclusively based upon the non-unitary dynamics induced by the environment. It will be shown that OQWs are a very useful tool for the formulation of dissipative quantum computing and quantum state preparation. In particular, it will be shown how to implement single qubit gates and the CNOT gate as OQWs on fully connected graphs. Also, OQWS make possible the dissipative quantum state preparation of arbitrary single qubit states and of all two-qubit Bell states. Finally, it will be shown how to reformulate efficiently a discrete time version of dissipative quantum computing in the language of OQWs.
Parallelizable adiabatic gate teleportation
NASA Astrophysics Data System (ADS)
Nakago, Kosuke; Hajdušek, Michal; Nakayama, Shojun; Murao, Mio
2015-12-01
To investigate how a temporally ordered gate sequence can be parallelized in adiabatic implementations of quantum computation, we modify adiabatic gate teleportation, a model of quantum computation proposed by Bacon and Flammia [Phys. Rev. Lett. 103, 120504 (2009), 10.1103/PhysRevLett.103.120504], to a form deterministically simulating parallelized gate teleportation, which is achievable only by postselection. We introduce a twisted Heisenberg-type interaction Hamiltonian, a Heisenberg-type spin interaction where the coordinates of the second qubit are twisted according to a unitary gate. We develop parallelizable adiabatic gate teleportation (PAGT) where a sequence of unitary gates is performed in a single step of the adiabatic process. In PAGT, numeric calculations suggest the necessary time for the adiabatic evolution implementing a sequence of L unitary gates increases at most as O (L5) . However, we show that it has the interesting property that it can map the temporal order of gates to the spatial order of interactions specified by the final Hamiltonian. Using this property, we present a controlled-PAGT scheme to manipulate the order of gates by a control qubit. In the controlled-PAGT scheme, two differently ordered sequential unitary gates F G and G F are coherently performed depending on the state of a control qubit by simultaneously applying the twisted Heisenberg-type interaction Hamiltonians implementing unitary gates F and G . We investigate why the twisted Heisenberg-type interaction Hamiltonian allows PAGT. We show that the twisted Heisenberg-type interaction Hamiltonian has an ability to perform a transposed unitary gate by just modifying the space ordering of the final Hamiltonian implementing a unitary gate in adiabatic gate teleportation. The dynamics generated by the time-reversed Hamiltonian represented by the transposed unitary gate enables deterministic simulation of a postselected event of parallelized gate teleportation in adiabatic
Interfacing external quantum devices to a universal quantum computer.
Lagana, Antonio A; Lohe, Max A; von Smekal, Lorenz
2011-01-01
We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer.
Benabbas, Abdelkrim; Salna, Bridget; Sage, J Timothy; Champion, Paul M
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical "gating" distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working near
Benabbas, Abdelkrim; Salna, Bridget; Sage, J. Timothy; Champion, Paul M.
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical “gating” distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working
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.
Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Ohzeki, Masayuki
2013-09-01
quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.
Kadmensky, S. G.
2007-09-15
In the framework of the quantum theory of spontaneous and low-energy induced fission, the nature of quantum and thermodynamical properties of a fissioning system is analyzed taking into account adiabatic and nonadiabatic modes of motion for different fission stages. It is shown that, owing to the influence of the Coriolis interaction, the states of the fissile nucleus and of primary fission products are cold and strongly nonequilibrium. The important role of superfluid and pairing nucleon-nucleon correlations for binary and ternary fission is demonstrated. The mechanism of pumping of high values of relative orbital momenta and spins of fission fragments for binary and ternary fission and the nonevaporation mechanism of formation of third particles for ternary fission are investigated. The anisotropies and P-odd, P-even, and T-odd asymmetries for angular distributions of fission products are analyzed.
Towards Quantum Computing With Light
NASA Astrophysics Data System (ADS)
Pysher, Matthew
This thesis presents experimental progress towards the realization of an optical quantum computer. Quantum computers replace the bits used in classical computing with quantum systems and promise an exponential speedup over their classical counterparts for certain tasks such as integer factoring and the simulation of quantum systems. A recently proposed quantum computing protocol known as one-way quantum computing has paved the way for the use of light in a functional quantum computer. One-way quantum computing calls for the generation of a large (consisting of many subsystems) entangled state known as a cluster state to serve as a quantum register. Entangled states are comprised of subsystems linked in such a way that the state cannot be separated into individual components. A recent proposal has shown that is possible to make arbitrarily large cluster states by linking the resonant frequency modes of a single optical parametric oscillator (OPO). In this thesis, we present two major steps towards the creation of such a cluster state. Namely, we successfully design and test the exotic nonlinear crystal needed in this proposal and use a slight variation on this proposal to simultaneously create over 15 four-mode cluster states in a single OPO. We also explore the possibility of scaling down the physical size of an optical quantum computer by generating squeezed states of light in a compact optical waveguide. Additionally, we investigate photon-number-resolving measurements on continuous quantum light sources, which will be necessary to obtain the desired speedups for a quantum computer over a classical computer.
Hoang, Thai M; Bharath, Hebbe M; Boguslawski, Matthew J; Anquez, Martin; Robbins, Bryce A; Chapman, Michael S
2016-08-23
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.
Spectral-gap analysis for efficient tunneling in quantum adiabatic optimization
NASA Astrophysics Data System (ADS)
Brady, Lucas T.; van Dam, Wim
2016-09-01
We investigate the efficiency of quantum adiabatic optimization when overcoming potential barriers to get from a local to a global minimum. Specifically we look at n qubit systems with symmetric cost functions f :{0,1 } n→R , where the ground state must tunnel through a potential barrier of width nα and height nβ. By the quantum adiabatic theorem the time delay sufficient to ensure tunneling grows quadratically with the inverse spectral gap during this tunneling process. We analyze barrier sizes with 1 /2 ≤α +β and α <1 /2 and show that the minimum gap scales polynomially as n1 /2 -α -β when 2 α +β ≤1 and exponentially as n-β /2exp(-C n(2 α +β -1 )/2) when 1 <2 α +β . Our proof uses elementary techniques and confirms and extends an unpublished folklore result by Goldstone from 2002, which used large spin and instanton methods. Parts of our result also refine recent results by Kong and Crosson [arXiv:1511.06991] and Jiang et al. [arXiv:1603.01293] about the exponential gap scaling.
Hoang, Thai M.; Bharath, Hebbe M.; Boguslawski, Matthew J.; Anquez, Martin; Robbins, Bryce A.; Chapman, Michael S.
2016-01-01
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu–Goldstone modes and massive Anderson–Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble–Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition. PMID:27503886
NASA Astrophysics Data System (ADS)
Hoang, Thai M.; Bharath, Hebbe M.; Boguslawski, Matthew J.; Anquez, Martin; Robbins, Bryce A.; Chapman, Michael S.
2016-08-01
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.
Quantum Nash Equilibria and Quantum Computing
NASA Astrophysics Data System (ADS)
Fellman, Philip Vos; Post, Jonathan Vos
In 2004, At the Fifth International Conference on Complex Systems, we drew attention to some remarkable findings by researchers at the Santa Fe Institute (Sato, Farmer and Akiyama, 2001) about hitherto unsuspected complexity in the Nash Equilibrium. As we progressed from these findings about heteroclinic Hamiltonians and chaotic transients hidden within the learning patterns of the simple rock-paper-scissors game to some related findings on the theory of quantum computing, one of the arguments we put forward was just as in the late 1990's a number of new Nash equilibria were discovered in simple bi-matrix games (Shubik and Quint, 1996; Von Stengel, 1997, 2000; and McLennan and Park, 1999) we would begin to see new Nash equilibria discovered as the result of quantum computation. While actual quantum computers remain rather primitive (Toibman, 2004), and the theory of quantum computation seems to be advancing perhaps a bit more slowly than originally expected, there have, nonetheless, been a number of advances in computation and some more radical advances in an allied field, quantum game theory (Huberman and Hogg, 2004) which are quite significant. In the course of this paper we will review a few of these discoveries and illustrate some of the characteristics of these new "Quantum Nash Equilibria". The full text of this research can be found at http://necsi.org/events/iccs6/viewpaper.php?id-234
Simulating chemistry using quantum computers.
Kassal, Ivan; Whitfield, James D; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán
2011-01-01
The difficulty of simulating quantum systems, well known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.
Algorithms on ensemble quantum computers.
Boykin, P Oscar; Mor, Tal; Roychowdhury, Vwani; Vatan, Farrokh
2010-06-01
In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and σ(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement.
Error suppression for Hamiltonian quantum computing in Markovian environments
NASA Astrophysics Data System (ADS)
Marvian, Milad; Lidar, Daniel A.
2017-03-01
Hamiltonian quantum computing, such as the adiabatic and holonomic models, can be protected against decoherence using an encoding into stabilizer subspace codes for error detection and the addition of energy penalty terms. This method has been widely studied since it was first introduced by Jordan, Farhi, and Shor (JFS) in the context of adiabatic quantum computing. Here, we extend the original result to general Markovian environments, not necessarily in Lindblad form. We show that the main conclusion of the original JFS study holds under these general circumstances: Assuming a physically reasonable bath model, it is possible to suppress the initial decay out of the encoded ground state with an energy penalty strength that grows only logarithmically in the system size, at a fixed temperature.
Causo, Maria Serena; Ciccotti, Giovanni; Montemayor, Daniel; Bonella, Sara; Coker, David F
2005-04-14
We generalize the linearized path integral approach to evaluate quantum time correlation functions for systems best described by a set of nuclear and electronic degrees of freedom, restricting ourselves to the adiabatic approximation. If the operators in the correlation function are nondiagonal in the electronic states, then this adiabatic linearized path integral approximation for the thermal averaged quantum dynamics presents interesting and distinctive features, which we derive and explore in this paper. The capability of these approximations to accurately reproduce the behavior of physical systems is demonstrated by calculating the diffusion constant for an excess electron in a metal-molten salt solution.
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.
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).
Geometric methods in quantum computation
NASA Astrophysics Data System (ADS)
Zhang, Jun
Recent advances in the physical sciences and engineering have created great hopes for new computational paradigms and substrates. One such new approach is the quantum computer, which holds the promise of enhanced computational power. Analogous to the way a classical computer is built from electrical circuits containing wires and logic gates, a quantum computer is built from quantum circuits containing quantum wires and elementary quantum gates to transport and manipulate quantum information. Therefore, design of quantum gates and quantum circuits is a prerequisite for any real application of quantum computation. In this dissertation we apply geometric control methods from differential geometry and Lie group representation theory to analyze the properties of quantum gates and to design optimal quantum circuits. Using the Cartan decomposition and the Weyl group, we show that the geometric structure of nonlocal two-qubit gates is a 3-Torus. After further reducing the symmetry, the geometric representation of nonlocal gates is seen to be conveniently visualized as a tetrahedron. Each point in this tetrahedron except on the base corresponds to a different equivalent class of nonlocal gates. This geometric representation is one of the cornerstones for the discussion on quantum computation in this dissertation. We investigate the properties of those two-qubit operations that can generate maximal entanglement. It is an astonishing finding that if we randomly choose a two-qubit operation, the probability that we obtain a perfect entangler is exactly one half. We prove that given a two-body interaction Hamiltonian, it is always possible to explicitly construct a quantum circuit for exact simulation of any arbitrary nonlocal two-qubit gate by turning on the two-body interaction for at most three times, together with at most four local gates. We also provide an analytic approach to construct a universal quantum circuit from any entangling gate supplemented with local gates
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.
Efficient universal blind quantum computation.
Giovannetti, Vittorio; Maccone, Lorenzo; Morimae, Tomoyuki; Rudolph, Terry G
2013-12-06
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.
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately. PMID:26738875
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-07
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.
NASA Astrophysics Data System (ADS)
Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can
2016-01-01
High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.
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
Insecurity of quantum secure computations
NASA Astrophysics Data System (ADS)
Lo, Hoi-Kwong
1997-08-01
It had been widely claimed that quantum mechanics can protect private information during public decision in, for example, the so-called two-party secure computation. If this were the case, quantum smart-cards, storing confidential information accessible only to a proper reader, could prevent fake teller machines from learning the PIN (personal identification number) from the customers' input. Although such optimism has been challenged by the recent surprising discovery of the insecurity of the so-called quantum bit commitment, the security of quantum two-party computation itself remains unaddressed. Here I answer this question directly by showing that all one-sided two-party computations (which allow only one of the two parties to learn the result) are necessarily insecure. As corollaries to my results, quantum one-way oblivious password identification and the so-called quantum one-out-of-two oblivious transfer are impossible. I also construct a class of functions that cannot be computed securely in any two-sided two-party computation. Nevertheless, quantum cryptography remains useful in key distribution and can still provide partial security in ``quantum money'' proposed by Wiesner.
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.
Quantum Estimation, meet Computational Statistics; Computational Statistics, meet Quantum Estimation
NASA Astrophysics Data System (ADS)
Ferrie, Chris; Granade, Chris; Combes, Joshua
2013-03-01
Quantum estimation, that is, post processing data to obtain classical descriptions of quantum states and processes, is an intractable problem--scaling exponentially with the number of interacting systems. Thankfully there is an entire field, Computational Statistics, devoted to designing algorithms to estimate probabilities for seemingly intractable problems. So, why not look to the most advanced machine learning algorithms for quantum estimation tasks? We did. I'll describe how we adapted and combined machine learning methodologies to obtain an online learning algorithm designed to estimate quantum states and processes.
Computational Power of Quantum Machines, Quantum Grammars and Feasible Computation
NASA Astrophysics Data System (ADS)
Krishnamurthy, E. V.
This paper studies the computational power of quantum computers to explore as to whether they can recognize properties which are in nondeterministic polynomial-time class (NP) and beyond. To study the computational power, we use the Feynman's path integral (FPI) formulation of quantum mechanics. From a computational point of view the Feynman's path integral computes a quantum dynamical analogue of the k-ary relation computed by an Alternating Turing machine (ATM) using AND-OR Parallelism. Hence, if we can find a suitable mapping function between an instance of a mathematical problem and the corresponding interference problem, using suitable potential functions for which FPI can be integrated exactly, the computational power of a quantum computer can be bounded to that of an alternating Turing machine that can solve problems in NP (e.g, factorization problem) and in polynomial space. Unfortunately, FPI is exactly integrable only for a few problems (e.g., the harmonic oscillator) involving quadratic potentials; otherwise, they may be only approximately computable or noncomputable. This means we cannot in general solve all quantum dynamical problems exactly except for those special cases of quadratic potentials, e.g., harmonic oscillator. Since there is a one to one correspondence between the quantum mechanical problems that can be analytically solved and the path integrals that can be exactly evaluated, we can say that the noncomputability of FPI implies quantum unsolvability. This is the analogue of classical unsolvability. The Feynman's path graph can be considered as a semantic parse graph for the quantum mechanical sentence. It provides a semantic valuation function of the terminal sentence based on probability amplitudes to disambiguate a given quantum description and obtain an interpretation in a linear time. In Feynman's path integral, the kernels are partially ordered over time (different alternate paths acting concurrently at the same time) and multiplied
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
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.
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 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
Optimizing Adiabaticity in NMR
NASA Astrophysics Data System (ADS)
Vandermause, Jonathan; Ramanathan, Chandrasekhar
We demonstrate the utility of Berry's superadiabatic formalism for numerically finding control sequences that implement quasi-adiabatic unitary transformations. Using an iterative interaction picture, we design a shortcut to adiabaticity that reduces the time required to perform an adiabatic inversion pulse in liquid state NMR. We also show that it is possible to extend our scheme to two or more qubits to find adiabatic quantum transformations that are allowed by the control algebra, and demonstrate a two-qubit entangling operation in liquid state NMR. We examine the pulse lengths at which the fidelity of these adiabatic transitions break down and compare with the quantum speed limit.
Chen, Ye-Hong; Xia, Yan; Song, Jie; Chen, Qing-Qin
2015-01-01
Berry’s approach on “transitionless quantum driving” shows how to set a Hamiltonian which drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final result of an adiabatic process in a shorter time. In this paper, motivated by transitionless quantum driving, we construct shortcuts to adiabatic passage in a three-atom system to create the Greenberger-Horne-Zeilinger states with the help of quantum Zeno dynamics and of non-resonant lasers. The influence of various decoherence processes is discussed by numerical simulation and the result proves that the scheme is fast and robust against decoherence and operational imperfection. PMID:26508283
Making Classical Ground State Spin Computing Fault-Tolerant
2010-06-24
teleportation ,” Phys. Rev. A, 70 (2004). [15] D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, “Adiabatic quantum computation is equiv...Adiabatic gate teleportation ,” Phys. Rev. Lett., 103, 120504 (2009). [25] D. Bacon and S. T. Flammia, “Adiabatic cluster state quantum computing...is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form
Sato, Taku J; Okuyama, Daisuke; Kimura, Hideo
2016-12-01
A tiny adiabatic-demagnetization refrigerator (T-ADR) has been developed for a commercial superconducting quantum interference device magnetometer [Magnetic Property Measurement System (MPMS) from Quantum Design]. The whole T-ADR system is fit in a cylindrical space of diameter 8.5 mm and length 250 mm, and can be inserted into the narrow sample tube of MPMS. A sorption pump is self-contained in T-ADR, and hence no complex gas handling system is necessary. With the single crystalline Gd3Ga5O12 garnet (∼2 g) used as a magnetic refrigerant, the routinely achievable lowest temperature is ∼0.56 K. The lower detection limit for a magnetization anomaly is ∼1 × 10(-7) emu, estimated from fluctuation of the measured magnetization. The background level is ∼5 × 10(-5) emu below 2 K at H = 100 Oe, which is largely attributable to a contaminating paramagnetic signal from the magnetic refrigerant.
NASA Astrophysics Data System (ADS)
Sato, Taku J.; Okuyama, Daisuke; Kimura, Hideo
2016-12-01
A tiny adiabatic-demagnetization refrigerator (T-ADR) has been developed for a commercial superconducting quantum interference device magnetometer [Magnetic Property Measurement System (MPMS) from Quantum Design]. The whole T-ADR system is fit in a cylindrical space of diameter 8.5 mm and length 250 mm, and can be inserted into the narrow sample tube of MPMS. A sorption pump is self-contained in T-ADR, and hence no complex gas handling system is necessary. With the single crystalline Gd3Ga5O12 garnet (˜2 g) used as a magnetic refrigerant, the routinely achievable lowest temperature is ˜0.56 K. The lower detection limit for a magnetization anomaly is ˜1 × 10-7 emu, estimated from fluctuation of the measured magnetization. The background level is ˜5 × 10-5 emu below 2 K at H = 100 Oe, which is largely attributable to a contaminating paramagnetic signal from the magnetic refrigerant.
Quantum computing measurement and intelligence
NASA Astrophysics Data System (ADS)
Ezziane, Zoheir
One of the grand challenges in the nanoscopic computing era is guarantees of robustness. Robust computing system design is confronted with quantum physical, probabilistic, and even biological phenomena, and guaranteeing high-reliability is much more difficult than ever before. Scaling devices down to the level of single electron operation will bring forth new challenges due to probabilistic effects and uncertainty in guaranteeing "zero-one" based computing. Minuscule devices imply billions of devices on a single chip, which may help mitigate the challenge of uncertainty by replication and redundancy. However, such device densities will create a design and validation nightmare with the sheer scale. The questions that confront computer engineers regarding the current status of nanocomputing material and the reliability of systems built from such minuscule devices are difficult to articulate and answer. This article illustrates and discusses two types of quantum algorithms as follows: (1) a simple quantum algorithm and (2) a quantum search algorithm. This article also presents a review of recent advances in quantum computing and intelligence and presents major achievements and obstacles for researchers in the near future.
Delegating private quantum computations12
NASA Astrophysics Data System (ADS)
Broadbent, Anne
2015-09-01
We give a protocol for the delegation of quantum computation on encrypted data. More specifically, we show that in a client-server scenario, where the client holds the encryption key for an encrypted quantum register held by the server, it is possible for the server to perform a universal set of quantum gates on the quantum data. All Clifford group gates are non-interactive, while the remaining non-Clifford group gate that we implement (the p/8 gate) requires the client to prepare and send a single random auxiliary qubit (chosen among four possibilities), and exchange classical communication. This construction improves on previous work, which requires either multiple auxiliary qubits or two-way quantum communication. Using a reduction to an entanglement-based protocol, we show privacy against any adversarial server according to a simulation-based security definition.
Quantum-enhanced Sensing and Efficient Quantum Computation
2015-07-27
AFRL-AFOSR-UK-TR-2015-0039 Quantum -enhanced sensing and efficient quantum computation Ian Walmsley THE UNIVERSITY OF...COVERED (From - To) 1 February 2013 - 31 January 2015 4. TITLE AND SUBTITLE Quantum -enhanced sensing and efficient quantum computation 5a. CONTRACT...accuracy. The system was used to improve quantum boson sampling tests. 15. SUBJECT TERMS EOARD, Quantum Information Processing, Transition Edge Sensors
Deng, Jiawen; Wang, Qing-hai; Liu, Zhihao; Hänggi, Peter; Gong, Jiangbin
2013-12-01
Under a general framework, shortcuts to adiabatic processes are shown to be possible in classical systems. We study the distribution function of the work done on a small system initially prepared at thermal equilibrium. We find that the work fluctuations can be significantly reduced via shortcuts to adiabatic processes. For example, in the classical case, probabilities of having very large or almost zero work values are suppressed. In the quantum case, negative work may be totally removed from the otherwise non-positive-definite work values. We also apply our findings to a micro Otto-cycle-based heat engine. It is shown that the use of shortcuts, which directly enhances the engine output power, can also increase the heat-engine efficiency substantially, in both quantum and classical regimes.
A Short Survey on Quantum Computers
Kanamori, Yoshito; Yoo, Seong-Moo; Pan, W. D.; Sheldon, Frederick T
2006-01-01
Quantum computing is an emerging technology. The clock frequency of current computer processor systems may reach about 40 GHz within the next 10 years. By then, one atom may represent one bit. Electrons under such conditions are no longer described by classical physics and a new model of the computer may be necessary by then. The quantum computer is one proposal that may have merit in dealing with the problems associated with the fact that certain important computationally intense problems present that current (classical) computers cannot solve because they require too much processing time. For example, Shor's algorithm performs factoring a large integer in polynomial time while classical factoring algorithms can do it in exponential time. In this paper we briefly survey the current status of quantum computers, quantum computer systems, and quantum simulators. Keywords Classical computers, quantum computers, quantum computer systems, quantum simulators, Shor's algorithm.
NASA Astrophysics Data System (ADS)
Jia, Dongming; Manz, Jörn; Paulus, Beate; Pohl, Vincent; Tremblay, Jean Christophe; Yang, Yonggang
2017-01-01
We design four linearly x- and y-polarized as well as circularly right (+) and left (-) polarized, resonant π / 2 -laser pulses that prepare the model benzene molecule in four different degenerate superposition states. These consist of equal (0.5) populations of the electronic ground state S0 (1A1g) plus one of four degenerate excited states, all of them accessible by dipole-allowed transitions. Specifically, for the molecule aligned in the xy-plane, these excited states include different complex-valued linear combinations of the 1E1u,x and 1E1u,y degenerate states. As a consequence, the laser pulses induce four different types of periodic adiabatic attosecond (as) charge migrations (AACM) in benzene, all with the same period, 504 as, but with four different types of angular fluxes. One of the characteristic differences of these fluxes are the two angles for zero fluxes, which appear as the instantaneous angular positions of the "source" and "sink" of two equivalent, or nearly equivalent branches of the fluxes which flow in pincer-type patterns from one molecular site (the "source") to the opposite one (the "sink"). These angles of zero fluxes are either fixed at the positions of two opposite carbon nuclei in the yz-symmetry plane, or at the centers of two opposite carbon-carbon bonds in the xz-symmetry plane, or the angles of zero fluxes rotate in angular forward (+) or backward (-) directions, respectively. As a resume, our quantum model simulations demonstrate quantum control of the electronic fluxes during AACM in degenerate superposition states, in the attosecond time domain, with the laser polarization as the key knob for control.
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
Semiconductor adiabatic qubits
Carroll, Malcolm S.; Witzel, Wayne; Jacobson, Noah Tobias; Ganti, Anand; Landahl, Andrew J.; Lilly, Michael; Nguyen, Khoi Thi; Bishop, Nathaniel; Carr, Stephen M.; Bussmann, Ezra; Nielsen, Erik; Levy, James Ewers; Blume-Kohout, Robin J.; Rahman, Rajib
2016-12-27
A quantum computing device that includes a plurality of semiconductor adiabatic qubits is described herein. The qubits are programmed with local biases and coupling terms between qubits that represent a problem of interest. The qubits are initialized by way of a tuneable parameter, a local tunnel coupling within each qubit, such that the qubits remain in a ground energy state, and that initial state is represented by the qubits being in a superposition of |0> and |1> states. The parameter is altered over time adiabatically or such that relaxation mechanisms maintain a large fraction of ground state occupation through decreasing the tunnel coupling barrier within each qubit with the appropriate schedule. The final state when tunnel coupling is effectively zero represents the solution state to the problem represented in the |0> and |1> basis, which can be accurately read at each qubit location.
Nanophotonic quantum computer based on atomic quantum transistor
Andrianov, S N; Moiseev, S A
2015-10-31
We propose a scheme of a quantum computer based on nanophotonic elements: two buses in the form of nanowaveguide resonators, two nanosized units of multiatom multiqubit quantum memory and a set of nanoprocessors in the form of photonic quantum transistors, each containing a pair of nanowaveguide ring resonators coupled via a quantum dot. The operation modes of nanoprocessor photonic quantum transistors are theoretically studied and the execution of main logical operations by means of them is demonstrated. We also discuss the prospects of the proposed nanophotonic quantum computer for operating in high-speed optical fibre networks. (quantum computations)
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.
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
An Early Quantum Computing Proposal
Lee, Stephen Russell; Alexander, Francis Joseph; Barros, Kipton Marcos; Daniels, Marcus G.; Gattiker, James R.; Hamada, Michael Scott; Howse, James Walter; Loncaric, Josip; Pakin, Scott D.; Somma, Rolando Diego; Vernon, Louis James
2016-04-04
The D-Wave 2X is the third generation of quantum processing created by D-Wave. NASA (with Google and USRA) and Lockheed Martin (with USC), both own D-Wave systems. Los Alamos National Laboratory (LANL) purchased a D-Wave 2X in November 2015. The D-Wave 2X processor contains (nominally) 1152 quantum bits (or qubits) and is designed to specifically perform quantum annealing, which is a well-known method for finding a global minimum of an optimization problem. This methodology is based on direct execution of a quantum evolution in experimental quantum hardware. While this can be a powerful method for solving particular kinds of problems, it also means that the D-Wave 2X processor is not a general computing processor and cannot be programmed to perform a wide variety of tasks. It is a highly specialized processor, well beyond what NNSA currently thinks of as an “advanced architecture.”A D-Wave is best described as a quantum optimizer. That is, it uses quantum superposition to find the lowest energy state of a system by repeated doses of power and settling stages. The D-Wave produces multiple solutions to any suitably formulated problem, one of which is the lowest energy state solution (global minimum). Mapping problems onto the D-Wave requires defining an objective function to be minimized and then encoding that function in the Hamiltonian of the D-Wave system. The quantum annealing method is then used to find the lowest energy configuration of the Hamiltonian using the current D-Wave Two, two-level, quantum processor. This is not always an easy thing to do, and the D-Wave Two has significant limitations that restrict problem sizes that can be run and algorithmic choices that can be made. Furthermore, as more people are exploring this technology, it has become clear that it is very difficult to come up with general approaches to optimization that can both utilize the D-Wave and that can do better than highly developed algorithms on conventional computers for
Computational quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, Rainer
2006-05-01
I will give an overview on recent attempts to solve the time-dependent Dirac equation for the electron-positron field operator. These numerical solutions permit a first temporally and spatially resolved insight into the mechanisms of how an electron-positron pair can be created from vacuum in a very strong force field. This approach has helped to illuminate a wide range of controversial questions. Some of these questions arise for complicated physical situations such as how an electron scatters off a supercritical potential barrier (Klein paradox). This requires the application of quantum field theory to study the combined effect of the pair-production due to the supercriticality of the potential together with the scattering at the barrier involving the Pauli-principle. Other phenomena include Schr"odinger's Zitterbewegung and the localization problem for a relativistic particle. This work has been supported by the NSF and Research Corporation. P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 93, 043004 (2004). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).
Experimental demonstration of blind quantum computing
NASA Astrophysics Data System (ADS)
Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joe; Zeilinger, Anton; Walther, Philip
2012-02-01
Quantum computers are among the most promising applications of quantum-enhanced technologies. Quantum effects such as superposition and entanglement enable computational speed-ups that are unattainable using classical computers. The challenges in realising quantum computers suggest that in the near future, only a few facilities worldwide will be capable of operating such devices. In order to exploit these computers, users would seemingly have to give up their privacy. It was recently shown that this is not the case and that, via the universal blind quantum computation protocol, quantum mechanics provides a way to guarantee that the user's data remain private. Here, we demonstrate the first experimental version of this protocol using polarisation-entangled photonic qubits. We demonstrate various blind one- and two-qubit gate operations as well as blind versions of the Deutsch's and Grover's algorithms. When the technology to build quantum computers becomes available, this will become an important privacy-preserving feature of quantum information processing.
Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires
NASA Astrophysics Data System (ADS)
Halperin, Bertrand I.; Oreg, Yuval; Stern, Ady; Refael, Gil; Alicea, Jason; von Oppen, Felix
2012-04-01
It has been proposed that localized zero-energy Majorana states can be realized in a two-dimensional network of quasi-one-dimensional semiconductor wires that are proximity coupled to a bulk superconductor. The wires should have strong spin-orbit coupling with appropriate symmetry, and their electrons should be partially polarized by a strong Zeeman field. Then, if the Fermi level is in an appropriate range, the wire can be in a topological superconducting phase, with Majorana states that occur at wire ends and at Y junctions, where three topological superconductor segments may be joined. Here we generalize these ideas to consider a three-dimensional network. The positions of Majorana states can be manipulated, and their non-Abelian properties made visible, by using external gates to selectively deplete portions of the network or by physically connecting and redividing wire segments. Majorana states can also be manipulated by reorientations of the Zeeman field on a wire segment, by physically rotating the wire about almost any axis, or by evolution of the phase of the order parameter in the proximity-coupled superconductor. We show how to keep track of sign changes in the zero-energy Hilbert space during adiabatic manipulations by monitoring the evolution of each Majorana state separately, rather than keeping track of the braiding of all possible pairs. This has conceptual advantages in the case of a three-dimensional network, and may be computationally useful even in two dimensions, if large numbers of Majorana sites are involved.
Adiabatic approximation via hodograph translation and zero-curvature equations
NASA Astrophysics Data System (ADS)
Karasev, M. V.
2014-04-01
For quantum as well classical slow-fast systems, we develop a general method which allows one to compute the adiabatic invariant (approximate integral of motion), its symmetries, the adiabatic guiding center coordinates and the effective scalar Hamiltonian in all orders of a small parameter. The scheme does not exploit eigenvectors or diagonalization, but is based on the ideas of isospectral deformation and zero-curvature equations, where the role of "time" is played by the adiabatic (quantization) parameter. The algorithm includes the construction of the zero-curvature adiabatic connection and its splitting generated by averaging up to an arbitrary order in the small parameter.
Ancilla-driven universal blind quantum computation
NASA Astrophysics Data System (ADS)
Sueki, Takahiro; Koshiba, Takeshi; Morimae, Tomoyuki
2013-06-01
Blind quantum computation is a new quantum secure protocol, which enables Alice who does not have enough quantum technology to delegate her computation to Bob who has a fully fledged quantum power without revealing her input, output, and algorithm. So far, blind quantum computation has been considered only for the circuit model and the measurement-based model. Here we consider the possibility and the limitation of blind quantum computation in the ancilla-driven model, which is a hybrid of the circuit and the measurement-based models.
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
NASA Technical Reports Server (NTRS)
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Finding Adiabatically Bound Anions of Guanine through a Combinatorial Computational Approach
Haranczyk, Maciej; Gutowski, Maciej S.
2005-09-15
In summary, guanine supports many adiabatically bound valence anions, which result from enamine-imine transformations of the most stable neutral tautomers. These stable anionic tautomers have been found using combinatorial-computational prescreening at the B3LYP level of theory followed by CCSD(T)/aug-cc-pVDZ calculations. The new anionic tautomers contradict a common opinion that guanine has the lowest electron affinity among nucleobases. The new anionic tautomers might be formed in the course of dissociative electron attachment followed by a hydrogen atom attachment to a carbon atom. They might affect the structure and properties of DNA and RNA exposed to low-energy electrons. Chemical transformations of DNA triggered by the new anionic tautomers will be explored in our future studies.
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 chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
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.
Holonomic Quantum Computation in Subsystems
NASA Astrophysics Data System (ADS)
Oreshkov, Ognyan
2009-08-01
We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.
Multibit gates for quantum computing.
Wang, X; Sørensen, A; Mølmer, K
2001-04-23
We present a general technique to implement products of many qubit operators communicating via a joint harmonic oscillator degree of freedom in a quantum computer. By conditional displacements and rotations we can implement Hamiltonians which are trigonometric functions of qubit operators. With such operators we can effectively implement higher order gates such as Toffoli gates and C(n)-NOT gates, and we show that the entire Grover search algorithm can be implemented in a direct way.
Toward a superconducting quantum computer. Harnessing macroscopic quantum coherence.
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.
Quantum Computing and the Onset of Quantum Chaotic Motion
2007-11-02
for Nuclear Theory Program on "Chaos and Interactions: from Nuclei to Quantum Dots’", University of Washington, Seattle, USA, 17 July, 2002. I...to Quantum Dots’", University of Washington, Seattle, USA, 17 July, 2002. G. Casati “Quantum computers and quantum chaos” Institute for Nuclear...Theory Program on "Chaos and Interactions: from Nuclei to Quantum Dots’", University of Washington, Seattle, USA, 17 July, 2002. 2. Scientific
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.
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
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.
Efficient simulation of open quantum system in duality quantum computing
NASA Astrophysics Data System (ADS)
Wei, Shi-Jie; Long, Gui-Lu
2016-11-01
Practical quantum systems are open systems due to interactions with their environment. Understanding the evolution of open systems dynamics is important for quantum noise processes , designing quantum error correcting codes, and performing simulations of open quantum systems. Here we proposed an efficient quantum algorithm for simulating the evolution of an open quantum system on a duality quantum computer. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality algorithm, the time evolution of open quantum system is realized by using Kraus operators which is naturally realized in duality quantum computing. Compared to the Lloyd's quantum algorithm [Science.273, 1073(1996)] , the dependence on the dimension of the open quantum system in our algorithm is decreased. Moreover, our algorithm uses a truncated Taylor series of the evolution operators, exponentially improving the performance on the precision compared with existing quantum simulation algorithms with unitary evolution operations.
Cotton, Stephen J.; Miller, William H.
2013-12-21
A recently described symmetrical windowing methodology [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] for quasi-classical trajectory simulations is applied here to the Meyer-Miller [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] model for the electronic degrees of freedom in electronically non-adiabatic dynamics. Results generated using this classical approach are observed to be in very good agreement with accurate quantum mechanical results for a variety of test applications, including problems where coherence effects are significant such as the challenging asymmetric spin-boson system.
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…
On the General Class of Models of Adiabatic Evolution
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Songfeng; Liu, Fang
2016-10-01
The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown [8] that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.
Efficient free energy calculations of quantum systems through computer simulations
NASA Astrophysics Data System (ADS)
Antonelli, Alex; Ramirez, Rafael; Herrero, Carlos; Hernandez, Eduardo
2009-03-01
In general, the classical limit is assumed in computer simulation calculations of free energy. This approximation, however, is not justifiable for a class of systems in which quantum contributions for the free energy cannot be neglected. The inclusion of quantum effects is important for the determination of reliable phase diagrams of these systems. In this work, we present a new methodology to compute the free energy of many-body quantum systems [1]. This methodology results from the combination of the path integral formulation of statistical mechanics and efficient non-equilibrium methods to estimate free energy, namely, the adiabatic switching and reversible scaling methods. A quantum Einstein crystal is used as a model to show the accuracy and reliability the methodology. This new method is applied to the calculation of solid-liquid coexistence properties of neon. Our findings indicate that quantum contributions to properties such as, melting point, latent heat of fusion, entropy of fusion, and slope of melting line can be up to 10% of the calculated values using the classical approximation. [1] R. M. Ramirez, C. P. Herrero, A. Antonelli, and E. R. Hernández, Journal of Chemical Physics 129, 064110 (2008)
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.
Quantum computing: In the 'death zone'?
NASA Astrophysics Data System (ADS)
van Dam, Wim
2007-04-01
An event advertised as the first demonstration of a commercial quantum computer raises the question of how far one can go with a 'do not care' attitude towards imperfections, without losing the quantum advantage.
Stimulated Raman adiabatic passage in a three-level superconducting circuit
Kumar, K. S.; Vepsäläinen, A.; Danilin, S.; Paraoanu, G. S.
2016-01-01
The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering—enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic–adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level. PMID:26902454
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.
Cencek, Wojciech; Przybytek, Michał; Komasa, Jacek; Mehl, James B; Jeziorski, Bogumił; Szalewicz, Krzysztof
2012-06-14
The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound
Mineo, H.; Kuo, J. L.; Niu, Y. L.; Lin, S. H.; Fujimura, Y.
2015-08-28
The results of application of the quantum-mechanical adiabatic theory to vibrational predissociation (VPD) of water dimers, (H{sub 2}O){sub 2} and (D{sub 2}O){sub 2}, are presented. We consider the VPD processes including the totally symmetric OH mode of the dimer and the bending mode of the fragment. The VPD in the adiabatic representation is induced by breakdown of the vibrational adiabatic approximation, and two types of nonadiabatic coupling matrix elements are involved: one provides the VPD induced by the low-frequency dissociation mode and the other provides the VPD through channel interactions induced by the low-frequency modes. The VPD rate constants were calculated using the Fermi golden rule expression. A closed form for the nonadiabatic transition matrix element between the discrete and continuum states was derived in the Morse potential model. All of the parameters used were obtained from the potential surfaces of the water dimers, which were calculated by the density functional theory procedures. The VPD rate constants for the two processes were calculated in the non-Condon scheme beyond the so-called Condon approximation. The channel interactions in and between the initial and final states were taken into account, and those are found to increase the VPD rates by 3(1) orders of magnitude for the VPD processes in (H{sub 2}O){sub 2} ((D{sub 2}O){sub 2}). The fraction of the bending-excited donor fragments is larger than that of the bending-excited acceptor fragments. The results obtained by quantum-mechanical approach are compared with both experimental and quasi-classical trajectory calculation results.
Blind topological measurement-based quantum computation.
Morimae, Tomoyuki; Fujii, Keisuke
2012-01-01
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.
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.
Wireless adiabatic power transfer
Rangelov, A.A.; Suchowski, H.; Silberberg, Y.; Vitanov, N.V.
2011-03-15
Research Highlights: > Efficient and robust mid-range wireless energy transfer between two coils. > The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. > Wireless energy transfer is insensitive to any resonant constraints. > Wireless energy transfer is insensitive to noise in the neighborhood of the coils. - Abstract: We propose a technique for efficient mid-range wireless power transfer between two coils, by adapting the process of adiabatic passage for a coherently driven two-state quantum system to the realm of wireless energy transfer. The proposed technique is shown to be robust to noise, resonant constraints, and other interferences that exist in the neighborhood of the coils.
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.
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.
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.
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.
Quantum computing with realistically noisy devices.
Knill, E
2005-03-03
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…
Preparation of Quantum States of H2 using Stark-induced Adiabatic Raman Passage (SARP)
2013-12-02
diatomic molecule to an excited rovibrational eigenstate. Based on this idea we carried out experiments using a sequence of overlapping pump (532 nm...overlapping pump and Stokes laser pulses it is possible to transfer the complete ground state population of an isolated diatomic molecule to an excited...wide energy gap ( diatoms like H2, D2, HCl, N2) between the ground and excited electronic states, where other adiabatic methods like STIRAP or SCRAP
Adiabatic quantum state transfer in tight-binding chains using periodic driving fields
NASA Astrophysics Data System (ADS)
Longhi, S.
2014-09-01
A method for high-fidelity coherent adiabatic transport in a zig-zag tight-binding chain, based on application of two external periodic driving fields, is theoretically proposed. The method turns out to be robust against imperfections and disorder of the static lattice Hamiltonian, is tolerant to next-nearest neighborhood interactions, and enables coherent transport in long chains without the need for a local control and timing of the trapping potential.
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
Computational quantum-classical boundary of noisy commuting quantum circuits.
Fujii, Keisuke; Tamate, Shuhei
2016-05-18
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.
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-08
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.
Adiabatic state preparation study of methylene
Veis, Libor Pittner, Jiří
2014-06-07
Quantum computers attract much attention as they promise to outperform their classical counterparts in solving certain type of problems. One of them with practical applications in quantum chemistry is simulation of complex quantum systems. An essential ingredient of efficient quantum simulation algorithms are initial guesses of the exact wave functions with high enough fidelity. As was proposed in Aspuru-Guzik et al. [Science 309, 1704 (2005)], the exact ground states can in principle be prepared by the adiabatic state preparation method. Here, we apply this approach to preparation of the lowest lying multireference singlet electronic state of methylene and numerically investigate preparation of this state at different molecular geometries. We then propose modifications that lead to speeding up the preparation process. Finally, we decompose the minimal adiabatic state preparation employing the direct mapping in terms of two-qubit interactions.
Quantum Computing in a Piece of Glass
2011-01-01
enabling technology. Additionally, we give credence to the projection operator approach of Sec. 4 by applying it to a quantum teleportation (QT...computing gates. 5. QUANTUM TELEPORTATION IN GLASS To best illustrate how a quantum algorithm can be encoded within a single hologram we will focus...our attention on quantum teleportation (QT ). This three qubit gate lives in an 8-dimensional state space. It exhibits all the essential features we
Quantum Computation and NP-Complete Problems
NASA Astrophysics Data System (ADS)
Nishino, Tetsuro
In this paper, we show the following two results on the relationships between quantum computers and NP-complete problems. First, we develop a theory of bulk quantum computation such as NMR (Nuclear Magnetic Resonance) quantum computation. For this purpose, we first define bulk quantum Turing machine (BQTM for short) as a model of bulk quantum computation. Then, we show that BQTMs can solve certain instances of NP-complete problems efficiently. Next, we show that the algorithm designed by Abrams and Lloyd can be simulated by a deterministic Turing machine in polynomial space. This suggests that their algorithm, which is based on non-standard quantum mechanics, can be simulated by a standard QTM with exponential time slow down.
Parallel Environment for Quantum Computing
NASA Astrophysics Data System (ADS)
Tabakin, Frank; Diaz, Bruno Julia
2009-03-01
To facilitate numerical study of noise and decoherence in QC algorithms,and of the efficacy of error correction schemes, we have developed a Fortran 90 quantum computer simulator with parallel processing capabilities. It permits rapid evaluation of quantum algorithms for a large number of qubits and for various ``noise'' scenarios. State vectors are distributed over many processors, to employ a large number of qubits. Parallel processing is implemented by the Message-Passing Interface protocol. A description of how to spread the wave function components over many processors, along with how to efficiently describe the action of general one- and two-qubit operators on these state vectors will be delineated.Grover's search and Shor's factoring algorithms with noise will be discussed as examples. A major feature of this work is that concurrent versions of the algorithms can be evaluated with each version subject to diverse noise effects, corresponding to solving a stochastic Schrodinger equation. The density matrix for the ensemble of such noise cases is constructed using parallel distribution methods to evaluate its associated entropy. Applications of this powerful tool is made to delineate the stability and correction of QC processes using Hamiltonian based dynamics.
Composite nonadiabatic holonomic quantum computation
NASA Astrophysics Data System (ADS)
Xu, G. F.; Zhao, P. Z.; Xing, T. H.; Sjöqvist, Erik; Tong, D. M.
2017-03-01
Nonadiabatic holonomic quantum computation has a robust feature in suppressing control errors because of its holonomic feature. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces errors due to systematic errors in the control parameters. To resolve this problem, we here propose a composite scheme to realize nonadiabatic holonomic gates. Our scheme can suppress systematic errors while preserving holonomic robustness. It is particularly useful when the evolution period is shorter than the coherence time. We further show that our composite scheme can be protected by decoherence-free subspaces. In this case, the strengthened robust feature of our composite gates and the coherence stabilization virtue of decoherence-free subspaces are combined.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
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.
NASA Astrophysics Data System (ADS)
Takeuchi, Naoki; Nagasawa, Shuichi; China, Fumihiro; Ando, Takumi; Hidaka, Mutsuo; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2017-03-01
Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic with zero static power consumption and very small switching energy. In this paper, we report a new AQFP cell library designed using the AIST 10 kA cm-2 Nb high-speed standard process (HSTP), which is a high-critical-current-density version of the AIST 2.5 kA cm-2 Nb standard process (STP2). Since the intrinsic damping of the Josephson junction (JJ) of HSTP is relatively strong, shunt resistors for JJs were removed and the energy efficiency improved significantly. Also, excitation transformers in the new cells were redesigned so that the cells can operate in a four-phase excitation mode. We described the detail of HSTP and the AQFP cell library designed using HSTP, and showed experimental results of cell test circuits.
NASA Astrophysics Data System (ADS)
Kaestner, Bernd; Kashcheyevs, Vyacheslavs
2015-10-01
Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property—the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of {{q}\\text{e}} f as function of control parameters, where {{q}\\text{e}} is the electron charge and f is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These devices allow modulation of charge exchange rates between the dot and the leads over many orders of magnitude and enable trapping of a precise number of electrons far away from equilibrium with the leads. The corresponding non-adiabatic pumping protocols focus on understanding of separate parts of the pumping cycle associated with charge loading, capture and release. In this report we review realizations, models and metrology applications of quantized charge pumps based on tunable-barrier quantum dots.
2015-11-23
The new refrigerator has been installed and is now fully operational. The PI has intensive research efforts in the area of Quantum Information... Quantum Information Science with Superconducting Circuits The views, opinions and/or findings contained in this report are those of the author(s) and... quantum information REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR/MONITOR’S ACRONYM(S) ARO 8. PERFORMING
Pure spin current induced by adiabatic quantum pumping in zigzag-edged graphene nanoribbons
Souma, Satofumi Ogawa, Matsuto
2014-05-05
We show theoretically that pure spin current can be generated in zigzag edged graphene nanoribbons through the adiabatic pumping by edge selective pumping potentials. The origin of such pure spin current is the spin splitting of the edge localized states, which are oppositely spin polarized at opposite edges. In the proposed device, each edge of the ribbon is covered by two independent time-periodic local gate potentials with a definite phase difference, inducing the edge spin polarized current. When the pumping phase difference is opposite in sign between two edges, the total charge currents is zero and the pure edge spin current is generated.
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.
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.
Numerical characteristics of quantum computer simulation
NASA Astrophysics Data System (ADS)
Chernyavskiy, A.; Khamitov, K.; Teplov, A.; Voevodin, V.; Voevodin, Vl.
2016-12-01
The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.
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.
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.
Hyper-parallel photonic quantum computation with coupled quantum dots
Ren, Bao-Cang; Deng, Fu-Guo
2014-01-01
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. PMID:24721781
Quantum state specific reactant preparation in a molecular beam by rapid adiabatic passage
Chadwick, Helen Hundt, P. Morten; Reijzen, Maarten E. van; Yoder, Bruce L.; Beck, Rainer D.
2014-01-21
Highly efficient preparation of molecules in a specific rovibrationally excited state for gas/surface reactivity measurements is achieved in a molecular beam using tunable infrared (IR) radiation from a single mode continuous wave optical parametric oscillator (cw-OPO). We demonstrate that with appropriate focusing of the IR radiation, molecules in the molecular beam crossing the fixed frequency IR field experience a Doppler tuning that can be adjusted to achieve complete population inversion of a two-level system by rapid adiabatic passage (RAP). A room temperature pyroelectric detector is used to monitor the excited fraction in the molecular beam and the population inversion is detected and quantified using IR bleaching by a second IR-OPO. The second OPO is also used for complete population transfer to an overtone or combination vibration via double resonance excitation using two spatially separated RAP processes.
Quantum state specific reactant preparation in a molecular beam by rapid adiabatic passage
NASA Astrophysics Data System (ADS)
Chadwick, Helen; Hundt, P. Morten; van Reijzen, Maarten E.; Yoder, Bruce L.; Beck, Rainer D.
2014-01-01
Highly efficient preparation of molecules in a specific rovibrationally excited state for gas/surface reactivity measurements is achieved in a molecular beam using tunable infrared (IR) radiation from a single mode continuous wave optical parametric oscillator (cw-OPO). We demonstrate that with appropriate focusing of the IR radiation, molecules in the molecular beam crossing the fixed frequency IR field experience a Doppler tuning that can be adjusted to achieve complete population inversion of a two-level system by rapid adiabatic passage (RAP). A room temperature pyroelectric detector is used to monitor the excited fraction in the molecular beam and the population inversion is detected and quantified using IR bleaching by a second IR-OPO. The second OPO is also used for complete population transfer to an overtone or combination vibration via double resonance excitation using two spatially separated RAP processes.
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.
del Campo, Adolfo; Rams, Marek M; Zurek, Wojciech H
2012-09-14
The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.
Pyshkin, P. V.; Luo, Da-Wei; Jing, Jun; You, J. Q.; Wu, Lian-Ao
2016-01-01
Holonomic quantum computation (HQC) may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Here we show that the conventional HQC can be dramatically accelerated by using external control fields, of which the effectiveness is exclusively determined by the integral of the control fields in the time domain. This control scheme can be realized with net zero energy cost and it is fault-tolerant against fluctuation and noise, significantly relaxing the experimental constraints. We demonstrate how to realize the scheme via decoherence-free subspaces. In this way we unify quantum robustness merits of this fault-tolerant control scheme, the conventional HQC and decoherence-free subspace, and propose an expedited holonomic quantum computation protocol. PMID:27886234
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.
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.
Decoherence and a simple quantum computer
Chuang, I.L.; Yamamoto, Y.; Laflamme, R.
1995-10-01
The authors analyze the effect of decoherence on the operation of part of a simple quantum computer. The results indicate that quantum bit coding techniques may be used to mitigate the effects of two sources of decoherence - amplitude damping and phase randomization.
Experimental comparison of two quantum computing architectures
Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A.; Wright, Kenneth; Monroe, Christopher
2017-01-01
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.research.ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future. PMID:28325879
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…
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).
Optimised resource construction for verifiable quantum computation
NASA Astrophysics Data System (ADS)
Kashefi, Elham; Wallden, Petros
2017-04-01
Recent developments have brought the possibility of achieving scalable quantum networks and quantum devices closer. From the computational point of view these emerging technologies become relevant when they are no longer classically simulatable. Hence a pressing challenge is the construction of practical methods to verify the correctness of the outcome produced by universal or non-universal quantum devices. A promising approach that has been extensively explored is the scheme of verification via encryption through blind quantum computation. We present here a new construction that simplifies the required resources for any such verifiable protocol. We obtain an overhead that is linear in the size of the input (computation), while the security parameter remains independent of the size of the computation and can be made exponentially small (with a small extra cost). Furthermore our construction is generic and could be applied to any universal or non-universal scheme with a given underlying graph.
Iterated Gate Teleportation and Blind Quantum Computation.
Pérez-Delgado, Carlos A; Fitzsimons, Joseph F
2015-06-05
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.
Iterated Gate Teleportation and Blind Quantum Computation
NASA Astrophysics Data System (ADS)
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.
Delayed Commutation in Quantum Computer Networks
NASA Astrophysics Data System (ADS)
García-Escartín, Juan Carlos; Chamorro-Posada, Pedro
2006-09-01
In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communication. We propose a nonclassical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes, we can route a qubit packet after part of it has left the network node.
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.
Dilution Refrigerator Technology for Scalable Quantum Computing
2014-05-22
has successfully designed, built, tested, and delivered a cryogen free dilution refrigerator for scalable quantum computing. This document is intended... Cryogenics , quantum computing REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR/MONITOR’S ACRONYM(S) ARO 8. PERFORMING...W911NF-10-C-0004. High Precision Devices, Inc. has successfully designed, built, tested, and delivered a cryogen free dilution refrigerator for
Quantum Computer Circuit Analysis and Design
2009-02-01
is a first order nonlinear differential matrix equation of the Lax type. This report gives derivations of the Levi-Civita connection, Riemann...computational paths in the )2( nSU manifold. It is a nonlinear first-order differential matrix equation of the same form as the Lax equation for...I. L. Quantum Information and Computation; Cambridge University Press, 2000. 2. Dowling , M. R.; Nielsen, M. A. The Geometry of Quantum
EDITORIAL: Quantum Computing and the Feynman Festival
NASA Astrophysics Data System (ADS)
Brandt, Howard E.; Kim, Young S.; Man'ko, Margarita A.
2003-12-01
The Feynman Festival is a new interdisciplinary conference developed for studying Richard Feynman and his physics. The first meeting of this new conference series was held at the University of Maryland on 23--28 August 2002 (http://www.physics.umd.edu/robot/feynman.html) and the second meeting is scheduled for August 2004 at the same venue. According to Feynman, the different aspects of nature are different aspects of the same thing. Therefore, the ultimate purpose of the conference is to find Feynman's same thing from all different theories. For this reason, the first meeting of the Festival did not begin with a fixed formula, but composed its scientific programme based on responses from the entire physics community. The conference drew the most enthusiastic response from the community of quantum computing, the field initiated by Feynman. Encouraged by the response, we decided to edit a special issue of Journal of Optics B: Quantum and Semiclassical Optics on quantum computing in connection with the first Feynman Festival. The authorship is not restricted to the participants of the Feynman Festival, and all interested parties were encouraged to submit their papers on this subject. Needless to say, all the papers were peer reviewed according to the well-established standards of the journal. The subject of quantum computing is not restricted to building and operating computers. It requires a deeper understanding of how quantum mechanics works in materials as well as in our minds. Indeed, it covers the basic foundations of quantum mechanics, measurement theory, information theory, quantum optics, atomic physics and condensed matter physics. It may be necessary to develop new mathematical tools to accommodate the language that nature speaks. It is gratifying to note that this special issue contains papers covering all these aspects of quantum computing. As Feynman noted, we could be discussing these diversified issues to study one problem. In our case, this `one
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.
NASA Astrophysics Data System (ADS)
Teplukhin, Alexander; Babikov, Dmitri
2014-10-01
The adiabatically-adjusting principal-axes hyperspherical (APH) coordinates reviewed in this letter are one of the best coordinate sets developed for computational treatment of spectroscopy and dynamics of triatomic molecules. Unfortunately, it is not so easy to understand and interpret them, compared to other simpler coordinates, like valence coordinates or Jacobi coordinates. To address this issue, we developed a desktop application called APHDemo. This tool visualizes the process of adjustment of the APH coordinates to the shape of a triatomic molecule during molecular vibrations or chemical reaction, and helps to understand their physical meaning without going into complicated math.
Waveguide-QED-based photonic quantum computation.
Zheng, Huaixiu; Gauthier, Daniel J; Baranger, Harold U
2013-08-30
We propose a new scheme for quantum computation using flying qubits--propagating photons in a one-dimensional waveguide interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a four-level system, based on which photon-photon π-phase gates (CONTROLLED-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible, given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
Quantum computing in a piece of glass
NASA Astrophysics Data System (ADS)
Miller, Warner A.; Alsing, Paul M.; Kreymerman, Grigoriy; McDonald, Jonathan R.; Tison, Christopher
2011-05-01
Quantum gates and simple quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photon's linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of quantum computing within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate - the timeless nature of quantum computing. Second, photon entanglement can be encoded as a superposition state of a single photon in a higher-dimensional state space afforded by LM. Our theoretical and numerical results indicate that OptiGrate's photo-thermal refractive (PTR) glass is an enabling technology. We will review our previous design of a quantum projection operator and give credence to this approach on a representative quantum gate grounded on coupled-mode theory and numerical simulations, all with parameters consistent with PTR glass. We discuss the strengths (high efficiencies, robustness to environment) and limitations (scalability, crosstalk) of this technology. While not scalable, the utility and robustness of such optical elements for broader quantum information processing applications can be substantial.
Quantum Fourier transform in computational basis
NASA Astrophysics Data System (ADS)
Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.
2017-03-01
The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
Simulating physical phenomena with a quantum computer
NASA Astrophysics Data System (ADS)
Ortiz, Gerardo
2003-03-01
In a keynote speech at MIT in 1981 Richard Feynman raised some provocative questions in connection to the exact simulation of physical systems using a special device named a ``quantum computer'' (QC). At the time it was known that deterministic simulations of quantum phenomena in classical computers required a number of resources that scaled exponentially with the number of degrees of freedom, and also that the probabilistic simulation of certain quantum problems were limited by the so-called sign or phase problem, a problem believed to be of exponential complexity. Such a QC was intended to mimick physical processes exactly the same as Nature. Certainly, remarks coming from such an influential figure generated widespread interest in these ideas, and today after 21 years there are still some open questions. What kind of physical phenomena can be simulated with a QC?, How?, and What are its limitations? Addressing and attempting to answer these questions is what this talk is about. Definitively, the goal of physics simulation using controllable quantum systems (``physics imitation'') is to exploit quantum laws to advantage, and thus accomplish efficient imitation. Fundamental is the connection between a quantum computational model and a physical system by transformations of operator algebras. This concept is a necessary one because in Quantum Mechanics each physical system is naturally associated with a language of operators and thus can be considered as a possible model of quantum computation. The remarkable result is that an arbitrary physical system is naturally simulatable by another physical system (or QC) whenever a ``dictionary'' between the two operator algebras exists. I will explain these concepts and address some of Feynman's concerns regarding the simulation of fermionic systems. Finally, I will illustrate the main ideas by imitating simple physical phenomena borrowed from condensed matter physics using quantum algorithms, and present experimental
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.
Universal quantum computation in a semiconductor quantum wire network
NASA Astrophysics Data System (ADS)
Sau, Jay D.; Tewari, Sumanta; Das Sarma, S.
2010-11-01
Universal quantum computation (UQC) using Majorana fermions on a two-dimensional topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include any two-qubit gate and also no single-qubit π/8 phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, etc.), to which the Majorana fermions are bound in a TS medium, can be quantum coherent. We show that these obstacles can be overcome using a semiconductor quantum wire network in the vicinity of an s-wave superconductor, by constructing topologically protected two-qubit gates and any arbitrary single-qubit phase gate in a topologically unprotected manner, which can be error corrected using magic-state distillation. Thus our strategy, using a judicious combination of topologically protected and unprotected gate operations, realizes UQC on a quantum wire network with a remarkably high error threshold of 0.14 as compared to 10-3 to 10-4 in ordinary unprotected quantum computation.
Simulating fermions on a quantum computer
NASA Astrophysics Data System (ADS)
Ortiz, G.; Gubernatis, J. E.; Knill, E.; Laflamme, R.
2002-07-01
The real-time probabilistic simulation of quantum systems in classical computers is known to be limited by the so-called dynamical sign problem, a problem leading to exponential complexity. In 1981 Richard Feynman raised some provocative questions in connection to the "exact imitation" of such systems using a special device named a "quantum computer". Feynman hesitated about the possibility of imitating fermion systems using such a device. Here we address some of his concerns and, in particular, investigate the simulation of fermionic systems. We show how quantum computers avoid the sign problem in some cases by reducing the complexity from exponential to polynomial. Our demonstration is based upon the use of isomorphisms of algebras. We present specific quantum algorithms that illustrate the main points of our algebraic approach.
Quantum Optical Implementations of Quantum Computing and Quantum Informatics Protocols
2007-11-20
REPORT NUMBER Institute for Quantum Studies and Department of Physics Texas A&M University College Station, TX 77843- 4242 9. SPONSORING / MONITORING...September 30, 2007 Principal Investigators: Marlan 0. Scully and M. Subail Zubairy Institute for Quantum Studies and Department of Physics Texas A&M...Thus, N has a simple physical meaning: It is the ratio of the delay time of the buffer and the pulse duration and corresponds to the number of
Transitionless driving on adiabatic search algorithm
Oh, Sangchul; Kais, Sabre
2014-12-14
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
Transitionless driving on adiabatic search algorithm
NASA Astrophysics Data System (ADS)
Oh, Sangchul; Kais, Sabre
2014-12-01
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
Transitionless driving on adiabatic search algorithm.
Oh, Sangchul; Kais, Sabre
2014-12-14
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
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.
NASA Astrophysics Data System (ADS)
Krajewski, Florian R.; Müser, Martin H.
2005-07-01
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent H=0), there is one regime in which the chain is pinned (large masses m of chain particles) and one in which it is unpinned (small m). If the embedding potential can be classified as a random walk on large length scales ( H=1/2), then the chain is always pinned irrespective of the value of m. For H=1/2, two phonon-like branches appear in the spectra.
Triple-server blind quantum computation using entanglement swapping
NASA Astrophysics Data System (ADS)
Li, Qin; Chan, Wai Hong; Wu, Chunhui; Wen, Zhonghua
2014-04-01
Blind quantum computation allows a client who does not have enough quantum resources or technologies to achieve quantum computation on a remote quantum server such that the client's input, output, and algorithm remain unknown to the server. Up to now, single- and double-server blind quantum computation have been considered. In this work, we propose a triple-server blind computation protocol where the client can delegate quantum computation to three quantum servers by the use of entanglement swapping. Furthermore, the three quantum servers can communicate with each other and the client is almost classical since one does not require any quantum computational power, quantum memory, and the ability to prepare any quantum states and only needs to be capable of getting access to quantum channels.
Nanoscale solid-state quantum computing
NASA Astrophysics Data System (ADS)
Ardavan, A.; Austwick, M.; Benjamin, S.C.; Briggs, G.A.D.; Dennis, T.J.S.; Ferguson, A.; Hasko, D.G.; Kanai, M.; Khlobystov, A.N.; Lovett, B.W.; Morley, G.W.; Oliver, R.A.; Pettifor, D.G.; Porfyrakis, K.; Reina, J.H.; Rice, J.H.; Smith, J.D.; Taylor, R.A.; Williams, D.A.; Adelmann, C.; Mariette, H.; Hamers, R.J.
2003-07-01
Most experts agree that it is too early to say how quantum computers will eventually be built, and several nanoscale solid-state schemes are being implemented in a range of materials. Nanofabricated quantum dots can be made in designer configurations, with established technology for controlling interactions and for reading out results. Epitaxial quantum dots can be grown in vertical arrays in semiconductors, and ultrafast optical techniques are available for controlling and measuring their excitations. Single-walled carbon nanotubes can be used for molecular self-assembly of endohedral fullerenes, which can embody quantum information in the electron spin. The challenges of individual addressing in such tiny structures could rapidly become intractable with increasing numbers of qubits, but these schemes are amenable to global addressing methods for computation.
Short Introduction to Quantum Computation
2007-11-02
Yves Pomeau. Lattice-gas automata for the navier - stokes equa- tion. Physical Review Letters, 56(14):1505–1508, 1986. [8] Stephen Wolfram. Cellular...quantum mechanical descrip- tion. Secondly, since all nonrelativistic dynamics at the nano-scale are governed by the Schroedinger wave equation with a
Plasmon Resonators for Quantum Computing
2007-06-01
quantum dot. For free atoms this strong coupling is achieved using high Q optical resonators, such as ultra-low-loss bulk Fabry - Perot cavities or...TR-07-0487 11. SUPPLEMENTARY NOTES 12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Unlimited UL 13. ABSTRACT (Maximum 200 words) The
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.
Introduction to Quantum Information/Computing
2005-06-01
mωX + iP) sqrt(2mhω) BCS Theory – Named for John Bardeen , Leon Cooper, and Robert Schrieffer. According to theory, the...Theory and Reliable Communication, John Wiley & Sons 1998 2. M.A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge...France and by John Wiley & Sons. 6. H. Goldstein, Classical Mechanics, 1950 Addison-Wesley Publishing Company, Inc. 7. L.S. Brown and G
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.
Efficient quantum computing of complex dynamics.
Benenti, G; Casati, G; Montangero, S; Shepelyansky, D L
2001-11-26
We propose a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics described by the quantum sawtooth map. The numerical study of the effect of static imperfections in the quantum computer hardware shows that the main elements of the phase space structures are accurately reproduced up to a time scale which is polynomial in the number of qubits. The errors generated by these imperfections are more significant than the errors of random noise in gate operations.
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.
Theoretical studies for experimental implementation of quantum computing with trapped ions
NASA Astrophysics Data System (ADS)
Yoshimura, Bryce T.
Certain quantum many-body physics problems, such as the transverse field Ising model are intractable on a classical computer, meaning that as the number of particles grows, or spins, the amount of memory and computational time required to solve the problem exactly increases faster than a polynomial behavior. However, quantum simulators are being developed to efficiently solve quantum problems that are intractable via conventional computing. Some of the most successful quantum simulators are based on ion traps. Their success depends on the ability to achieve long coherence time, precise spin control, and high fidelity in state preparation. In this work, I present calculations that characterizes the oblate Paul trap that creates two-dimensional Coulomb crystals in a triangular lattice and phonon modes. We also calculate the spin-spin Ising-like interaction that can be generated in the oblate Paul trap using the same techinques as the linear radiofrequency Paul trap. In addition, I discuss two possible challenges that arise in the Penning trap: the effects of defects ( namely when Be+ → BeH+) and the creation of a more uniform spin-spin Ising-like interaction. We show that most properties are not significantly influenced by the appearance of defects, and that by adding two potentials to the Penning trap a more uniform spin-spin Ising-like interaction can be achieved. Next, I discuss techniques tfor preparing the ground state of the Ising-like Hamiltonian. In particular, we explore the use of the bang-bang protocol to prepare the ground state and compare optimized results to conventional adiabatic ramps ( the exponential and locally adiabatic ramp ). The bang-bang optimization in general outperforms the exponential; however the locally adiabatic ramp consistently is somewhat better. However, compared to the locally adiabatic ramp, the bang-bang optimization is simpler to implement, and it has the advantage of providingrovide a simple procedure for estimating the
Universal two-body-Hamiltonian quantum computing
NASA Astrophysics Data System (ADS)
Nagaj, Daniel
2012-03-01
We present a Hamiltonian quantum-computation scheme universal for quantum computation. Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of constant-norm, time-independent, two-body interaction terms. Furthermore, each qubit in the system interacts only with a constant number of other qubits in a three-layer, geometrically local layout. The computer runs in three steps—it starts in a simple initial product state, evolves according to a time-independent Hamiltonian for time of order L2 (up to logarithmic factors), and finishes with a two-qubit measurement. Our model improves previous universal two-local-Hamiltonian constructions, as it avoids using perturbation gadgets and large energy-penalty terms in the Hamiltonian, which would result in a large required run time.
Ancilla-driven universal quantum computation
Anders, Janet; Browne, Dan E.; Oi, Daniel K. L.; Kashefi, Elham; Andersson, Erika
2010-08-15
We introduce a model of quantum computation intermediate between the gate-based and measurement-based models. A quantum register is manipulated remotely with the help of a single ancilla that ''drives'' the evolution of the register. The fully controlled ancilla qubit is coupled to the computational register only via a fixed unitary two-qubit interaction and then measured in suitable bases, driving both single- and two-qubit operations on the register. Arbitrary single-qubit operations directly on register qubits are not needed. We characterize all interactions E that induce a unitary, stepwise deterministic measurement back-action on the register sufficient to implement any quantum channel. Our scheme offers experimental advantages for computation, state preparation, and generalized measurements, since no tunable control of the register is required.
Superconducting Qubits for Quantum Computation
2006-05-31
based on the Aharonov - Casher effect for flux tunneling, and the extension of the concept of the quantum non-demolition measurements to the measurement...consists of a Bloch transistor included in the superconducting loop with finite inductance and uses the Aharonov - Casher effect to modulate the flux...tunneling amplitude. The Aharonov - Casher effect in a simple system of Josephson junctions is of considerable interest of its own, and we expect that the
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.
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
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.
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…
Quantum game simulator, using the circuit model of quantum computation
NASA Astrophysics Data System (ADS)
Vlachos, Panagiotis; Karafyllidis, Ioannis G.
2009-10-01
We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2×2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well-known quantum games, the Battle of Sexes and the Chicken game. Program summaryProgram title: Quantum Game Simulator (QGS) Catalogue identifier: AEED_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEED_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3416 No. of bytes in distributed program, including test data, etc.: 583 553 Distribution format: tar.gz Programming language: Matlab R2008a (C) Computer: Any computer that can sufficiently run Matlab R2008a Operating system: Any system that can sufficiently run Matlab R2008a Classification: 4.15 Nature of problem: Simulation of two player quantum games described by a payoff matrix. Solution method: The program calculates the matrices that comprise the Eisert setup for quantum games based on the quantum circuit model. There are 5 parameters that can be altered. We define 3 of them as constant. We play the quantum game for all possible values for the other 2 parameters and store the results in a matrix. Unusual features: The software provides an easy way of simulating any two-player quantum games. Running time: Approximately
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.
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
Blind Quantum Computing with Weak Coherent Pulses
NASA Astrophysics Data System (ADS)
Dunjko, Vedran; Kashefi, Elham; Leverrier, Anthony
2012-05-01
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 ɛ blindness for UBQC, in analogy to the concept of ɛ 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 ɛ-blind UBQC for any ɛ>0, even if the channel between the client and the server is arbitrarily lossy.
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.
Quantum computation with Turaev-Viro codes
Koenig, Robert; Kuperberg, Greg; Reichardt, Ben W.
2010-12-15
For a 3-manifold with triangulated boundary, the Turaev-Viro topological invariant can be interpreted as a quantum error-correcting code. The code has local stabilizers, identified by Levin and Wen, on a qudit lattice. Kitaev's toric code arises as a special case. The toric code corresponds to an abelian anyon model, and therefore requires out-of-code operations to obtain universal quantum computation. In contrast, for many categories, such as the Fibonacci category, the Turaev-Viro code realizes a non-abelian anyon model. A universal set of fault-tolerant operations can be implemented by deforming the code with local gates, in order to implement anyon braiding. We identify the anyons in the code space, and present schemes for initialization, computation and measurement. This provides a family of constructions for fault-tolerant quantum computation that are closely related to topological quantum computation, but for which the fault tolerance is implemented in software rather than coming from a physical medium.
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.
Adiabatic transport of qubits around a black hole
NASA Astrophysics Data System (ADS)
Viennot, David; Moro, Olivia
2017-03-01
We consider localized qubits evolving around a black hole following a quantum adiabatic dynamics. We develop a geometric structure (based on fibre bundles) permitting to describe the quantum states of a qubit and the spacetime geometry in a single framework. The quantum decoherence induced by the black hole on the qubit is analysed in this framework (the role of the dynamical and geometric phases in this decoherence is treated), especially for the quantum teleportation protocol when one qubit falls to the event horizon. A simple formula to compute the fidelity of the teleportation is derived. The case of a Schwarzschild black hole is analysed.
Error-resistant distributed quantum computation in a trapped ion chain
Braungardt, Sibylle; Sen, Aditi; Sen, Ujjwal; Lewenstein, Maciej
2007-10-15
We consider experimentally feasible chains of trapped ions with pseudospin 1/2 and find models that can potentially be used to implement error-resistant quantum computation. Similar in spirit to classical neural networks, the error resistance of the system is achieved by encoding the qubits distributed over the whole system. We therefore call our system a quantum neural network and present a quantum neural network model of quantum computation. Qubits are encoded in a few quasi degenerated low-energy levels of the whole system, separated by a large gap from the excited states and large energy barriers between themselves. We investigate protocols for implementing a universal set of quantum logic gates in the system by adiabatic passage of a few low-lying energy levels of the whole system. Naturally appearing and potentially dangerous distributed noise in the system leaves the fidelity of the computation virtually unchanged, if it is not too strong. The computation is also naturally resilient to local perturbations of the spins.
Optically Driven Spin Based Quantum Dots for Quantum Computing
2008-01-01
system approach to quantum optics, Lecture Notes in Physics (Springer, Berlin, 1993). [5] H. M. Wiseman and G. J. Milburn, Phys. Rev. Lett. 70, 548 (1993...Electrical Engineering and Computer Science Department of Physics Harrison M. Randall Laboratory of Physics The University of Michigan Ann Arbor, MI...48109 Phone: 734-764-4469 Email: dst@umich.edu Co-Principal Investigator: L.J. Sham Department of Physics The University of California – San
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
Causo, Maria Serena; Ciccotti, Giovanni; Bonella, Sara; Vuilleumier, Rodolphe
2006-08-17
Linearized mixed quantum-classical simulations are a promising approach for calculating time-correlation functions. At the moment, however, they suffer from some numerical problems that may compromise their efficiency and reliability in applications to realistic condensed-phase systems. In this paper, we present a method that improves upon the convergence properties of the standard algorithm for linearized calculations by implementing a cumulant expansion of the relevant averages. The effectiveness of the new approach is tested by applying it to the challenging computation of the diffusion of an excess electron in a metal-molten salt solution.
Ion Trap Quantum Computers: Performance Limits and Experimental Progress
NASA Astrophysics Data System (ADS)
Hughes, Richard
1998-03-01
In a quantum computer information would be represented by the quantum mechanical states of suitable atomic-scale systems. (A single bit of information represented by a two-level quantum system is known as a qubit.) This notion leads to the possibility of computing with quantum mechanical superpositions of numbers ("quantum parallelism"), which for certain problems would make Quantum/quantum.html>quantum computation very much more efficient than classical computation. The possibility of rapidly factoring the large integers used in public-key cryptography is an important example. (Public key cryptosystems derive their security from the difficuty of factoring, and similar problems, with conventional computers.) Quantum computational hardware development is in its infancy, but an experimental study of quantum computation with laser-cooled trapped calcium ions that is under way at Los Alamos will be described. One of the pricipal obstacles to practical quantum computation is the inevitable loss of quantum coherence of the complex quantum states involved. The results of a theoretical analysis showing that quantum factoring of small integers should be possible with trapped ions will be presented. The prospects for larger-scale computations will be discussed.
Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes
NASA Astrophysics Data System (ADS)
Marvian, Milad; Lidar, Daniel A.
2017-01-01
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.
Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes.
Marvian, Milad; Lidar, Daniel A
2017-01-20
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.
Measurement-Based and Universal Blind Quantum Computation
NASA Astrophysics Data System (ADS)
Broadbent, Anne; Fitzsimons, Joseph; Kashefi, Elham
Measurement-based quantum computation (MBQC) is a novel approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operation. We review here the mathematical model underlying MBQC and the first quantum cryptographic protocol designed using the unique features of MBQC.
Quantum computing gates via optimal control
NASA Astrophysics Data System (ADS)
Atia, Yosi; Elias, Yuval; Mor, Tal; Weinstein, Yossi
2014-10-01
We demonstrate the use of optimal control to design two entropy-manipulating quantum gates which are more complex than the corresponding, commonly used, gates, such as CNOT and Toffoli (CCNOT): A two-qubit gate called polarization exchange (PE) and a three-qubit gate called polarization compression (COMP) were designed using GRAPE, an optimal control algorithm. Both gates were designed for a three-spin system. Our design provided efficient and robust nuclear magnetic resonance (NMR) radio frequency (RF) pulses for 13C2-trichloroethylene (TCE), our chosen three-spin system. We then experimentally applied these two quantum gates onto TCE at the NMR lab. Such design of these gates and others could be relevant for near-future applications of quantum computing devices.
Quantum Computation using Arrays of N Polar Molecules in Pendular States.
Wei, Qi; Cao, Yudong; Kais, Sabre; Friedrich, Bretislav; Herschbach, Dudley
2016-11-18
We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state |00⋯0⟩ and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state |00⋯0⟩ . This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole-dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 10(-4) , confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement-based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states.
Dual-code quantum computation model
NASA Astrophysics Data System (ADS)
Choi, Byung-Soo
2015-08-01
In this work, we propose the dual-code quantum computation model—a fault-tolerant quantum computation scheme which alternates between two different quantum error-correction codes. Since the chosen two codes have different sets of transversal gates, we can implement a universal set of gates transversally, thereby reducing the overall cost. We use code teleportation to convert between quantum states in different codes. The overall cost is decreased if code teleportation requires fewer resources than the fault-tolerant implementation of the non-transversal gate in a specific code. To analyze the cost reduction, we investigate two cases with different base codes, namely the Steane and Bacon-Shor codes. For the Steane code, neither the proposed dual-code model nor another variation of it achieves any cost reduction since the conventional approach is simple. For the Bacon-Shor code, the three proposed variations of the dual-code model reduce the overall cost. However, as the encoding level increases, the cost reduction decreases and becomes negative. Therefore, the proposed dual-code model is advantageous only when the encoding level is low and the cost of the non-transversal gate is relatively high.
Applications of computational quantum mechanics
NASA Astrophysics Data System (ADS)
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts
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.
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.
Quantum computation architecture using optical tweezers
Weitenberg, Christof; Kuhr, Stefan; Moelmer, Klaus; Sherson, Jacob F.
2011-09-15
We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits require the transport of atoms to neighboring sites. We numerically optimize the nonadiabatic transport of the atoms through the lattice and the intensity ramps of the optical tweezer in order to maximize the gate fidelities. We find overall gate times of a few 100 {mu}s, while keeping the error probability due to vibrational excitations and spontaneous scattering below 10{sup -3}. The requirements on the positioning error and intensity noise of the optical tweezer and the magnetic field stability are analyzed and we show that atoms in optical lattices could meet the requirements for fault-tolerant scalable quantum computing.
Computational models for the berry phase in semiconductor quantum dots
NASA Astrophysics Data System (ADS)
Prabhakar, S.; Melnik, R. V. N.; Sebetci, A.
2014-10-01
By developing a new model and its finite element implementation, we analyze the Berry phase low-dimensional semiconductor nanostructures, focusing on quantum dots (QDs). In particular, we solve the Schrödinger equation and investigate the evolution of the spin dynamics during the adiabatic transport of the QDs in the 2D plane along circular trajectory. Based on this study, we reveal that the Berry phase is highly sensitive to the Rashba and Dresselhaus spin-orbit lengths.
Computational models for the berry phase in semiconductor quantum dots
Prabhakar, S. Melnik, R. V. N.; Sebetci, A.
2014-10-06
By developing a new model and its finite element implementation, we analyze the Berry phase low-dimensional semiconductor nanostructures, focusing on quantum dots (QDs). In particular, we solve the Schrödinger equation and investigate the evolution of the spin dynamics during the adiabatic transport of the QDs in the 2D plane along circular trajectory. Based on this study, we reveal that the Berry phase is highly sensitive to the Rashba and Dresselhaus spin-orbit lengths.
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.
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.
Fischer, Sean A; Lingerfelt, David B; May, Joseph W; Li, Xiaosong
2014-09-07
The unique electronic structure of Mn(2+)-doped ZnO quantum dots gives rise to photoionization states that can be used to manipulate the magnetic state of the material and to generate zero-reabsorption luminescence. Fast formation and long non-radiative decay of this photoionization state is a necessary requirement for these important applications. In this work, surface hopping based non-adiabatic molecular dynamics are used to demonstrate the fast formation of a metal-to-ligand charge transfer state in a Mn(2+)-doped ZnO quantum dot. The formation occurs on an ultrafast timescale and is aided by the large density of states and significant mixing of the dopant Mn(2+) 3dt2 levels with the valence-band levels of the ZnO lattice. The non-radiative lifetime of the photoionization states is also investigated.
2011-09-01
collisions were computationally simulated. The alkali metals were potassium, rubidium, and cesium and the noble gas partners were helium, neon, and argon...195 20. Spin-Orbit split energies of Potassium, Rubidium, and Cesium ...composed of an alkali metal typically Rubidium[26, 37] or Cesium [5, 18]. The unique character of the alkali atoms, having a single valence electron in
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.
NASA Astrophysics Data System (ADS)
Li, Dafa
2016-05-01
The adiabatic theorem was proposed about 90 years ago and has played an important role in quantum physics. The quantitative adiabatic condition constructed from eigenstates and eigenvalues of a Hamiltonian is a traditional tool to estimate adiabaticity and has proven to be the necessary and sufficient condition for adiabaticity. However, recently the condition has become a controversial subject. In this paper, we list some expressions to estimate the validity of the adiabatic approximation. We show that the quantitative adiabatic condition is invalid for the adiabatic approximation via the Euclidean distance between the adiabatic state and the evolution state. Furthermore, we deduce general necessary and sufficient conditions for the validity of the adiabatic approximation by different definitions.
Quantum gates by periodic driving
Shi, Z. C.; Wang, W.; Yi, X. X.
2016-01-01
Topological quantum computation has been extensively studied in the past decades due to its robustness against decoherence. One way to realize the topological quantum computation is by adiabatic evolutions—it requires relatively long time to complete a gate, so the speed of quantum computation slows down. In this work, we present a method to realize single qubit quantum gates by periodic driving. Compared to adiabatic evolution, the single qubit gates can be realized at a fixed time much shorter than that by adiabatic evolution. The driving fields can be sinusoidal or square-well field. With the sinusoidal driving field, we derive an expression for the total operation time in the high-frequency limit, and an exact analytical expression for the evolution operator without any approximations is given for the square well driving. This study suggests that the period driving could provide us with a new direction in regulations of the operation time in topological quantum computation. PMID:26911900
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.
Hybrid architecture for encoded measurement-based quantum computation
Zwerger, M.; Briegel, H. J.; Dür, W.
2014-01-01
We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurement-based way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within the considered error model a threshold of the order of 10% local noise per particle for fault-tolerant quantum computation and quantum communication. PMID:24946906
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.
Computer simulations to study the effect of adiabatic heating on rod penetration
Reaugh, J.E.
1993-08-01
We use computer simulations to help us understand the experimental observation that depleted uranium (DU) rods penetrate more steel than equal density tungsten alloy (WA) rods, and that this advantage depends on velocity and fineness ratio. Our simulations used thermal softening. Although the DU rods exhibit shear fracture instead, both phenomena result in a loss of hoop strength, and help to keep the projectile residue from interfering with the incoming rod. Our simulations show that rods of DU (or other alloy with strong thermal softening) penetrate more steel than rods of WA (for alloys with little thermal softening), and show velocity and fineness ratio dependencies that are in qualitative agreement with experiment.
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
2016-01-27
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.
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
Homomorphic encryption experiments on IBM's cloud quantum computing platform
NASA Astrophysics Data System (ADS)
Huang, He-Liang; Zhao, You-Wei; Li, Tan; Li, Feng-Guang; Du, Yu-Tao; Fu, Xiang-Qun; Zhang, Shuo; Wang, Xiang; Bao, Wan-Su
2017-02-01
Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users is likely to be on the cloud. However, the adoption of cloud computing is possible only if security is ensured. Homomorphic encryption is a cryptographic protocol that allows computation to be performed on encrypted data without decrypting them, so it is well suited to cloud computing. Here, we first applied homomorphic encryption on IBM's cloud quantum computer platform. In our experiments, we successfully implemented a quantum algorithm for linear equations while protecting our privacy. This demonstration opens a feasible path to the next stage of development of cloud quantum information technology.
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.
Verification for measurement-only blind quantum computing
NASA Astrophysics Data System (ADS)
Morimae, Tomoyuki
2014-06-01
Blind quantum computing is a new secure quantum computing protocol where a client who does not have any sophisticated quantum technology can delegate her quantum computing to a server without leaking any privacy. It is known that a client who has only a measurement device can perform blind quantum computing [T. Morimae and K. Fujii, Phys. Rev. A 87, 050301(R) (2013), 10.1103/PhysRevA.87.050301]. It has been an open problem whether the protocol can enjoy the verification, i.e., the ability of the client to check the correctness of the computing. In this paper, we propose a protocol of verification for the measurement-only blind quantum computing.
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.
Experimental Implementation of Efficient Linear Optics Quantum Computation
2007-11-02
Experimental Implementation of Efficient Linear Optics Quantum Computation Final Report G. J. Milburn, T. C. Ralph, and A. G. White University of...Queensland, Australia 1. Statement of Problem. One of the earliest proposals [1] for implementing quantum computation was based on encoding...containing few photons. In 2001 Knill, Laflamme and Milburn (KLM) found a way to circumvent this restriction and implement efficient quantum computation
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.
Modeling fluid dynamics on type II quantum computers
NASA Astrophysics Data System (ADS)
Scoville, James; Weeks, David; Yepez, Jeffrey
2006-03-01
A quantum algorithm is presented for modeling the time evolution of density and flow fields governed by classical equations, such as the diffusion equation, the nonlinear Burgers equation, and the damped wave equation. The algorithm is intended to run on a type-II quantum computer, a parallel quantum computer consisting of a lattice of small type I quantum computers undergoing unitary evolution and interacting via information interchanges represented by an orthogonal matrices. Information is effectively transferred between adjacent quantum computers over classical communications channels because of controlled state demolition following local quantum mechanical qubit-qubit interactions within each quantum computer. The type-II quantum algorithm presented in this paper describes a methodology for generating quantum logic operations as a generalization of classical operations associated with finite-point group symmetries. The quantum mechanical evolution of multiple qubits within each node is described. Presented is a proof that the parallel quantum system obeys a finite-difference quantum Boltzman equation at the mesoscopic scale, leading in turn to various classical linear and nonlinear effective field theories at the macroscopic scale depending on the details of the local qubit-qubit interactions.
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.
NMR quantum computation with optically polarized molecules
NASA Astrophysics Data System (ADS)
Verhulst, Anne; Yannoni, Constantino; Sherwood, Mark; Pomerantz, Drew; Vandersypen, Lieven; Chuang, Isaac
2000-03-01
Current methods for bulk NMR quantum computation rely on nuclear spin polarization present at high temperature equilibrium. This presents a challenging obstacle as the probability to find a spin in a specific state decreases exponentially in the number of spins used as qubits, causing a corresponding decrease in the signal to noise ratio of the desired NMR signal. One way to address this problem is to provide an artificial source of high polarization, such as optically pumped ^129Xe. For comparison, thermal equilibrium polarizations are only about 10-3% for ^1H in a typical NMR experiment at room temperature and in a 10 Tesla magnetic field, but with ^129Xe polarizations as high as 18% have been achieved [Happer et. al., Chem.Phys.Lett., 284, p.87-92, Feb 1998]. Using this technique, we prepare hyperpolarized liquid Xe and use it as a solvent for chloroform molecules (CHCl_3). Cross polarization (SPINOE) between ^129Xe and ^1H results in measured enhancements of the proton signal of over 300%, and evidence of transfer to ^13C. These results provide hope for the scalability of quantum computation.
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.
A quantum computer on the basis of an atomic quantum transistor with built-in quantum memory
NASA Astrophysics Data System (ADS)
Moiseev, S. A.; Andrianov, S. N.
2016-12-01
A quantum transistor based quantum computer where the multiqubit quantum memory is a component of the quantum transistor and, correspondingly, takes part in the performance of quantum logical operations is considered. Proceeding from the generalized Jaynes-Cummings model, equations for coefficients of the wave function of the quantum system under consideration have been obtained for different stages of its evolution in processes of performing logical operations. The solution of the system of equations allows one to establish requirements that are imposed on the parameters of the initial Hamiltonian and must be satisfied for the effective operation of the computer; it also demonstrates the possibility of a universal set of quantum operations. Thus, based on the proposed approach, the possibility of constructing a compact multiatomic ensemble based on quantum computer using a quantum transistor for the implementation of two-qubit gates has been demonstrated.
Quantum computing with Josephson junction circuits
NASA Astrophysics Data System (ADS)
Xu, Huizhong
This work concerns the study of Josephson junction circuits in the context of their usability for quantum computing. The zero-voltage state of a current-biased Josephson junction has a set of metastable quantum energy levels. If a junction is well isolated from its environment, it will be possible to use the two lowest states as a qubit in a quantum computer. I first examine the meaning of isolation theoretically. Using a master equation, I analyzed the effect of dissipation on escape rates and suggested a simple method, population depletion technique, to measure the relaxation time (T1). Using a stochastic Bloch equation to analyze the dependence of microwave resonance peak width on current noise, I found decoherence due to current noise depends on the noise spectrum. For high frequency noise with a cutoff frequency fc much larger than 1/T1, I found decoherence due to noise can be described by a dephasing rate that is proportional to the noise spectral density. However, for low frequency noise such that its cutoff frequency fc is much smaller than 1/T 1, decoherence due to noise depends on the total rms current noise. I then analyze and test a few qubit isolation schemes, including resistive isolation, inductor-capacitor (LC) isolation, half-wavelength resonant isolation and inductor-junction (LJ) isolation. I found the resistive isolation scheme has a severe heating problem. Macroscopic quantum tunneling and energy level quantization were observed in the LC isolated Nb/AlOx/Nb and AL/ALOx/Al junction qubits at 25 mK. Relaxation times of 4--12 ns and spectroscopic coherence times of 1--3 ns were obtained for these LC isolated qubits. I found the half-wavelength isolated junction qubit has a relaxation time of about 20 ns measured by the population-depletion techniques, but no energy levels were observed in this qubit. Experimental results suggest the LJ isolated qubit has a longer relaxation and coherence times than all my previously examined samples. Using a
Fast quantum computation at arbitrarily low energy
NASA Astrophysics Data System (ADS)
Jordan, Stephen P.
2017-03-01
One version of the energy-time uncertainty principle states that the minimum time T⊥ for a quantum system to evolve from a given state to any orthogonal state is h /(4 Δ E ) , where Δ E is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that T⊥≥h /(2
Preparing projected entangled pair states on a quantum computer.
Schwarz, Martin; Temme, Kristan; Verstraete, Frank
2012-03-16
We present a quantum algorithm to prepare injective projected entangled pair states (PEPS) on a quantum computer, a class of open tensor networks representing quantum states. The run time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS's parent Hamiltonian.
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.
Quantum Speedup by Quantum Annealing
NASA Astrophysics Data System (ADS)
Somma, Rolando D.; Nagaj, Daniel; Kieferová, Mária
2012-08-01
We study the glued-trees problem from A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. Spielman, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing (ACM, San Diego, CA, 2003), p. 59. in the adiabatic model of quantum computing and provide an annealing schedule to solve an oracular problem exponentially faster than classically possible. The Hamiltonians involved in the quantum annealing do not suffer from the so-called sign problem. Unlike the typical scenario, our schedule is efficient even though the minimum energy gap of the Hamiltonians is exponentially small in the problem size. We discuss generalizations based on initial-state randomization to avoid some slowdowns in adiabatic quantum computing due to small gaps.
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.
Topological quantum computation--from basic concepts to first experiments.
Stern, Ady; Lindner, Netanel H
2013-03-08
Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantum computation aims to achieve this goal by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Recently, substantial progress in this field has been made on both theoretical and experimental fronts. We review the basic concepts of non-Abelian phases and their topologically protected use in quantum information processing tasks. We discuss different possible realizations of these concepts in experimentally available solid-state systems, including systems hosting Majorana fermions, their recently proposed fractional counterparts, and non-Abelian quantum Hall states.
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
Blueprint for a microwave trapped ion quantum computer
Lekitsch, Bjoern; Weidt, Sebastian; Fowler, Austin G.; Mølmer, Klaus; Devitt, Simon J.; Wunderlich, Christof; Hensinger, Winfried K.
2017-01-01
The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion–based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation–based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error–threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects. PMID:28164154
Blueprint for a microwave trapped ion quantum computer.
Lekitsch, Bjoern; Weidt, Sebastian; Fowler, Austin G; Mølmer, Klaus; Devitt, Simon J; Wunderlich, Christof; Hensinger, Winfried K
2017-02-01
The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion-based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation-based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error-threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects.
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
2014-01-07
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.
From transistor to trapped-ion computers for quantum chemistry
NASA Astrophysics Data System (ADS)
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.
Computational quantum magnetism: Role of noncollinear magnetism
NASA Astrophysics Data System (ADS)
Freeman, Arthur J.; Nakamura, Kohji
2009-04-01
We are witnessing today a golden age of innovation with novel magnetic materials and with discoveries important for both basic science and device applications. Computation and simulation have played a key role in the dramatic advances of the past and those we are witnessing today. A goal-driving computational science—simulations of every-increasing complexity of more and more realistic models has been brought into greater focus with greater computing power to run sophisticated and powerful software codes like our highly precise full-potential linearized augmented plane wave (FLAPW) method. Indeed, significant progress has been achieved from advanced first-principles FLAPW calculations for the predictions of surface/interface magnetism. One recently resolved challenging issue is the role of noncollinear magnetism (NCM) that arises not only through the SOC, but also from the breaking of symmetry at surfaces and interfaces. For this, we will further review some specific advances we are witnessing today, including complex magnetic phenomena from noncollinear magnetism with no shape approximation for the magnetization (perpendicular MCA in transition-metal overlayers and superlattices; unidirectional anisotropy and exchange bias in FM and AFM bilayers; constricted domain walls important in quantum spin interfaces; and curling magnetic nano-scale dots as new candidates for non-volatile memory applications) and most recently providing new predictions and understanding of magnetism in novel materials such as magnetic semiconductors and multi-ferroic systems.
Parallel Photonic Quantum Computation Assisted by Quantum Dots in One-Side Optical Microcavities
Luo, Ming-Xing; Wang, Xiaojun
2014-01-01
Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantum computations dependent on two DOFs of photon systems. We construct deterministic hyper-controlled-not (hyper-CNOT) gates operating on the spatial-mode and the polarization DOFs of two-photon or one-photon systems by exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities. These hyper-CNOT gates show that the quantum states of two DOFs can be viewed as independent qubits without requiring auxiliary DOFs in theory. This result can reduce the quantum resources by half for quantum applications with large qubit systems, such as the quantum Shor algorithm. PMID:25030424
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.
Quantum Computing in Fock Space Systems
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
1997-04-01
Fock space system (FSS) has unfixed number (N) of particles and/or degrees of freedom. In quantum computing (QC) main requirement is sustainability of coherent Q-superpositions. This normally favoured by low noise environment. High excitation/high temperature (T) limit is hence discarded as unfeasible for QC. Conversely, if N is itself a quantized variable, the dimensionality of Hilbert basis for qubits may increase faster (say, N-exponentially) than thermal noise (likely, in powers of N and T). Hence coherency may win over T-randomization. For this type of QC speed (S) of factorization of long integers (with D digits) may increase with D (for 'ordinary' QC speed polynomially decreases with D). This (apparent) paradox rests on non-monotonic bijectivity (cf. Georg Cantor's diagonal counting of rational numbers). This brings entire aleph-null structurality ("Babylonian Library" of infinite informational content of integer field) to superposition determining state of quantum analogue of Turing machine head. Structure of integer infinititude (e.g. distribution of primes) results in direct "Platonic pressure" resembling semi-virtual Casimir efect (presure of cut-off vibrational modes). This "effect", the embodiment of Pythagorean "Number is everything", renders Godelian barrier arbitrary thin and hence FSS-based QC can in principle be unlimitedly efficient (e.g. D/S may tend to zero when D tends to infinity).
Quantum Optical Implementations of Current Quantum Computing Paradigms
2005-05-01
Bacterial Spores,” at DARPA, Jan. 29, 2002. 10. M. O. Scully, “Quantum Maxwell demons ,” at Texas A&M University, March 19 (2002). 11. M. O...detectors,” at NEC, Princeton, April 5 (2002). 13. M. O. Scully, “Quantum thermodynamics: From quantum heat engines to Maxwell’s demons and beyond,” at...quantum heat engines to Maxwell’s demons and beyond,” International Conference on Quantum Information (ICQI), Oviedo, Spain, July 14-18, 2002. 18. M. O
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…
Quantum computing using electron-nuclear double resonances
NASA Astrophysics Data System (ADS)
Bowden, Charles M.; Dowling, Jonathan P.; Hotaling, Steven P.
1997-07-01
We consider the use of Electron-Nuclear Double Resonance (ENDOR) techniques in quantum computing. ENDOR resolution as a possible limiting factor is discussed. It is found that ENDOR and double-ENDOR techniques have sufficient resolution for quantum computing applications.
Demonstration of a small programmable quantum computer with atomic qubits.
Debnath, S; Linke, N M; Figgatt, C; Landsman, K A; Wright, K; Monroe, C
2016-08-04
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
2016-09-02
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
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.
Reversibility and energy dissipation in adiabatic superconductor logic.
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2017-12-01
Reversible computing is considered to be a key technology to achieve an extremely high energy efficiency in future computers. In this study, we investigated the relationship between reversibility and energy dissipation in adiabatic superconductor logic. We analyzed the evolution of phase differences of Josephson junctions in the reversible quantum-flux-parametron (RQFP) gate and confirmed that the phase differences can change time reversibly, which indicates that the RQFP gate is physically, as well as logically, reversible. We calculated energy dissipation required for the RQFP gate to perform a logic operation and numerically demonstrated that the energy dissipation can fall below the thermal limit, or the Landauer bound, by lowering operation frequencies. We also investigated the 1-bit-erasure gate as a logically irreversible gate and the quasi-RQFP gate as a physically irreversible gate. We calculated the energy dissipation of these irreversible gates and showed that the energy dissipation of these gate is dominated by non-adiabatic state changes, which are induced by unwanted interactions between gates due to logical or physical irreversibility. Our results show that, in reversible computing using adiabatic superconductor logic, logical and physical reversibility are required to achieve energy dissipation smaller than the Landauer bound without non-adiabatic processes caused by gate interactions.
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.
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.
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
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.
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 Computation by Optically Coupled Steady Atoms/Quantum-Dots Inside a Quantum Cavity
NASA Technical Reports Server (NTRS)
Pradhan, P.; Wang, K. L.; Roychowdhury, V. P.; Anantram, M. P.; Mor, T.; Saini, Subhash (Technical Monitor)
1999-01-01
We present a model for quantum computation using $n$ steady 3-level atoms kept inside a quantum cavity, or using $n$ quantum-dots (QDs) kept inside a quantum cavity. In this model one external laser is pointed towards all the atoms/QDs, and $n$ pairs of electrodes are addressing the atoms/QDs, so that each atom is addressed by one pair. The energy levels of each atom/QD are controlled by an external Stark field given to the atom/QD by its external pair of electrodes. Transition between two energy levels of an individual atom/ QD are controlled by the voltage on its electrodes, and by the external laser. Interactions between two atoms/ QDs are performed with the additional help of the cavity mode (using on-resonance condition). Laser frequency, cavity frequency, and energy levels are far off-resonance most of the time, and they are brought to the resonance (using the Stark effect) only at the time of operations. Steps for a controlled-NOT gate between any two atoms/QDs have been described for this model. Our model demands some challenging technological efforts, such as manufacturing single-electron QDs inside a cavity. However, it promises big advantages over other existing models which are currently implemented, and might enable a much easier scale-up, to compute with many more qubits.
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.
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.
Geometric phase gates based on stimulated Raman adiabatic passage in tripod systems
Moeller, Ditte; Madsen, Lars Bojer; Moelmer, Klaus
2007-06-15
We consider stimulated Raman adiabatic passage (STIRAP) processes in tripod systems and show how to generate purely geometric phase changes of the quantum states involved. The geometric phases are controlled by three laser fields where pulse shapes, relative field strength, and phases can be controlled. We present a robust set of universal gates for quantum computing based on these geometric phases: a one-qubit phase gate, a Hadamard gate, and a two-qubit phase gate.
Non-quantum implementation of quantum computation algorithm using a spatial coding technique
NASA Astrophysics Data System (ADS)
Tate, N.; Ogura, Y.; Tanida, J.
2005-07-01
Non-quantum implementation of quantum information processing is studied. A spatial coding technique, which is one effective digital optical computing technique, is utilized to implement quantum teleportation efficiently. In the coding, quantum information is represented by the intensity and the phase of elemental cells. Correct operation is confirmed within the proposed scheme, which indicates the effectiveness of the proposed approach and a motive for further investigation.
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.
Cryogenic setup for trapped ion quantum computing.
Brandl, M F; van Mourik, M W; Postler, L; Nolf, A; Lakhmanskiy, K; Paiva, R R; Möller, S; Daniilidis, N; Häffner, H; Kaushal, V; Ruster, T; Warschburger, C; Kaufmann, H; Poschinger, U G; Schmidt-Kaler, F; Schindler, P; Monz, T; Blatt, R
2016-11-01
We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120 dB reduction of 50 Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than ±20 nm over 2 s. In addition to the cryogenic apparatus, we describe the setup required for an operation with (40)Ca(+) and (88)Sr(+) ions. The instability of the laser manipulating the optical qubits in (40)Ca(+) is characterized by yielding a minimum of its Allan deviation of 2.4 ⋅ 10(-15) at 0.33 s. To evaluate the performance of the apparatus, we trapped (40)Ca(+) ions, obtaining a heating rate of 2.14(16) phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8) ms.
Cryogenic setup for trapped ion quantum computing
NASA Astrophysics Data System (ADS)
Brandl, M. F.; van Mourik, M. W.; Postler, L.; Nolf, A.; Lakhmanskiy, K.; Paiva, R. R.; Möller, S.; Daniilidis, N.; Häffner, H.; Kaushal, V.; Ruster, T.; Warschburger, C.; Kaufmann, H.; Poschinger, U. G.; Schmidt-Kaler, F.; Schindler, P.; Monz, T.; Blatt, R.
2016-11-01
We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120 dB reduction of 50 Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than ±20 nm over 2 s. In addition to the cryogenic apparatus, we describe the setup required for an operation with 40Ca+ and 88Sr+ ions. The instability of the laser manipulating the optical qubits in 40Ca+ is characterized by yielding a minimum of its Allan deviation of 2.4 ṡ 10-15 at 0.33 s. To evaluate the performance of the apparatus, we trapped 40Ca+ ions, obtaining a heating rate of 2.14(16) phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8) ms.
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
Universal continuous-variable quantum computation without cooling
NASA Astrophysics Data System (ADS)
Lau, Hoi-Kwan; Plenio, Martin B.
2017-02-01
One limitation of the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are conventionally pure physical states that are constructed from the ground state. In this work, we present an alternative quantum computing formalism that encodes logical quantum information in mixed physical states. We introduce a class of mixed-state protocols that are based on a parity encoding, and propose an implementation of the universal logic gates by using realistic hybrid interactions. When compared with the conventional pure-state protocols, our formalism could relax the necessity, and hence the systemic requirements, of cooling. Additionally, the mixed-state protocols are inherently resilient to a wider class of noise processes and reduce the fundamental energy consumption in initialization. Our work broadens the range of candidates for continuous-variable quantum computers.
NASA Astrophysics Data System (ADS)
Cao, Zhenwei
Over the years, people have found Quantum Mechanics to be extremely useful in explaining various physical phenomena from a microscopic point of view. Anderson localization, named after physicist P. W. Anderson, states that disorder in a crystal can cause non-spreading of wave packets, which is one possible mechanism (at single electron level) to explain metal-insulator transitions. The theory of quantum computation promises to bring greater computational power over classical computers by making use of some special features of Quantum Mechanics. The first part of this dissertation considers a 3D alloy-type model, where the Hamiltonian is the sum of the finite difference Laplacian corresponding to free motion of an electron and a random potential generated by a sign-indefinite single-site potential. The result shows that localization occurs in the weak disorder regime, i.e., when the coupling parameter lambda is very small, for energies E ≤ --Clambda 2. The second part of this dissertation considers adiabatic quantum computing (AQC) algorithms for the unstructured search problem to the case when the number of marked items is unknown. In an ideal situation, an explicit quantum algorithm together with a counting subroutine are given that achieve the optimal Grover speedup over classical algorithms, i.e., roughly speaking, reduce O(2n) to O(2n/2), where n is the size of the problem. However, if one considers more realistic settings, the result shows this quantum speedup is achievable only under a very rigid control precision requirement (e.g., exponentially small control error).
Novel Approaches to Quantum Computation Using Solid State Qubits
2007-12-31
Han, A scheme for the teleportation of multiqubit quantum information via the control of many agents in a network, submitted to Phys. Lett. A, 343...approach, Phys. Rev. B 70, 094513 (2004). 22. C.-P. Yang, S.-I. Chu, and S. Han, Efficient many party controlled teleportation of multiqubit quantum ...June 1, 2001- September 30, 2007 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER "Novel Approaches to Quantum Computation Using Solid State Qubits" F49620
Combining Dynamical Decoupling with Fault-Tolerant Quantum Computation
2009-11-17
ar X iv :0 91 1. 32 02 v1 [ qu an t- ph ] 1 7 N ov 2 00 9 Combining dynamical decoupling with fault-tolerant quantum computation Hui Khoon Ng,1...Daniel A. Lidar,2 and John Preskill1 1Institute for Quantum Information, California Institute of Technology, Pasadena, CA 91125, USA 2Departments...of Chemistry, Electrical Engineering, and Physics, and Center for Quantum Information Science & Technology, University of Southern California, Los
Scalable Quantum Networks for Distributed Computing and Sensing
2016-04-01
AFRL-AFOSR-UK-TR-2016-0007 Scalable Quantum Networks for Distributed Computing and Sensing Ian Walmsley THE UNIVERSITY OF OXFORD Final Report 04/01...MM-YYYY) 12/07/2015 2. REPORT TYPE Final 3. DATES COVERED (From - To) 01-Sep-2012 to 31-Aug-2015 4. TITLE AND SUBTITLE Scalable Quantum Networks...SUPPLEMENTARY NOTES 14. ABSTRACT We identified two barriers to the implementation of large-scale photonic quantum networks. First, as scalability requires
Single Photon Holographic Qudit Elements for Linear Optical Quantum Computing
2011-05-01
in optical volume holography and designed and simulated practical single-photon, single-optical elements for qudit MUB-state quantum in- formation...Independent of the representation we use, the MUB states will ordinarily be modulated in both amplitude and phase. Recently a practical method has been...quantum computing with qudits (d ≥ 3) has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both
Resilience to Time-Correlated Noise in Quantum Computation
NASA Astrophysics Data System (ADS)
Bombín, Héctor
2016-10-01
Fault-tolerant quantum computation techniques rely on weakly correlated noise. Here, I show that it is enough to assume weak spatial correlations: Time correlations can take any form. In particular, single-shot error-correction techniques exhibit a noise threshold for quantum memories under spatially local stochastic noise.
Quantum-dot cluster-state computing with encoded qubits
Weinstein, Yaakov S.; Hellberg, C. Stephen; Levy, Jeremy
2005-08-15
A class of architectures is advanced for cluster-state quantum computation using quantum dots. These architectures include using single and multiple dots as logical qubits. Special attention is given to supercoherent qubits introduced by Bacon et al. [Phys. Rev. Lett. 87, 247902 (2001)] for which we discuss the effects of various errors and present a means of error protection.
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 sqrt[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
2013-06-07
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.
Blind quantum computation protocol in which Alice only makes measurements
NASA Astrophysics Data System (ADS)
Morimae, Tomoyuki; Fujii, Keisuke
2013-05-01
Blind quantum computation is a new secure quantum computing protocol which enables Alice (who does not have sufficient quantum technology) to delegate her quantum computation to Bob (who has a full-fledged quantum computer) in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. In previous protocols, Alice needs to have a device which generates quantum states, such as single-photon states. Here we propose another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector. In several experimental setups, such as optical systems, the measurement of a state is much easier than the generation of a single-qubit state. Therefore our protocols ease Alice's burden. Furthermore, the security of our protocol is based on the no-signaling principle, which is more fundamental than quantum physics. Finally, our protocols are device independent in the sense that Alice does not need to trust her measurement device in order to guarantee the security.
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.
Experimental demonstration of a programmable quantum computer by NMR.
Kim, Jaehyun; Lee, Jae-Seung; Hwang, Taesoon; Lee, Soonchil
2004-01-01
A programmable quantum computer is experimentally demonstrated by nuclear magnetic resonance using one qubit for the program and two qubits for data. A non-separable two-qubit operation is performed in a programmable way to show the successful demonstration. Projective measurements required in the programmable quantum computer are simulated by averaging the results of experiments just like when producing an effective pure state.
A transmon quantum annealer: decomposing many-body Ising constraints into pair interactions
NASA Astrophysics Data System (ADS)
Leib, Martin; Zoller, Peter; Lechner, Wolfgang
2016-12-01
Adiabatic quantum computing is an analogue quantum computing scheme with various applications in solving optimisation problems. In the parity picture of quantum optimization, the problem is encoded in local fields that act on qubits that are connected via local four-body terms We present an implementation of a parity annealer with Transmon qubits with a specifically tailored Ising interaction from Josephson ring modulators.
Thermalization in nature and on a quantum computer.
Riera, Arnau; Gogolin, Christian; Eisert, Jens
2012-02-24
In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.
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.
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.
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.
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
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
2016-12-01
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.
New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy
Colvin, M; Krishnan, V V
2003-02-07
The power of a quantum computer (QC) relies on the fundamental concept of the superposition in quantum mechanics and thus allowing an inherent large-scale parallelization of computation. In a QC, binary information embodied in a quantum system, such as spin degrees of freedom of a spin-1/2 particle forms the qubits (quantum mechanical bits), over which appropriate logical gates perform the computation. In classical computers, the basic unit of information is the bit, which can take a value of either 0 or 1. Bits are connected together by logic gates to form logic circuits to implement complex logical operations. The expansion of modern computers has been driven by the developments of faster, smaller and cheaper logic gates. As the size of the logic gates become smaller toward the level of atomic dimensions, the performance of such a system is no longer considered classical but is rather governed by quantum mechanics. Quantum computers offer the potentially superior prospect of solving computational problems that are intractable to classical computers such as efficient database searches and cryptography. A variety of algorithms have been developed recently, most notably Shor's algorithm for factorizing long numbers into prime factors in polynomial time and Grover's quantum search algorithm. The algorithms that were of only theoretical interest as recently, until several methods were proposed to build an experimental QC. These methods include, trapped ions, cavity-QED, coupled quantum dots, Josephson junctions, spin resonance transistors, linear optics and nuclear magnetic resonance. Nuclear magnetic resonance (NMR) is uniquely capable of constructing small QCs and several algorithms have been implemented successfully. NMR-QC differs from other implementations in one important way that it is not a single QC, but a statistical ensemble of them. Thus, quantum computing based on NMR is considered as ensemble quantum computing. In NMR quantum computing, the spins with
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.
Yamada, Atsushi; Okazaki, Susumu
2008-01-28
We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.
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…
NASA Astrophysics Data System (ADS)
Liu, Cheng-Wei
Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the
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
Computational Role of Tunneling in a Programmable Quantum Annealer
NASA Technical Reports Server (NTRS)
Boixo, Sergio; Smelyanskiy, Vadim; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Amin, Mohammad; Mohseni, Masoud; Denchev, Vasil S.; Neven, Hartmut
2016-01-01
Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.
Limits on the Power of Some Models of Quantum Computation
NASA Astrophysics Data System (ADS)
Ortiz, Gerardo; Somma, Rolando; Barnum, Howard; Knill, Emanuel
2006-09-01
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, regardless of the dimension of the Hilbert space where the algebra acts. Similar results hold for the computation of the expectation value of operators implemented by a gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field Hamiltonians and show that they are efficiently (exactly) solvable by means of a Jacobi-like diagonalization method. Our results generalize earlier ones on fermionic linear optics computation and provide insight into the source of the power of the conventional model of quantum computation.
Limits on the Power of Some Models of Quantum Computation
NASA Astrophysics Data System (ADS)
Ortiz, Gerardo; Somma, Rolando; Barnum, Howard; Knill, Emanuel
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, regardless of the dimension of the Hilbert space where the algebra acts. Similar results hold for the computation of the expectation value of operators implemented by a gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field Hamiltonians and show that they are efficiently (exactly) solvable by means of a Jacobi-like diagonalization method. Our results generalize earlier ones on fermionic linear optics computation and provide insight into the source of the power of the conventional model of quantum computation.
Fast non-Abelian geometric gates via transitionless quantum driving.
Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-12-21
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
Continuous-Variable Instantaneous Quantum Computing is Hard to Sample.
Douce, T; Markham, D; Kashefi, E; Diamanti, E; Coudreau, T; Milman, P; van Loock, P; Ferrini, G
2017-02-17
Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.
Continuous-Variable Instantaneous Quantum Computing is Hard to Sample
NASA Astrophysics Data System (ADS)
Douce, T.; Markham, D.; Kashefi, E.; Diamanti, E.; Coudreau, T.; Milman, P.; van Loock, P.; Ferrini, G.
2017-02-01
Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.
Computational Multiqubit Tunnelling in Programmable Quantum Annealers
2016-08-25
Masoud Mohseni1 & Hartmut Neven1 Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the...the initial temperature must be high to overcome tall energy barriers. As the algorithm progresses, the temperature is gradually lowered to distinguish...between local minima with small energy differences. This causes the stochastic process to freeze once the thermal energy is lower than the height of
Entropic Lattice Boltzmann Models and Quantum Computation
2008-04-01
cellular automata, quantum cellular automata, action principles, periodic orbits, turbulence U U U UL 8 Bruce M. Boghosian (617) 627–3054 Contents 1...thereof . . 6 2.5 Lattice Boltzmann algorithm for periodic unstable orbits . . . . . . . . . . . . . . . . . . . . . 7 3 Personnel Supported 7 3.1 2005...continue to work on it in the remaining period of this grant. There are reasons for optimism in the search for quantum circuits described above. First, if
Computational Issues in the Control of Quantum Dynamics
NASA Astrophysics Data System (ADS)
Rabitz, Herschel
2003-03-01
Computational Issues in the Control of Quantum Dynamics Phenomena Herschel Rabitz Department of Chemistry Princeton University The control of quantum phenomena embraces a variety of applications, with the most common implementation involving tailored laser pulses to steer the dynamics of a quantum system towards some specified observable outcome. The theoretical and computational aspects of this subject are intimately tied to the growing experimental capabilities, especially the ability to perform massive numbers of high throughput experiments. Computational studies in this context have special roles. Especially important is the use of computational techniques to develop new control algorithms, which ultimately would be implemented in the laboratory to guide the control of complex quantum systems. Beyond control alone, many of the same concepts can be exploited for the performance of experiments optimally tuned for inversion, to extract Hamiltonian information. The latter scenario poses very high demands on the efficiency of solving the quantum dynamics equations to extract the information content from the experimental data. The concept of exploiting a computational quantum control tool kit will be introduced as a means for addressing many of these challenges.
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.
Geometric algebra and information geometry for quantum computational software
NASA Astrophysics Data System (ADS)
Cafaro, Carlo
2017-03-01
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to enhance the algebraic efficiency and the geometrical significance of the digital and analog representations of Grover's algorithm, respectively. Specifically, GA is used to describe the Grover iterate and the discretized iterative procedure that exploits quantum interference to amplify the probability amplitude of the target-state before measuring the query register. The transition from digital to analog descriptions occurs via Stone's theorem which relates the (unitary) Grover iterate to a suitable (Hermitian) Hamiltonian that controls Schrodinger's quantum mechanical evolution of a quantum state towards the target state. Once the discrete-to-continuos transition is completed, IG is used to interpret Grover's iterative procedure as a geodesic path on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover's algorithm. Finally, we discuss the dissipationless nature of quantum computing, recover the quadratic speedup relation, and identify the superfluity of the Walsh-Hadamard operation from an IG perspective with emphasis on statistical mechanical considerations.
Quantum computing on lattices using global two-qubit gates
Ivanyos, G.; Massar, S.; Nagy, A. B.
2005-08-15
We study the computation power of lattices composed of two-dimensional systems (qubits) on which translationally invariant global two-qubit gates can be performed. We show that if a specific set of six global two qubit gates can be performed and if the initial state of the lattice can be suitably chosen, then a quantum computer can be efficiently simulated.
Wu, Guorong; Neville, Simon P.; Schalk, Oliver; Sekikawa, Taro; Ashfold, Michael N. R.; Worth, Graham A.; Stolow, Albert
2016-01-07
The dynamics of N-methylpyrrole following excitation at wavelengths in the range 241.5-217.0 nm were studied using a combination of time-resolved photoelectron spectroscopy (TRPES), ab initio quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree method, as well as high-level photoionization cross section calculations. Excitation at 241.5 and 236.2 nm results in population of the A{sub 2}(πσ{sup ∗}) state, in agreement with previous studies. Excitation at 217.0 nm prepares the previously neglected B{sub 1}(π3p{sub y}) Rydberg state, followed by prompt internal conversion to the A{sub 2}(πσ{sup ∗}) state. In contrast with the photoinduced dynamics of pyrrole, the lifetime of the wavepacket in the A{sub 2}(πσ{sup ∗}) state was found to vary with excitation wavelength, decreasing by one order of magnitude upon tuning from 241.5 nm to 236.2 nm and by more than three orders of magnitude when excited at 217.0 nm. The order of magnitude difference in lifetimes measured at the longer excitation wavelengths is attributed to vibrational excitation in the A{sub 2}(πσ{sup ∗}) state, facilitating wavepacket motion around the potential barrier in the N–CH{sub 3} dissociation coordinate.
Computational quantum chemistry and adaptive ligand modeling in mechanistic QSAR.
De Benedetti, Pier G; Fanelli, Francesca
2010-10-01
Drugs are adaptive molecules. They realize this peculiarity by generating different ensembles of prototropic forms and conformers that depend on the environment. Among the impressive amount of available computational drug discovery technologies, quantitative structure-activity relationship approaches that rely on computational quantum chemistry descriptors are the most appropriate to model adaptive drugs. Indeed, computational quantum chemistry descriptors are able to account for the variation of the intramolecular interactions of the training compounds, which reflect their adaptive intermolecular interaction propensities. This enables the development of causative, interpretive and reasonably predictive quantitative structure-activity relationship models, and, hence, sound chemical information finalized to drug design and discovery.
Qudit quantum computation on matrix product states with global symmetry
NASA Astrophysics Data System (ADS)
Wang, Dong-Sheng; Stephen, David T.; Raussendorf, Robert
2017-03-01
Resource states that contain nontrivial symmetry-protected topological order are identified for universal single-qudit measurement-based quantum computation. Our resource states fall into two classes: one as the qudit generalizations of the one-dimensional qubit cluster state, and the other as the higher-symmetry generalizations of the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) state, namely, with unitary, orthogonal, or symplectic symmetry. The symmetry in cluster states protects information propagation (identity gate), while the higher symmetry in AKLT-type states enables nontrivial gate computation. This work demonstrates a close connection between measurement-based quantum computation and symmetry-protected topological order.
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.
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.
Continuous-variable quantum computing on encrypted data.
Marshall, Kevin; Jacobsen, Christian S; Schäfermeier, Clemens; Gehring, Tobias; Weedbrook, Christian; Andersen, Ulrik L
2016-12-14
The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a user's privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits (from a quantum perspective) that could one day allow the potential widespread adoption of this quantum technology in future cloud-based computing networks.
Continuous-variable quantum computing on encrypted data
NASA Astrophysics Data System (ADS)
Marshall, Kevin; Jacobsen, Christian S.; Schäfermeier, Clemens; Gehring, Tobias; Weedbrook, Christian; Andersen, Ulrik L.
2016-12-01
The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a user's privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits (from a quantum perspective) that could one day allow the potential widespread adoption of this quantum technology in future cloud-based computing networks.
Continuous-variable quantum computing on encrypted data
Marshall, Kevin; Jacobsen, Christian S.; Schäfermeier, Clemens; Gehring, Tobias; Weedbrook, Christian; Andersen, Ulrik L.
2016-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the security of a user's privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits (from a quantum perspective) that could one day allow the potential widespread adoption of this quantum technology in future cloud-based computing networks. PMID:27966528
Kochen-Specker Theorem as a Precondition for Quantum Computing
NASA Astrophysics Data System (ADS)
Nagata, Koji; Nakamura, Tadao
2016-12-01
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.
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
Towards a fullerene-based quantum computer
NASA Astrophysics Data System (ADS)
Benjamin, Simon C.; Ardavan, Arzhang; Briggs, G. Andrew D.; Britz, David A.; Gunlycke, Daniel; Jefferson, John; Jones, Mark A. G.; Leigh, David F.; Lovett, Brendon W.; Khlobystov, Andrei N.; Lyon, S. A.; Morton, John J. L.; Porfyrakis, Kyriakos; Sambrook, Mark R.; Tyryshkin, Alexei M.
2006-05-01
Molecular structures appear to be natural candidates for a quantum technology: individual atoms can support quantum superpositions for long periods, and such atoms can in principle be embedded in a permanent molecular scaffolding to form an array. This would be true nanotechnology, with dimensions of order of a nanometre. However, the challenges of realizing such a vision are immense. One must identify a suitable elementary unit and demonstrate its merits for qubit storage and manipulation, including input/output. These units must then be formed into large arrays corresponding to an functional quantum architecture, including a mechanism for gate operations. Here we report our efforts, both experimental and theoretical, to create such a technology based on endohedral fullerenes or 'buckyballs'. We describe our successes with respect to these criteria, along with the obstacles we are currently facing and the questions that remain to be addressed.
Quantum computing with spin cluster qubits.
Meier, Florian; Levy, Jeremy; Loss, Daniel
2003-01-31
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.
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.
Wu, Guorong; Neville, Simon P.; Worth, Graham A.; Schalk, Oliver; Sekikawa, Taro; Ashfold, Michael N. R.; Stolow, Albert
2015-02-21
The dynamics of pyrrole excited at wavelengths in the range 242-217 nm are studied using a combination of time-resolved photoelectron spectroscopy and wavepacket propagations performed using the multi-configurational time-dependent Hartree method. Excitation close to the origin of pyrrole’s electronic spectrum, at 242 and 236 nm, is found to result in an ultrafast decay of the system from the ionization window on a single timescale of less than 20 fs. This behaviour is explained fully by assuming the system to be excited to the A{sub 2}(πσ{sup ∗}) state, in accord with previous experimental and theoretical studies. Excitation at shorter wavelengths has previously been assumed to result predominantly in population of the bright A{sub 1}(ππ{sup ∗}) and B{sub 2}(ππ{sup ∗}) states. We here present time-resolved photoelectron spectra at a pump wavelength of 217 nm alongside detailed quantum dynamics calculations that, together with a recent reinterpretation of pyrrole’s electronic spectrum [S. P. Neville and G. A. Worth, J. Chem. Phys. 140, 034317 (2014)], suggest that population of the B{sub 1}(πσ{sup ∗}) state (hitherto assumed to be optically dark) may occur directly when pyrrole is excited at energies in the near UV part of its electronic spectrum. The B{sub 1}(πσ{sup ∗}) state is found to decay on a timescale of less than 20 fs by both N-H dissociation and internal conversion to the A{sub 2}(πσ{sup ∗}) state.
Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco; Sorella, Sandro; Casula, Michele
2015-06-07
We study the ionization energy, electron affinity, and the π → π(∗) ((1)La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the (1)La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral (1)La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Dupuy, Nicolas; Bouaouli, Samira; Mauri, Francesco Casula, Michele; Sorella, Sandro
2015-06-07
We study the ionization energy, electron affinity, and the π → π{sup ∗} ({sup 1}L{sub a}) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the {sup 1}L{sub a} excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral {sup 1}L{sub a} excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
Noise tailoring for scalable quantum computation via randomized compiling
NASA Astrophysics Data System (ADS)
Wallman, Joel J.; Emerson, Joseph
2016-11-01
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors are even partially coherent, they present a major obstacle to performing robust computations. Here, we propose a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged. We prove that this randomization tailors the noise into stochastic Pauli errors, which can dramatically reduce error rates while introducing little or no experimental overhead. Moreover, we prove that our technique is robust to the inevitable variation in errors over the randomizing gates and numerically illustrate the dramatic reductions in worst-case error that are achievable. Given such tailored noise, gates with significantly lower fidelity—comparable to fidelities realized in current experiments—are sufficient to achieve fault-tolerant quantum computation. Furthermore, the worst-case error rate of the tailored noise can be directly and efficiently measured through randomized benchmarking protocols, enabling a rigorous certification of the performance of a quantum computer.
A scalable architecture for quantum computation with molecular nanomagnets.
Jenkins, M D; Zueco, D; Roubeau, O; Aromí, G; Majer, J; Luis, F
2016-11-14
A proposal for a magnetic quantum processor that consists of individual molecular spins coupled to superconducting coplanar resonators and transmission lines is carefully examined. We derive a simple magnetic quantum electrodynamics Hamiltonian to describe the underlying physics. It is shown that these hybrid devices can perform arbitrary operations on each spin qubit and induce tunable interactions between any pair of them. The combination of these two operations ensures that the processor can perform universal quantum computations. The feasibility of this proposal is critically discussed using the results of realistic calculations, based on parameters of existing devices and molecular qubits. These results show that the proposal is feasible, provided that molecules with sufficiently long coherence times can be developed and accurately integrated into specific areas of the device. This architecture has an enormous potential for scaling up quantum computation thanks to the microscopic nature of the individual constituents, the molecules, and the possibility of using their internal spin degrees of freedom.
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.
Characterization of scalable ion traps for quantum computation
NASA Astrophysics Data System (ADS)
Epstein, R. J.; Bollinger, J. J.; Leibfried, D.; Seidelin, S.; Britton, J.; Wesenberg, J. H.; Shiga, N.; Amini, J. M.; Blakestad, R. B.; Brown, K. R.; Home, J. P.; Itano, W. M.; Jost, J. D.; Langer, C.; Ozeri, R.; Wineland, D. J.
2007-03-01
We discuss the experimental characterization of several scalable ion trap architectures for quantum information processing. We have developed an apparatus for testing planar ion trap chips which features: a standardized chip carrier for ease of interchanging traps, a single-laser Raman cooling scheme, and photo-ionization loading of Mg^+ ions. The primary benchmark for a given trap is the heating rate of the ion motional degrees of freedom, which can reduce multi-ion quantum gate fidelities. As the heating rate depends on the ion trap geometry and materials, our testing apparatus allows for efficient iteration and optimization of trap parameters. With the recent ability to fabricate planar traps with sufficiently low heating rates for quantum computation ^2, we describe current results on the simulation and fabrication of planar traps with multiple intersecting trapping zones for versatile ion choreography. S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006). J. Kim, et al., Quantum Inf. Comput. 5, 515 (2005).
How to simulate a universal quantum computer using negative probabilities
NASA Astrophysics Data System (ADS)
Hofmann, Holger F.
2009-07-01
The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical communication) between the qubits. For a single gate, the probabilities of the three operations are 1, 1 and -1. This decomposition can be applied in a probabilistic simulation of quantum computation by randomly choosing one of the three operations for each gate and assigning a negative statistical weight to the outcomes of sequences with an odd number of negative probability operations. The maximal exponential speed-up of a quantum computer can then be evaluated in terms of the increase in the number of sequences needed to simulate a single operation of the quantum circuit.