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This is the homepage of "an Australian multi-university collaboration undertaking research on the fundamental physics and technology of building, at the atomic level, a solid state quantumcomputer in silicon together with other high potential implementations." Although attempts to develop a quantumcomputer have met with limited success, the centre has substantial resources invested in advancing toward practical uses of quantumcomputingtechnology. The site provides a very good introduction to the principles and implications of quantumcomputing, as well as details about various research projects underway at the Australian universities. Links to conference and journal papers produced by members of the centre, many from 2003, are also provided.

QUANTUM CRYPTOGRAPHY QUANTUMCOMPUTING 1. Quantum cryptography : from basic principles to practical realizations. 2. Quantumcomputing : a conceptual revolution hard to materialize Philippe Grangier, Institut d computers, better algorithms (obviously kept secret) ? - Article by Peter Shor (1994) : a "quantumcomputer

Moore's Law is a famous rule of thumb that says transistor density, and hence microprocessor performance, doubles approximately every eighteen months. While this trend has stood the test of time, many experts believe it will eventually grind to a halt when physical limitations prevent further miniaturization. Although this will likely not happen for twenty years or more, researchers are already looking at a potential solution.The concept of quantumcomputing has been around since the 1970's, but the science is still in its infancy. To learn about its profound implications, Liquid Logic (1) is a solid article with some remarkable insights into the technology. One of the most comprehensive sources on the Web is at the Centre for QuantumComputation (2) (last mentioned in the June 24, 1998 Scout Report). This has lots of introductory materials and tutorials that explain many of the basic concepts of quantumcomputing. The Centre's research efforts are also detailed on the site. Another good site for people new to the subject is the home page of Magiq Technologies (3). A very informative section about quantum information processing looks at some of the history of its development and its applications for the future. The company addresses some key issues in the frequently asked questions section, such as why research in this area could be so important. The Quantum Logic and Coherent Control Project Web site (4) presents extensive advanced theory about several experiments conducted with an rf (Paul) ion trap. The discussions are replete with equations and graphs, probably most suited for post graduate research. The Institute for Quantum Information (5) offers over 30 of its publications online, most of which are very recent. Because it is located at the California Institute of Technology, there are links to course home pages with lecture notes and solutions to problems. Users of the popular Mathematica software can add a powerful library of quantumcomputation functions with the free QuCalc package (6). The download site has documentation for the software and a few examples that include Mathematica code. Quantum Leap: Seize the Light (7) is an insightful article that discusses two recently published papers that address two promising methods of harnessing qubits (the fundamental unit of storage for quantumcomputation). This is necessary for the advancement of the technology, because the current methods are quite limited. EE Times hosts another article (8) about one of the newest breakthroughs in quantum information processing. Researchers at Harvard University have successfully transferred quantum information from a laser beam into and out of the spin state of rubidium atoms. The article considers the accomplishment and looks at what the group is planning next.

QuantumComputation and Quantum Information Samuel J. Lomonaco, Jr. and Howard E. Brandt editors Searches with a Quantum Robot .............................................. 12 pages Benioff, Paul Perturbation Theory and Numerical Modeling Quantum Logic Operations with a Large of Qubits

In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantumcomputers, if built, might be used as a dramatically powerful computational tool. This review is about to tell the story of theoretical quantumcomputation. I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantumcomputation. The review begins with background on theoretical computer science, Turing machines and Boolean circuits. In light of these models, I define quantumcomputers, and discuss the issue of universal quantum gates. Quantum algorithms, including Shor's factorization algorithm and Grover's algorithm for searching databases, are explained. I will devote much attention to understanding what the origins of the quantumcomputational power are, and what the limits of this power are. Finally, I describe the recent theoretical results which show that quantumcomputers maintain their complexity power even in the presence of noise, inaccuracies and finite precision. I tried to put all results in their context, asking what the implications to other issues in computer science and physics are. In the end of this review I make these connections explicit, discussing the possible implications of quantumcomputation on fundamental physical questions, such as the transition from quantum to classical physics.

We identify "proper quantumcomputation" with computational processes that cannot be efficiently simulated on a classical computer. For optical quantumcomputation, we establish "no-go" theorems for classes of quantum optical experiments that cannot yield proper quantumcomputation, and we identify requirements for optical proper quantumcomputation that correspond to violations of assumptions underpinning the no-go theorems.

This paper investigates a variety of unconventional quantumcomputation devices, including fermionic quantumcomputers and computers that exploit nonlinear quantum mechanics. It is shown that unconventional quantumcomputing devices can in principle compute some quantities more rapidly than `conventional' quantumcomputers.

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 quantumcomputers is under acti...

Quantum communication is built on a set of disruptive concepts and technologies. It is driven by fascinating physics and by promising applications. It requires a new mix of competencies, from telecom engineering to theoretical physics, from theoretical computer science to mechanical and electronic engineering. First applications have already found their way to niche markets and university labs are working on futuristic quantum networks, but most of the surprises are still ahead of us. Quantum communication, and more generally quantum information science and technologies, are here to stay and will have a profound impact on the XXI century.

This article surveys quantumcomputational complexity, with a focus on three fundamental notions: polynomial-time quantumcomputations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of quantum complexity classes based on these notions, such as BQP, QMA, and QIP, are presented. Other topics in quantum complexity, including quantum advice, space-bounded quantumcomputation, and bounded-depth quantum circuits, are also discussed.

Classical and quantum information are very different. Together they can perform feats that neither could achieve alone, such as quantumcomputing, quantum cryptography and quantum teleportation. Some of the applications range from helping to preventing spies from reading private communications. Among the tools that will facilitate their implementation, we note quantum purification and quantum error correction. Although some of these ideas are still beyond the grasp of current technology, quantum cryptography has been implemented and the prospects are encouraging for small-scale prototypes of quantumcomputation devices before the end of the millennium.

Students will learn the history of computers as well as how computers work. COMPUTERTECHNOLOGY (9-12) - 52.0417 ComputerTechnology is an introduction to computer application software that includes word processing, spreadsheet, database, and telecommunications. An awareness of career opportunities, business ethics, and trends is included. Everything is done with computers. Your job will most likely have a computer to save files, write ...

Tasked with the challenge to build better and better computers, quantumcomputing and classical computing face the same conundrum: the success of classical computing systems. Small quantumcomputing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantumcomputing systems that out-compute classical systems capable of some logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends.

The significance of quantumcomputation for cryptography is discussed. Following a brief survey of the requirements for quantumcomputational hardware, an overview of the ion trap quantumcomputation project at Los Alamos is presented. The physical limitations to quantumcomputation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.

The significance of quantumcomputation for cryptography is discussed. Following a brief survey of the requirements for quantumcomputational hardware, an overview of the ion trap quantumcomputation project at Los Alamos is presented. The physical limitations to quantumcomputation with trapped ions are analyzed and an assessment of the computational potential of the technology is made.

We present a constructive method to translate small quantum circuits into their optical analogues, using linear components of present-day quantum optics technology only. These optical circuits perform precisely the computation that the quantum circuits are designed for, and can thus be used to test the performance of quantum algorithms. The method relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). The optical implementation of Brassard et al.'s teleportation circuit, a non-trivial 3-bit quantumcomputation, is presented as an illustration.

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…

Necessary and sufficient conditions are given for the construction of a hybrid quantumcomputer that operates on both continuous and discrete quantum variables. Such hybrid computers are shown to be more efficient than conventional quantumcomputers for performing a variety of quantum algorithms, such as computing eigenvectors and eigenvalues.

Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantumcomputers 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 quantumcomputers that interact with environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.

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 quantumcomputers 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 quantumcomputers 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.

We formulate a novel ground state quantumcomputation approach that requires no unitary evolution of qubits in time: the qubits are fixed in stationary states of the Hamiltonian. This formulation supplies a completely time-independent approach to realizing quantumcomputers. We give a concrete suggestion for a ground state quantumcomputer involving linked quantum dots.

Integrable quantumcomputation is defined as quantumcomputing via the integrable condition, in which two-qubit gates are either nontrivial unitary solutions of the Yang--Baxter equation or the Swap gate (permutation). To make the definition clear, in this article, we explore the physics underlying the quantum circuit model, and then present a unified description on both quantumcomputing via the Bethe ansatz and quantumcomputing via the Yang--Baxter equation.

An introduction to quantum probability, quantum mechanics, and quantumcomputation Greg Kuperberg". Recently quantumcomputation has entered as a new reason for both mathematicians and computer scientists deterministic algorithms for some computational problems, quantum algorithms can be moderately faster

The discovery of an algorithm for factoring which runs in polynomial time on a quantumcomputer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantumcomputing. At the same time, many different quantum systems are being explored for their suitability to serve as a physical substrate for the quantumcomputer of the future. I discuss some of the theoretical foundations of quantumcomputer science, including algorithms and error correction, and present a few physical systems that have shown promise as a quantumcomputing platform. Finally, we discuss a spin-off of the quantumcomputing revolution: quantumtechnologies.

- tum computation and information was accelerated in several fronts: hardware for quantumcomputationQUANTUMCOMPUTATION AND INFORMATION AmÂ´ilcar Sernadas,1 Paulo Mateus1 and Yasser Omar2 1CLC, Dep After a very brief survey of the key milestones and open problems in quantumcomputation and information

QuantumComputing Peter Shor M.I.T. Cambridge, MA 1 #12;What is the difference between a computer (physical) device can perform efficiently. (Various theoretical computer scientists, 1960's). If quantumcomputers can be built, this would imply this "folk thesis" is not true. 14 #12;Misconceptions about Quantum

The discovery of quantum error correction has greatly improved the long-term prospects for quantumcomputingtechnology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantumcomputation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantumcomputing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.

This article introduces quantumcomputation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.

Quantumcomputation poses challenging engineering and basic physics issues for the control of nanoscale systems. In particular, experimental realizations of up to seven-qubit NMR quantumcomputers have acutely illustrated ...

QuantumComputational Complexity John Watrous Institute for QuantumComputing and School computations V. Quantum proofs VI. Quantum interactive proof systems VII. Other selected notions in quantum studied model of quantumcomputation. Quantum complexity class. A quantum complexity class is a collection

We briefly review what a quantumcomputer 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 quantum simulation of quantum systems. While most quantumcomputation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data is encoded in the quantumcomputer. 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 quantumcomputer. This type of direct correspondence is how data is 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 quantumcomputers (CVQC) 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.

We present authorized quantumcomputation, where only a user with a non-cloneable quantum authorization key can perform a unitary operation created by an authenticated programmer. The security of our authorized quantumcomputation is based on the quantumcomputational complexity problem of forging the keys from an obfuscated quantum gate sequence. Under the assumption of the existence of a \\textit{sufficiently-random gate shuffling algorithm}, the problem is shown to be in the NQP (Non-deterministic Quantum Polynomial)-hard class by reducing it to a NQP-Complete problem, the exact non-identity check problem. Therefore, our authorized quantumcomputation can be computationally secure against attacks using quantumcomputers.

Blind quantumcomputation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantumtechnology at her disposal, to delegate her quantumcomputation to Bob, who has a fully fledged quantumcomputer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantumcomputation in an optical system has raised new challenges regarding the scalability of blind quantumcomputation in realistic noisy conditions. Here we show that fault-tolerant blind quantumcomputation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 0.0043, which is comparable to that (0.0075) of non-blind topological quantumcomputation. As the error per gate of the order 0.001 was already achieved in some experimental systems, our result implies that secure cloud quantumcomputation is within reach.

Systems of spin 1, such as triplet pairs of spin-1/2 fermions (like orthohydrogen nuclei) make useful three-terminal elements for quantumcomputation, and when interconnected by qubit equality relations are universal for quantumcomputation. This is an instance of quantum-statistical computation: some of the logical relations of the problem are satisfied identically in virtue of quantum statistics, which takes no time. We show heuristically that quantum-statistical ground-mode computation is substantially faster than pure ground-mode computation when the ground mode is reached by annealing.

Do quantumcomputers already exist in Nature? It is proposed that they do. Photosynthesis is one example in which a 'quantumcomputer' component may play a role in the 'classical' world of complex biological systems. A 'translation' of the standard metabolic description of the 'front-end' light harvesting complex in photosynthesis into the language of quantumcomputers is presented. Biological systems represent an untapped resource for thinking about the design and operation of hybrid quantum-classical computers and expanding our current conceptions of what defines a 'quantumcomputer' in Nature.

I provide an introduction to quantumcomputers, describing how they might be\\u000arealized using language accessible to a solid state physicist. A listing of the\\u000aminimal requirements for creating a quantumcomputer is given. I also discuss\\u000aseveral recent developments in the area of quantum error correction, a subject\\u000aof importance not only to quantumcomputation, but also to some

Topological quantumcomputation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantumcomputation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantumtechnologies fuelled the fascination in this field. This ‘focus on’ collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.

Topological quantumcomputation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantumcomputation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterisation of topological phases of matter and their experimental realisation. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantumtechnologies fuelled the fascination in this field. This `focus on' brings together several of the latest developments in the field and facilitates the synergy between different approaches.

We propose a fluxon-controlled quantumcomputer 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 quantumcomputer acts exactly like a knitting machine at home.

We propose a fluxon-controlled quantumcomputer 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 quantumcomputer acts exactly like a knitting machine at home.

QuantumComputing Abbas Edalat 18 lectures + 9 tutorials Lecture Notes and Exercise Sheets 1 Topics of the Course . Introduction to Quantum Mechanics . Quantum Bits and Complex Vector Spaces computational machines. The prominent English logician/mathematician, Alan Turing, formulated the classical

QuantumComputing Abbas Edalat 18 lectures + 9 tutorials Lecture Notes and Exercise Sheets 1 #12;Topics of the Course Â· Introduction to Quantum Mechanics Â· Quantum Bits and Complex Vector computational machines. The prominent English logician/mathematician, Alan Turing, formulated the classical

Topological quantumcomputing promises error-resistant quantumcomputation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantumcomputing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantumcomputing with these topological quantumcomputing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.

Chris Cesare; Andrew J. Landahl; Dave Bacon; Steven T. Flammia; Alice Neels

The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantumcomputation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantumcomputer storing about 10^6 qubits, with a probability of error per quantum gate of order 10^{-6}, would be a formidable factoring engine. Even a smaller, less accurate quantumcomputer would be able to perform many useful tasks. (This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18 December 1996.)

In everyday life, practically all the information which is processed, exchanged or stored is coded in the form of discrete entities called bits, which take two values only, by convention 0 and 1. With the present technology for computers and optical fibers, bits are carried by electrical currents and electromagnetic waves corresponding to macroscopic fluxes of electrons and photons, and they are stored in memories of various kinds, for example, magnetic memories. Although quantum physics is the basic physics which underlies the operation of a transistor (Chapter 6) or of a laser (Chapter 4), each exchanged or processed bit corresponds to a large number of elementary quantum systems, and its behavior can be described classically due to the strong interaction with the environment (Chapter 9). For about thirty years, physicists have learned to manipulate with great accuracy individual quantum systems: photons, electrons, neutrons, atoms, and so forth, which opens the way to using two-state quantum systems, such as the polarization states of a photon (Chapter 2) or the two energy levels of an atom or an ion (Chapter 4) in order to process, exchange or store information. In § 2.3.2, we used the two polarization states of a photon, vertical (V) and horizontal (H), to represent the values 0 and 1 of a bit and to exchange information. In what follows, it will be convenient to use Dirac's notation (see Appendix A.2.2 for more details), where a vertical polarization state is denoted by |V> or |0> and a horizontal one by |H> or |1>, while a state with arbitrary polarization will be denoted by |?>. The polarization states of a photon give one possible realization of a quantum bit, or for short a qubit. Thanks to the properties of quantum physics, quantumcomputers using qubits, if they ever exist, would outperform classical computers for some specific, but very important, problems. In Sections 8.1 and 8.2, we describe some typical quantum algorithms and, in order to do so, we shall not be able to avoid some technical developments. However, these two sections may be skipped in a first reading, as they are not necessary for understanding the more general considerations of Sections 8.3 and 8.4.

A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but\\u000a it is a process that takes place in nature and as such it is subject to the laws of physics. Quantumcomputers are machines\\u000a that rely on characteristically quantum phenomena, such as quantum interference and quantum

Blind quantumcomputation is a secure delegated quantumcomputing protocol where Alice who does not have sufficient quantumtechnology at her disposal delegates her computation to Bob who has a fully-fledged quantumcomputer in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. Protocols of blind quantumcomputation have been proposed for several qubit 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 quantumcomputation for the continuous-variable measurement-based model. We show that blind quantumcomputation 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 quantumcomputation.

Blind quantumcomputation is a secure delegated quantumcomputing protocol where Alice, who does not have sufficient quantumtechnology at her disposal, delegates her computation to Bob, who has a fully fledged quantumcomputer, in such a way that Bob cannot learn anything about Alice’s input, output, and algorithm. Protocols of blind quantumcomputation 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 quantumcomputation for the continuous-variable measurement-based model. We show that blind quantumcomputation 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 quantumcomputation.

We discuss how quantum information distribution can improve the performance of some quantumcomputation tasks. This distribution can be naturally implemented with different types of quantum cloning procedures. We give two examples of tasks for which cloning provides some enhancement in performance, and briefly discuss possible extensions of the idea.

We show that in quantumcomputation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates.

Holonomic QuantumComputation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of unitary quantum gates is realized by driving adiabatically the Hamiltonian parameters along loops in a control manifold. By properly designing such loops the non-trivial curvature of the underlying bundle geometry gives rise to unitary transformations i.e., holonomies that implement the desired unitary transformations. Conditions necessary for universal QC are stated in terms of the curvature associated to the non-abelian gauge potential (connection) over the control manifold. In view of their geometrical nature the holonomic gates are robust against several kind of perturbations and imperfections. This fact along with the adiabatic fashion in which gates are performed makes in principle HQC an appealing way towards universal fault-tolerant QC.

We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantumcomputation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantumcomputation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantumcomputation.

A. Ekert; M. Ericsson; P. Hayden; H. Inamori; J. A. Jones; D. K. L. Oi; V. Vedral

We discuss the usefulness of quantum cloning and present examples of quantumcomputation tasks for which cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantumcomputations, we need to distribute quantum information contained in states about which we have some partial information. To perform quantumcomputations, we use state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantumcomputation.

The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a molecule as well as most other properties, can be calculated by solving the Schrodinger equation. However, the computational resources required to obtain exact solutions on a conventional computer generally increase exponentially with the number of atoms involved. This renders such calculations intractable for all but the smallest of systems. Recently, an efficient algorithm has been proposed enabling a quantumcomputer to overcome this problem by achieving only a polynomial resource scaling with system size. Such a tool would therefore provide an extremely powerful tool for new science and technology. Here we present a photonic implementation for the smallest problem: obtaining the energies of H2, the hydrogen molecule in a minimal basis. We perform a key algorithmic step - the iterative phase estimation algorithm - in full, achieving a high level of precision and robustness to error. We implement other algorithmic steps with assistance from a classical computer and explain how this non-scalable approach could be avoided. Finally, we provide new theoretical results which lay the foundations for the next generation of simulation experiments using quantumcomputers. We have made early experimental progress towards the long-term goal of exploiting quantum information to speed up quantum chemistry calculations.

Benjamin P. Lanyon; James D. Whitfield; Geoff G. Gillet; Michael E. Goggin; Marcelo P. Almeida; Ivan Kassal; Jacob D. Biamonte; Masoud Mohseni; Ben J. Powell; Marco Barbieri; Alán Aspuru-Guzik; Andrew G. White

Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit quantum features could factor large composite integers. This task is believed to be out of reach of classical computers as soon as the number of digits

Blind quantumcomputation is a new quantum secure protocol, which enables Alice who does not have enough quantumtechnology to delegate her computation to Bob who has a fully-fledged quantum power without revealing her input, output and algorithm. So far, blind quantumcomputation has been considered only for the circuit model and the measurement-based model. Here we consider the possibility and the limitation of blind quantumcomputation in the ancilla-driven model, which is a hybrid of the circuit and the measurement-based models.

Quantum Statistical Mechanics and QuantumComputation 22-23 March 2012 Room 111, Jadwin Hall, focused meeting to explore the intersection between quantum statistical mechanics and quantumcomputation, specifically quantum complexity theory. Advances in complexity theory have interesting implications for physics

The QuantumComputation and Quantum Error Prevention Wiki is a collaborative and live document to compliment courses on quantumcomputing. All edits must be made by registered users in order to maintain accuracy and integrity for the document. It is produced by Qunet, a network for quantum physicists, particularly those working in the fields of quantum information and quantumcomputation. It was developed as a part of a NSF funded project led by Prof. M. S. Byrd at Southern Illinois University Carbondale.

We report recent results on the spin dynamics of coupled quantum dots and their potential as quantumcomputer devices. Using the Heitler-London approach, we obtain the exchange coupling J(B,a) between the excess electrons of coupled dots.(D.P. DiVincenzo and D. Loss, QuantumComputation is Physical), to appear in Superlattices and Microstructures. Special Issue on the occasion of Rolf Landauer's 70th Birthday, ed. S. Datta. See cond- mat/9710259. The dependence of J on the magnetic field B and the interdot distance 2a is of great importance for controlling the coherent time-evolution of the two-spin system as required for quantumcomputation.(D. Loss and D.P. DiVincenzo, Phys. Rev. A, in press. See cond- mat/9701055.) Our result, which is in good agreement with a more refined LCAO calculation, is accessible to experimental tests via magnetic response measurements.

Quantumcomputation Samuel L. Braunstein Computer Science, University of York, York YO10 5DD, UK and logic gates 3.1. FANOUT and ERASE 3.2. Computation without ERASE 4. Elementary quantum notation 5. Logic gates for quantum bits 6. Logic gates in the laboratory 7. Model quantumcomputer and quantum code 8

Chapter 52. Quantum Information and QuantumComputation 52-1 Quantum Information and Quantum Sullivan, Rita Tavilla Introduction Quantumcomputers and communication systems are devices that store and process information on quantum systems such as atoms, photons, superconducting systems, etc. Quantum

Quantumcomputers are expected to offer substantial speedups over their classical counterparts and to solve problems that are intractable for classical computers. Beyond such practical significance, the concept of quantumcomputation opens up new fundamental questions, among them the issue whether or not quantumcomputations can be certified by entities that are inherently unable to compute the results themselves. Here we present the first experimental verification of quantumcomputations. We show, in theory and in experiment, how a verifier with minimal quantum resources can test a significantly more powerful quantumcomputer. The new verification protocol introduced in this work utilizes the framework of blind quantumcomputing and is independent of the experimental quantum-computation platform used. In our scheme, the verifier is only required to generate single qubits and transmit them to the quantumcomputer. We experimentally demonstrate this protocol using four photonic qubits and show how the verifier can test the computer's ability to perform measurement-based quantumcomputations.

Stefanie Barz; Joseph F. Fitzsimons; Elham Kashefi; Philip Walther

This series of video lectures is designed to be used either as an introduction to the quantum theory of computation or as an introduction to quantum physics itself. The level of mathematics used is relatively low, requiring only that the viewer understand the concepts of eigenvalues and vector spaces. The lectures are accompanied by problem and solutions sets.

We describe a simulation method for a quantum spin model of a generic, general purpose quantumcomputer. The use of this quantumcomputer simulator is illustrated through several implementations of Grover's database search algorithm. Some preliminary results on the stability of quantum algorithms are presented.

H. De Raedt; A. H. Hams; K. Michielsen; S. Miyashita; K. Saito

This review gives a survey of numerical algorithms and software to simulate quantumcomputers.It covers the basic concepts of quantumcomputation and quantum algorithms and includes a few examples that illustrate the use of simulation software for ideal and physical models of quantumcomputers.

We review the field of Optical QuantumComputation, considering the various implementations that have been proposed and the experimental progress that has been made toward realizing them. We examine both linear and nonlinear approaches and both particle and field encodings. In particular we discuss the prospects for large scale optical quantumcomputing in terms of the most promising physical architectures and the technical requirements for realizing them.

The theory of quantumcomputation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantumcomputation is presented in detail. Throughout there is an emphasis on the physical as well as the abstract aspects of computation and the interplay between them. This report is presented as a Master's thesis at the department of Computer Science and Engineering at G{\\"o}teborg University, G{\\"o}teborg, Sweden. The text is part of a larger work that is planned to include chapters on quantum algorithms, the quantum Turing machine model and abstract approaches to quantumcomputation.

The theory of quantumcomputation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantumcomputation is presented in detail. Throughout there is an emphasis on the physical as well as the abstract aspects of computation and the interplay between them. This report is presented as a Master's thesis at the department of Computer Science and Engineering at G{\\"o}teborg University, G{\\"o}teborg, Sweden. The text is part of a larger work that is planned to include chapters on quantum algorithms, the quantum Turing machine model and abstract approaches to quantumcomputation.

Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantumcomputer to simulate such quantum systems has been viewed as a key application of quantumcomputation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantumcomputers. In this paper we survey the theoretical and experimental development of quantum simulation using quantumcomputers, from the first ideas to the intense research efforts currently underway.

Katherine L Brown; William J Munro; Vivien M Kendon

Quantumcomputer possesses quantum parallelism and offers great computing power over classical computer \\cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantumcomputer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \\cite{r1}. Simply put it, a duality computer is a moving quantumcomputer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantumcomputer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantumcomputer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantumcomputer to run classical algorithms in a $O(2^n)$-bit classical computer. The duality mode provides a natural link between classical computing and quantumcomputing. Here we also propose a recycling computing mode in which a quantumcomputer will continue to compute until the result is obtained. These two modes provide new tool for algorithm design. A search algorithm for the unsorted database search problem is designed.

QUANTUMCOMPUTING: AN OVERVIEW MIKIO NAKAHARA Department of Physics and Research Center for Quantum of quantumcomputing and quantum infromation processing are introduced for mathe- matics students. Subjects. INTRODUCTION Quantumcomputing and quantum information processing are emerging disciplines in which

The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A way toward the realization of intelligent quantum robots is to adopt a quantum metalanguage to control quantum robots. A physical implementation of a quantum metalanguage might be the use of coherent states in brain signals.

We propose a realization of quantumcomputing using polarized photons. The information is coded in two polarization directions of the photons and two-qubit operations are done using conditional Faraday effect. We investigate the performance of the system as a computing device.

We discuss the notion of quantumcomputational webs: These are quantum states universal for measurement-based computation, which can be built up from a collection of simple primitives. The primitive elements--reminiscent of building blocks in a construction kit--are (i) one-dimensional states (computationalquantum wires) with the power to process one logical qubit and (ii) suitable couplings, which connect the wires to a computationally universal web. All elements are preparable by nearest-neighbor interactions in a single pass, of the kind accessible in a number of physical architectures. We provide a complete classification of qubit wires, a physically well-motivated class of universal resources that can be fully understood. Finally, we sketch possible realizations in superlattices and explore the power of coupling mechanisms based on Ising or exchange interactions.

Gross, D. [Institute for Theoretical Physics, Leibniz University Hannover, D-30167 Hannover (Germany); Eisert, J. [Institute for Physics and Astronomy, University of Potsdam, D-14476 Potsdam (Germany); Institute for Advanced Study Berlin, D-14193 Berlin (Germany)

Adiabatic quantumcomputation for performing quantumcomputations such as Shor's algorithm is protected against thermal errors by an energy gap of size $O(1/n)$, where $n$ is the length of the computation to be performed.

From the Academy Quantumcomputing Shu-Shen Li* , Gui-Lu LongÂ§Â¶ , Feng-Shan Bai , Song-Lin Feng University, Beijing 100084, China Quantumcomputing is a quickly growing research field. This article introduces the basic concepts of quantumcomputing, recent developments in quantum searching, and decoherence

In 2001 all-optical quantumcomputing became feasible with the discovery that scalable quantumcomputing 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 quantumcomputer. 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.

QuantumComputation Models Foundational Problems Qualitative Questions Conjectural Answer to All Questions Locality in QuantumComputation, II Eric Rowell1 with Z. Wang2, C. Galindo3, S.-M. Hong4 1:Texas A Computation, II #12;QuantumComputation Models Foundational Problems Qualitative Questions Conjectural Answer

QuantumComputing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantumcomputing. The paper begins by motivating the central ideas of quantum mechanics and quantumcomputation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantumcomputation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.

Quantumcomputers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantumcomputing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantumcomputation 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 quantumcomputers widely available. PMID:22267806

Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip

Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantumcomputing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantumcomputing.

Linear optical quantumcomputing with photonic qubits Pieter Kok* Department of Materials, Oxford-ku, Tokyo 101-8430, Japan T. C. Ralph Centre for QuantumComputerTechnology, University of Queensland, St-4242, USA G. J. Milburn Centre for QuantumComputerTechnology, University of Queensland, St. Lucia

We propose a parallel quantumcomputing mode for ensemble quantumcomputer. In this mode, some qubits can be in pure states while other qubits in mixed states. It enables a single ensemble quantumcomputer to perform $"$single-instruction-multi-data" type of parallel computation. In Grover's algorithm and Shor's algorithm, parallel quantumcomputing can provide additional speedup. In addition, it also makes a fuller use of qubit resources in an ensemble quantumcomputer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani, and the Cleve-DiVincenzo algorithms can be re-utilized.

We propose a quantumcomputer structure based on coupled asymmetric single-electron quantum dots. Adjacent dots are strongly coupled by means of electric dipole-dipole interactions enabling rapid computation rates. Further, the asymmetric structures can be tailored for a long coherence time. The result maximizes the number of computation cycles prior to loss of coherence.

A quantumcomputer is a machine that can perform certain calculations much faster than a classical computer by using the laws of quantum mechanics. Quantumcomputers do not exist yet, because it is extremely difficult to control quantum mechanical systems to the necessary degree. What is more, we do at this moment not know which physical system is the best suited for making a quantumcomputer (although we have some ideas). It is likely that a mature quantum information processing technology will use (among others) light, because photons are ideal carriers for quantum information. These notes are an expanded version of the five lectures I gave on the possibility of making a quantumcomputer using light, at the Summer School in Theoretical Physics in Durban, 14-24 January, 2007. There are quite a few proposals using light for quantumcomputing, and I can highlight only a few here. I will focus on photonic qubits, and leave out continuous variables completely. I assume that the reader is familiar with basic quantum mechanics and introductory quantumcomputing.

A quantumcomputer is a machine that can perform certain calculations much faster than a classical computer by using the laws of quantum mechanics. Quantumcomputers do not exist yet, because it is extremely difficult to control quantum mechanical systems to the necessary degree. What is more, we do at this moment not know which physical system is the best suited for making a quantumcomputer (although we have some ideas). It is likely that a mature quantum information processing technology will use (among others) light, because photons are ideal carriers for quantum information. These notes are an expanded version of the five lectures I gave on the possibility of making a quantumcomputer using light, at the Summer School in Theoretical Physics in Durban, 14-24 January, 2007. There are quite a few proposals using light for quantumcomputing, and I can highlight only a few here. I will focus on photonic qubits, and leave out continuous variables completely.1 I assume that the reader is familiar with basic quantum mechanics and introductory quantumcomputing.

In this thesis, I investigate aspects of local Hamiltonians in quantumcomputing. First, I focus on the Adiabatic QuantumComputing model, based on evolution with a time- dependent Hamiltonian. I show that to succeed using ...

Mathew Johnson is a Ball State junior majoring in Mathematics (Option 1) with a minor in Physics. In his sophomore year, he participated in the student- faculty colloquium, where he explored quantum com- puting with several other students and faculty. Quantum mechanics is a scientific theory that seeks to describe atomic and subatomic particles (or quantum particles) as well as

With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantumcomputation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The required computational overhead scales efficiently both with $1/p$ and $n$, where $n$ is the number of qubits in the computation. This approach provides an efficient way to combat noise in a class of quantumcomputation implementation schemes, where the dominant noise leads to probabilistic signaled errors with an error probability $1-p$ far beyond any threshold requirement.

Quantumcomputation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantumcomputer - have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the sheer number of these gates required to implement even small quantum algorithms. Here we present and demonstrate a general technique that harnesses higher dimensions of quantum systems to significantly reduce this number, allowing the construction of key quantum circuits with existing technology. We are thereby able to present the first implementation of two key quantum circuits: the three-qubit Toffoli and the two-qubit controlled-unitary. The gates are realised in a linear optical architecture, which would otherwise be absolutely infeasible with current technology.

Lanyon, B P; Almeida, M P; Jennewein, T; Ralph, T C; Resch, K J; Pryde, G J; O'Brien, J L; Gilchrist, A; White, A G

Quantumcomputation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantumcomputer - have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the sheer number of these gates required to implement even small quantum algorithms. Here we present and demonstrate a general technique that harnesses higher dimensions of quantum systems to significantly reduce this number, allowing the construction of key quantum circuits with existing technology. We are thereby able to present the first implementation of two key quantum circuits: the three-qubit Toffoli and the two-qubit controlled-unitary. The gates are realised in a linear optical architecture, which would otherwise be absolutely infeasible with current technology.

B. P. Lanyon; M. Barbieri; M. P. Almeida; T. Jennewein; T. C. Ralph; K. J. Resch; G. J. Pryde; J. L. O'Brien; A. Gilchrist; A. G. White

Quantumcomputing 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 quantumcomputing model. In this regard, we are particularly interested in the potential applications of quantumcomputers 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 quantumcomputational model, several of the problems associated to the practical implementation of real-life complex software systems in quantumcomputers are often ignored. In this presentation we will argue that practical quantumcomputation 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 quantumcomputing in the areas of memories, I/O, addressing schemes, compilers, oracles, approximate information copying, logical debugging, error correction and fault-tolerant computing protocols.

Program -- 2013 UTS-AMSS Joint Annual Workshop on QuantumComputing and Quantum Information, CAS University of Technology Sydney (UTS) #12;UTS-AMSS Joint Annual Workshop on QuantumComputingComputing power of Turing machines based on quantum logic Afternoon 13:30--14:20 Yuan Feng Symbolic

We present a hybrid model of the unitary-evolution-based quantumcomputation model and the measurement-based quantumcomputation model. In the hybrid model, part of a quantum circuit is simulated by unitary evolution and the rest by measurements on star graph states, thereby combining the advantages of the two standard quantumcomputation models. In the hybrid model, a complicated unitary gate under simulation is decomposed in terms of a sequence of single-qubit operations, the controlled-z gates, and multiqubit rotations around the z axis. Every single-qubit and the controlled-z gate are realized by a respective unitary evolution, and every multiqubit rotation is executed by a single measurement on a required star graph state. The classical information processing in our model requires only an information flow vector and propagation matrices. We provide the implementation of multicontrol gates in the hybrid model. They are very useful for implementing Grover's search algorithm, which is studied as an illustrative example.

Sehrawat, Arun; Englert, Berthold-Georg [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore (Singapore); Zemann, Daniel [Institut fuer Quantenoptik und Quanteninformation, Technikerstrasse 21a, A-6020 Innsbruck (Austria)

We propose to use a single mesoscopic ensemble of trapped polar molecules for quantumcomputing. A "holographic quantum register" with hundreds of qubits is encoded in collective excitations with definite spatial phase variations. Each phase pattern is uniquely addressed by optical Raman processes with classical optical fields, while one- and two-qubit gates and qubit readout are accomplished by transferring the qubit states to a stripline microwave cavity field and a Cooper pair box where controllable two-level unitary dynamics and detection is governed by classical microwave fields. PMID:18764313

This paper describes a quantum cellular automaton capable of performing universal quantumcomputation. The automaton has an elementary transition function that acts on Margolus cells of 2x2 qubits, and both the 'quantum input' and the program are encoded in the initial state of the system.

Raussendorf, Robert [Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)

Adiabatic quantumcomputation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantumcomputation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models provides a new vantage point from which to tackle the central issues in quantumcomputation, namely designing new quantum algorithms and constructing fault tolerant quantumcomputers. In particular, by translating the main open questions in the area of quantum algorithms to the language of spectral gaps of sparse matrices, the result makes these questions accessible to a wider scientific audience, acquainted with mathematical physics, expander theory and rapidly mixing Markov chains.

Dorit Aharonov; Wim van Dam; Julia Kempe; Zeph Landau; Seth Lloyd; Oded Regev

In this paper we present a new unified theoretical framework that describes the full dynamics of quantumcomputation. Our formulation allows any questions pertaining to the physical behavior of a quantumcomputer to be framed, and in principle, answered. We refer to the central organizing principle developed in this paper, on which our theoretical structure is based, as the *QuantumComputer Condition* (QCC), a rigorous mathematical statement that connects the irreversible dynamics of the quantumcomputing machine, with the reversible operations that comprise the quantumcomputation intended to be carried out by the quantumcomputing machine. Armed with the QCC, we derive a powerful result that we call the *Encoding No-Go Theorem*. This theorem gives a precise mathematical statement of the conditions under which fault-tolerant quantumcomputation becomes impossible in the presence of dissipation and/or decoherence. In connection with this theorem, we explicitly calculate a universal critical damping value for...

Gilbert, G; Thayer, F J; Gilbert, Gerald; Hamrick, Michael

We develop a layered quantumcomputer architecture, which is a systematic framework for tackling the individual challenges of developing a quantumcomputer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantumcomputing and introduce several new methods, with an emphasis on employing surface code quantum error correction. In doing so, we propose a new quantumcomputer architecture based on optical control of quantum dots. The timescales 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 timescale of days.

N. Cody Jones; Rodney Van Meter; Austin G. Fowler; Peter L. McMahon; Jungsang Kim; Thaddeus D. Ladd; Yoshihisa Yamamoto

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 quantumcomputation 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 quantumcomputation 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 quantumcomputation 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 quantumcomputation 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. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between quantum walk Hamiltonians and Hamiltonians for qubit systems and quantum circuits; this is done for both single-excitation and multiexcitation encodings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are mapped to quantum walks, and walks on hyperlattices and hypercubes are mapped to various gate systems. We also show how to map a quantum circuit performing the quantum Fourier transform, the key element of Shor's algorithm, to a quantum walk system doing the same. The results herein are an essential preliminary to a Hamiltonian formulation of quantum walks in which coupling to a dynamic quantum environment is included.

Hines, Andrew P. [Pacific Institute of Theoretical Physics and Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, V6T 1Z1 (Canada); Pacific Institute for the Mathematical Sciences, 1933 West Mall, University of British Columbia, Vancouver, British Columbia, V6T 1Z2 (Canada); Stamp, P. C. E. [Pacific Institute of Theoretical Physics and Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, V6T 1Z1 (Canada)

We propose a quantumcomputer architecture based on quantum dots both for short distance and for long distance communication/computation. Our scheme exploits the natural characteristics of self-assembled quantum dots and it is scalable. It is centered on the idea of a quantum bus based on semiconductor self-assembled quantum dots. This allows for transmission of qubits between the different quantum registers, and could be integrated in most of the present proposal for semiconductor quantum dot-based quantumcomputation. Our proposal exploits the peculiar properties of {\\it relatively short} spin-chains, and advantages and disadvantages of two possible implementations, both based on spin-chain global dynamics, are discussed in details. A clear advantage of the scheme is to avoid the use of microcavities for long distance communication between different elements of the quantumcomputer. In this respect our scheme is comparatively faster than hybrid quantum dot-microcavity schemes.

In this paper we present a new unified theoretical framework that describes the full dynamics of quantumcomputation. Our formulation allows any questions pertaining to the physical behavior of a quantumcomputer to be framed, and in principle, answered. We refer to the central organizing principle developed in this paper, on which our theoretical structure is based, as the *Quantum

We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantumcomputer 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.

Algorithmic cooling and scalable NMR quantumcomputers P. Oscar Boykin*, Tal MorÂ§ , Vwani, Israel; Computer Science Department, Technion, Technion City, Haifa 32000, Israel; Â¶Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109; and RAS Computer

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 quantumcomputations 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 quantumcomputations. Because our protocol requires few extra resources compared to 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.

K. Fisher; A. Broadbent; L. K. Shalm; Z. Yan; J. Lavoie; R. Prevedel; T. Jennewein; K. J. Resch

Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantumcomputer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV(-1)) center stands out for its robustness--its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV(-1) center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors. PMID:20404195

Weber, J R; Koehl, W F; Varley, J B; Janotti, A; Buckley, B B; Van de Walle, C G; Awschalom, D D

Identifying and designing physical systems for use as qubits, the basic units of quantum information, are critical steps in the development of a quantumcomputer. Among the possibilities in the solid state, a defect in diamond known as the nitrogen-vacancy (NV-1) center stands out for its robustness—its quantum state can be initialized, manipulated, and measured with high fidelity at room temperature. Here we describe how to systematically identify other deep center defects with similar quantum-mechanical properties. We present a list of physical criteria that these centers and their hosts should meet and explain how these requirements can be used in conjunction with electronic structure theory to intelligently sort through candidate defect systems. To illustrate these points in detail, we compare electronic structure calculations of the NV-1 center in diamond with those of several deep centers in 4H silicon carbide (SiC). We then discuss the proposed criteria for similar defects in other tetrahedrally coordinated semiconductors. PMID:20404195

Weber, J. R.; Koehl, W. F.; Varley, J. B.; Janotti, A.; Buckley, B. B.; Van de Walle, C. G.; Awschalom, D. D.

Computational equivalence between quantum Turing machines and quantum circuit families Christian by quantum circuit families . . . . . . . . . . . 18 3 Computational equivalence 19 3.1 Encoding with my master's study was to obtain a knowledge about the theoretical foundation of quantumcomputing

Motivation: QuantumComputation Sequences of Representations Outlook Localizing Unitary Braid Representations #12;Motivation: QuantumComputation Sequences of Representations Outlook Outline 1 Motivation: QuantumComputationQuantum Circuit and Topological Models 2 Sequences of Representations Matrix

To make arbitrarily accurate quantumcomputation possible, practical realization of quantumcomputers will require suppressing noise in quantum memory and gate operations to make it below a threshold value. A scheme based on realistic quantumcomputer models is described for suppressing noise in quantumcomputation without the cost of stringent quantumcomputing resources.

A quantumcomputer is a machine that can perform certain calculations much faster than a classical computer by using the laws of quantum mechanics. Quantumcomputers do not exist yet, because it is extremely difficult to control quantum mechanical systems to the necessary degree. What is more, we do at this moment not know which physical system is the best suited for making a quantumcomputer (although we have some ideas). It is likely that a mature quantum information processing technology will use (among others) light, because photons are ideal carriers for quantum information. These notes are an expanded version of the five lectures I gave on the possibility of making a quantumcomputer using light, at the Summer School in Theoretical Physics in Durban, 14-24 January, 2007. There are quite a few proposals using light for quantumcomputing, and I can highlight only a few here. I will focus on photonic qubits, and leave out continuous variables completely. I assume that the reader is familiar with basic quan...

A QuantumComputer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantumcomputer threatens the security of public key encryption systems because these systems rely on the fact that prime factorization is computationally difficult. Errors limit the effectiveness of quantumcomputers. Because of the exponential nature of quantum com puters, simulating the effect of errors on them requires a vast amount of processing and memory resources. In this paper we describe a parallel simulator which accesses the feasibility of quantumcomputers. We also derive and validate an analytical model of execution time for the simulator, which shows that parallel quantumcomputer simulation is very scalable.

Quantumcomputers require error correction protocols to repair the state of the quantum bits. This has now been demonstrated using a 'majority voting' protocol among a cluster of three defect spins in diamond.

Quantumcomputing: pro and con BY JOHN PRESKILL Charles C. Lauritsen Laboratory of High Energy Physics, California Institute of Technology, Pasadena, CA 91125, USA I assess the potential of quantumcomputation. Broad and important applications must be found to justify construction of a quantumcomputer; I

Harnessing non-abelian statistics of anyons to perform quantumcomputational 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---$D(S_3)$, the quantum double of $S_3$. Since all anyons in $D(S_3)$ have finite images of braid group representations, they cannot be universal for quantumcomputation 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.

COMPUTER SCIENCE and INFORMATION TECHNOLOGY POSTGRADUATE STUDIES 2006 School of Mathematics, Statistics and Computer Science The University of New England Armidale, NSW, Australia Printed courses in computer science and the graduate level topics in computer science which are offered

In this paper we present a new unified theoretical framework that describes the full dynamics of quantumcomputation. Our formulation allows any questions pertaining to the physical behavior of a quantumcomputer to be framed, and in principle, answered. We refer to the central organizing principle developed in this paper, on which our theoretical structure is based, as the *QuantumComputer Condition* (QCC), a rigorous mathematical statement that connects the irreversible dynamics of the quantumcomputing machine, with the reversible operations that comprise the quantumcomputation intended to be carried out by the quantumcomputing machine. Armed with the QCC, we derive a powerful result that we call the *Encoding No-Go Theorem*. This theorem gives a precise mathematical statement of the conditions under which fault-tolerant quantumcomputation becomes impossible in the presence of dissipation and/or decoherence. In connection with this theorem, we explicitly calculate a universal critical damping value for fault-tolerant quantumcomputation. In addition we show that the recently-discovered approach to quantum error correction known as "operator quantum error-correction" (OQEC) is a special case of our more general formulation. Our approach furnishes what we will refer to as "operator quantum fault-tolerance" (OQFT). In particular, we show how the QCC allows one to derive error thresholds for fault tolerance in a completely general context. We prove the existence of solutions to a class of time-dependent generalizations of the Lindblad equation. Using the QCC, we also show that the seemingly different circuit, graph- (including cluster-) state, and adiabatic paradigms for quantumcomputing are in fact all manifestations of a single, universal paradigm for all physical quantumcomputation.

Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantumcomputation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantumcomputation. Moreover, it is possible to see new connections between principal models of computation, namely, computation over the continuum and computation over the integers (Turing computation). Thus we identify a basic problem in QFT, namely Wightman's computation problem for domains of holomorphy, which we call WHOLO. Inspired by the same analytic functions which are central to the famous CPT theorem of QFT, it is possible to obtain a computational complexity structure for QFT and shed new light on certain complexity classes for this problem WHOLO.

This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so, just what kind of computer it is. I will show that the universe can be regarded as a giant quantumcomputer. The quantumcomputational model of the universe explains a variety of observed phenomena not encompassed by the ordinary laws of physics. In particular, the model shows that the the quantumcomputational universe automatically gives rise to a mix of randomness and order, and to both simple and complex systems.

Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantumcomputation has since been growing. One of the main difficulties of realizing quantumcomputation is that decoherence tends to destroy the information in a superposition of states in a quantumcomputer, thus making long computations impossible. A futher difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering the output of long computations unreliable. It was previously known that a quantum circuit with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per gate. We show, for any quantumcomputation with t gates, how to build a polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of inaccuracy and decoherence per gate, for some constant c. We do this by showing how to compute using quantum error correcting codes. These codes were previously known to provide resistance to errors while storing and transmitting quantum data.

We investigate definitions of and protocols for multi-party quantumcomputing in the scenario where the secret data are quantum systems. We work in the quantum information-theoretic model, where no assumptions are made on the computational power of the adversary. For the slightly weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to establish that any multi-party quantumcomputation can be securely performed as long as the number of dishonest players is less than n/6.

Applications of quantum chaos to realistic quantumcomputations and sound treatment on quantum dynamics on quantumcomputers in presence of imper- fections. The effects of random errors and static computer can be recognized and restored with a minimal number of measurements in presence of random quantum

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantumcomputation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one timestep apart.

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum ''walker'' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantumcomputation in which a quantum walker takes discrete steps of continuous evolution. This ''discontinuous'' quantum walk employs perfect quantum-state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one time step apart.

Underwood, Michael S.; Feder, David L. [Institute for Quantum Information Science, University of Calgary, Calgary, Alberta T2N 1N4 (Canada)

We interpret quantumcomputing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge transformations on the connections play a role of unitary quantum operations. Thereby, a geometrical model for quantumcomputation is presented, which is equivalent to the quantum circuit model. This result shows a geometric way of realizing quantumcomputing and as such, provides an alternative proposal of building a quantumcomputer.

I assess the potential of quantumcomputation. Broad and important applications must be found to justify construction of a quantumcomputer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantumcomputers are notoriously susceptible to making errors; I discuss recently developed fault-tolerant procedures that enable a quantumcomputer with noisy gates to perform reliably. Quantumcomputing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantumcomputation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high-precision experimental physics. A broad interdisciplinary effort will be needed if quantumcomputers are to fulfill their destiny as the world's fastest computing devices. (This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)

The realisation of large-scale quantumcomputing is no longer simply a hardware question. The rapid development of quantumtechnology has resulted in dozens of control and programming problems that should be directed towards the classical computer science and engineering community. One such problem is known as Pauli tracking. Methods for implementing quantum algorithms that are compatible with crucial error correction technology utilise extensive quantum teleportation protocols. These protocols are intrinsically probabilistic and result in correction operators that occur as byproducts of teleportation. These byproduct operators do not need to be corrected in the quantum hardware itself. Instead, byproduct operators are tracked through the circuit and output results reinterpreted. This tracking is routinely ignored in quantum information as it is assumed that tracking algorithms will eventually be developed. In this work we help fill this gap and present an algorithm for tracking byproduct operators through a quantumcomputation. We formulate this work based on quantum gate sets that are compatible with all major forms of quantum error correction and demonstrate the completeness of the algorithm.

Alexandru Paler; Simon J. Devitt; Kae Nemoto; Ilia Polian

Topological quantumcomputing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction code, required to correct for inevitable hardware faults that will exist for a large scale quantum device. It is also a measurement based model of quantumcomputation, meaning that the quantum hardware is responsible only for the construction of a large, computationally universal quantum state. This quantum state is then strategically consumed, allowing for the realisation of a fully error corrected quantum algorithm. The number of physical qubits needed by the quantum hardware and the amount of time required to implement an algorithm is dictated by the manner in which this universal quantum state is consumed. In this paper we examine the problem of algorithmic optimisation in the topological lattice and introduce the required elements that will be needed when designing a classical software package to compile and implement a large scale algorithm on a topological quantumcomputer.

The quantum circuit model is the most widely used model of quantumcomputation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantumcomputers. However, ...

One of the motivating ideas of quantumcomputation 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 quantumcomputer, 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.

DiVincenzo, David (IBM Watson Research Center) [IBM Watson Research Center

One of the motivating ideas of quantumcomputation 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 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 quantumcomputing 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 quantumcomputing. 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.

Warner A. Miller; Grigoriy Kreymerman; Christopher Tison; Paul M. Alsing; Jonathan R. McDonald

In ensemble (or bulk) quantumcomputation, measurements of qubits in an individual computer cannot be performed. Instead, only expectation values can be measured. As a result of this limitation on the model of computation, various important algorithms cannot be processed directly on such computers, and must be modified. We provide modifications of various existing protocols, including algorithms for universal fault--tolerant computation, Shor's factorization algorithm (which can be extended to any algorithm computing an NP function), and some search algorithms to enable processing them on ensemble quantumcomputers.

P. Oscar Boykin; Tal Mor; Vwani Roychowdhury; Farrokh Vatan

Recent advances in the physical sciences and engineering have created great hopes for new computational paradigms and substrates. One such new approach is the quantumcomputer, 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 quantumcomputer 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 quantumcomputation. 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 quantumcomputation 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. Closed form solutions have been derived for each step in this explicit construction procedure. Moreover, the minimum upper bound is found to construct a universal quantum circuit from any Controlled-Unitary gate. A near optimal explicit construction of universal quantum circuits from a given Controlled-Unitary is provided. For the Controlled-NOT and Double-CNOT gate, we then develop simple analytic ways to construct universal quantum circuits with exactly three applications, which is the least possible for these gates. We further discover a new quantum gate (named B gate) that achieves the desired universality with minimal number of gates. Optimal implementation of single-qubit quantum gates is also investigated. Finally, as a real physical application, a constructive way to implement any arbitrary two-qubit operation on a spin electronics system is discussed.

Technical Report No. 2005-496 QUANTUMCOMPUTATION AND QUANTUM INFORMATION Marius Nagy and Selim G the eld of quantumcomputation and quantum information. The reader is rst familiarized with those features-correction are then discussed. Prospects for building a practical quantumcomputer are also analyzed. 1 Introduction

to harness quantum effects in order to speed up computation or find useful applications, the field of quantum, causing computer science to be reconsidered (and effectively rewritten) in the new quantum light substance. 1.1 Origins of quantumcomputing Most people involved in the field associate the birth of quantum

The main ideas behind developments in the theory and technology of quantumcomputation were formulated in the late 1970s and early 1980s by two physicists in the West and a mathematician in the former Soviet Union. It is not generally known in the West that the subject has roots in the Russian technical literature. The author hopes to present as impartial a synthesis as possible of the early history of thought on this subject. The role of reversible and irreversible computational processes is examined briefly as it relates to the origins of quantumcomputing and the so-called Information Paradox in physics.

Manipulating a database system on a quantumcomputer is an essential aim to benefit from the promising speed-up of quantumcomputers over classical computers in areas that take a vast amount of storage and processing time such as in databases. In this paper, the basic operations for manipulating the data in a quantum database will be defined, e.g. INSERT, UPDATE, DELETE, SELECT, backing up and restoring a database file. This gives the ability to perform the data processing that usually takes a long processing time on a classical database system, in a simultaneous way on a quantumcomputer. Defining a quantum version of more advanced concepts used in database systems, e.g. the referential integrity and the relational algebra, is a normal extension to this work

We provide algorithms for efficiently moving and addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with a low overhead by a more realistic model of a distributed quantum ...

We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantumcomputer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our perspectives on quantumcomputation, we study quantumcomputing in one-dimensional nonrelativistic system with delta-function interaction, where the two-body scattering matrix satisfies the factorisation equation (the quantum Yang--Baxter equation) and acts as a parametric two-body quantum gate. We conclude by comparing quantumcomputing via the factorisable scattering with topological quantumcomputing.

Compilers and computer-aided design tools will be essential for quantumcomput- ing. We present a computer-aided design flow that transforms a high-level language program representing a quantumcomputing algorithm into a technology-specific im- plementation. We trace the significant steps in this flow and illustrate the transfor- mations to the representation of the quantum program. The focus of this paper is

VolterraÂCIRM International School Quantumcomputer and quantum information Levico Terme, Italy Ricerca Matematica (CIRM), Istituto Trentino di Cultura The theory of quantum information and computing examples 3. general principles of quantumcomputation (qÂbits, computational bases, gates, dis- crete

Scalable quantumcomputation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear interaction between the two photons, and the efficiency of this nonlinear interaction is typically very tiny in bulk materials. However, we recently have shown that this barrier can be circumvented with effective nonlinearities produced by projective measurements, and with this work linear-optical quantumcomputing becomes a new possibility of scalable quantumcomputation. We review several issues concerning its principles and requirements.

Jonathan P. Dowling; James D. Franson; Hwang Lee; Gerald J. Milburn

With increasing accessibility and affordability, computers are being relied on in classrooms throughout the undergraduate curriculum. The computer algebra systems Mathematica and Maple, which facilitate symbolic manipulation of formulas and their numeric evaluation, offer a variety of resources for modernizing the classroom while teaching students important tools for postgraduate occupations. I will describe and compare experiences with integrating the computer fully into quantum mechanics courses on Maple (M.Horbatsch, Quantum Mechanics using Maple, Springer, New York, 1995) and on Mathematica (J.M. Feagin, Quantum Mechanics with Mathematica, Springer-TELOS, Santa Clara, 1994.).

Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass delusion concerning the problem, how a quantumcomputer can be made. The idea of quantumcomputation can be described within the limits of quantum formalism. But in order to understand how this idea can be put into practice one should realize the question: "What could the quantum formalism describe?", in spite of the absence of an universally recognized answer. Only a realization of this question and the undecided problem of quantum foundations allows to see in which quantum systems the superposition and EPR correlation could be expected. Because of the "specialization barbarism" many authors are sure that Bell proved full impossibility of any hidden-variables interpretation. Therefore it is important to emphasize that in reality Bell has restricted to validity limits of the no- hidden-variables proof and has shown that two-state quantum system can be described by hidden variables. The later means that no experimental result obtained on two-state quantum system can prove the existence of superposition and violation of the realism. One should not assume before unambiguous experimental evidence that any two-state quantum system is quantum bit. No experimental evidence of superposition of macroscopically distinct quantum states and of a quantum bit on base of superconductor structure was obtained for the present. Moreover same experimental results can not be described in the limits of the quantum formalism.

This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of exactly computing symmetric functions (without intermediate measurements for a distributed and superposed input), if the number of parties is given to every party. A corollary of this result is a more efficient quantum leader election algorithm than existing ones: the new quantum algorithm runs in O(n) rounds with bit complexity O(mn^2), on an anonymous quantum network with n parties and m communication links. Another corollary is the first quantum algorithm that exactly computes any computable Boolean function with round complexity O(n) and with smaller bit complexity than that of existing classical algorithms in the worst case over all (computable) Boolean functions and network topologies. More generally, any n-qubit state can be shared with that complexity on an anonymous quantum network with n parties.

Hirotada Kobayashi; Keiji Matsumoto; Seiichiro Tani

QUANTUMCOMPUTATION AND GROVER'S ALGORITHM AARON KRAHN Abstract. This paper provides an introduction to quantumcomputation by develop- ing the qubit, quantum gate, and quantum circuits. Three simple with standard quantumcomputational techniques. Finally, we provide a detailed proof of Grover's searching

Schemes of universal quantumcomputation in which the interactions between the computational elements, in a computational register, are mediated by some ancillary system are of interest due to their relevance to the physical implementation of a quantumcomputer. Furthermore, reducing the level of control required over both the ancillary and register systems has the potential to simplify any experimental implementation. In this paper we consider how to minimise the control needed to implement universal quantumcomputation in an ancilla-mediated fashion. Considering computational schemes which require no measurements and hence evolve by unitary dynamics for the global system, we show that when employing an ancilla qubit there are certain fixed-time ancilla-register interactions which, along with ancilla initialisation in the computational basis, are universal for quantumcomputation with no additional control of either the ancilla or the register. We develop two distinct models based on locally inequivalent interactions and we then discuss the relationship between these unitary models and the measurement-based ancilla-mediated models known as ancilla-driven quantumcomputation.

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.

It is indicated that principal models of computation are indeed significantly related. The quantum field computation model contains the quantumcomputation model of Feynman. (The term "quantum field computer" was used by Freedman.) Quantum field computation (as enhanced by Wightman's model of quantum field theory) involves computation over the continuum which is remarkably related to the real computation model of Smale. The latter model was established as a generalization of Turing computation. All this is not surprising since it is well known that the physics of quantum field theory (which includes Einstein's special relativity) contains quantum mechanics which in turn contains classical mechanics. The unity of these computing models, which seem to have grown largely independently, could shed new light into questions of computational complexity, into the central P (Polynomial time) versus NP (Non-deterministic Polynomial time) problem of computer science, and also into the description of Nature by fundamental physics theories.

communication and I/O complexity, methods for quantum data compression. and quantum er- Surface address of auxiliary registers for storage of the input. 3.1.2 An Introduction to QuantumComputationComputationsChapter 3: QuantumComputing John H. Reif Department of Computer Science Duke University 3

Quantum Topology and QuantumComputing by Louis H. Kauffman Department of Mathematics, Statistics discussion of the relationships of quantum topology to quantumcomputing. This paper is intended and Computer Science 851 South Morgan Street University of Illinois at Chicago Chicago, Illinois 60607

Quantum Chaos and QuantumComputers D. L. Shepelyansky* Laboratoire de Physique Quantique, UMR 5626: 03.67.Lx, 05.45.Mt, 24.10.Cn Abstract The standard generic quantumcomputer model is studied and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantumcomputer

Usually models for quantumcomputations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantumcomputations in which the state is an operator of density matrix and the gates are quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of $4^{n}$-dimensional operator Hilbert space. Unitary quantum gates and nonunitary quantum operations for n-qubit system are considered as generalized quantum gates acting on mixed state. In this paper we study universality for quantumcomputations by quantum operations on mixed states.

Mechanical Computation: its Computational Complexity and Technologies Chapter, Encyclopedia Importance II. Introduction to Computational Complexity III. Computational Complexity of Mechanical Devices and their Movement Problems IV. Concrete Mechanical Computing Devices V. Future Directions VI. Bibliography Glossary

Quantum states of matter can be exploited as high performance sensors for measuring time, gravity, rotation, and electromagnetic fields, and quantum states of light provide powerful new tools for imaging and communication. Much attention is being paid to the ultimate limits of this quantumtechnology. For example, it has already been shown that exotic quantum states can be used to measure or image with higher precision or higher resolution or lower radiated power than any conventional technologies, and proof-of-principle experiments demonstrating measurement precision below the standard quantum limit (shot noise) are just starting to appear. However, quantumtechnologies have another powerful advantage beyond pure sensing performance that may turn out to be more important in practical applications: the potential for building devices with lower size/weight/power (SWaP) and cost requirements than existing instruments. The organizers of QuantumTechnology Applications Workshop (QTAW) have several goals: (1) Bring together sponsors, researchers, engineers and end users to help build a stronger quantumtechnology community; (2) Identify how quantum systems might improve the performance of practical devices in the near- to mid-term; and (3) Identify applications for which more long term investment is necessary to realize improved performance for realistic applications. To realize these goals, the QTAW II workshop included fifty scientists, engineers, managers and sponsors from academia, national laboratories, government and the private-sector. The agenda included twelve presentations, a panel discussion, several breaks for informal exchanges, and a written survey of participants. Topics included photon sources, optics and detectors, squeezed light, matter waves, atomic clocks and atom magnetometry. Corresponding applications included communication, imaging, optical interferometry, navigation, gravimetry, geodesy, biomagnetism, and explosives detection. Participants considered the physics and engineering of quantum and conventional technologies, and how quantum techniques could (or could not) overcome limitations of conventional systems. They identified several auxiliary technologies that needed to be further developed in order to make quantumtechnology more accessible. Much of the discussion also focused on specific applications of quantumtechnology and how to push the technology into broader communities, which would in turn identify new uses of the technology. Since our main interest is practical improvement of devices and techniques, we take a liberal definition of 'quantumtechnology': a system that utilizes preparation and measurement of a well-defined coherent quantum state. This nomenclature encompasses features broader than entanglement, squeezing or quantum correlations, which are often more difficult to utilize outside of a laboratory environment. Still, some applications discussed in the workshop do take advantage of these 'quantum-enhanced' features. They build on the more established quantumtechnologies that are amenable to manipulation at the quantum level, such as atom magnetometers and atomic clocks. Understanding and developing those technologies through traditional engineering will clarify where quantum-enhanced features can be used most effectively, in addition to providing end users with improved devices in the near-term.

Boshier, Malcolm [Los Alamos National Laboratory; Berkeland, Dana [USG; Govindan, Tr [ARO; Abo - Shaeer, Jamil [DARPA

Quantumcomputers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure communications. APL is developing an optical approach to quantumcomputing in which the bits, or "qubits", are represented by single photons. Our approach allows the use of ordinary (linear) optical elements that are available for the most part as off-the-shelf components. Recent experimental demonstrations of a variety of logic gates for single photons, a prototype memory device, and other devices will be described.

A class of problems is described which can be solved more efficiently by quantumcomputation than by any classical or stochastic method. The quantumcomputation solves the problem with certainty in exponentially less time than any classical deterministic computation.

This paper addresses foundational issues related to quantumcomputing. The need for a universally valid theory such as quantum mechanics to describe to some extent its own validation is noted. This includes quantum mechanical descriptions of systems that do theoretical calculations (i.e. quantumcomputers) and systems that perform experiments. Quantum robots interacting with an environment are a small first step in this direction. Quantum robots are described here as mobile quantum systems with on-board quantumcomputers that interact with environments. Included are discussions on the carrying out of tasks and the division of tasks into computation and action phases. Specific models based on quantum Turing machines are described. Differences and similarities between quantum robots plus environments and quantumcomputers are discussed.

Reliable quantumcomputers BY JOHN PRESKILL Charles C. Lauritsen Laboratory of High Energy Physics long quantumcomputation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantumcomputer storing

quantÂph/9802065 25 Feb 1998 Basics of QuantumComputation Vlatko Vedral and Martin B. Plenio) Quantumcomputers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantumcomputation over its classical counter

Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantumcomputer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantumcomputer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmission of phase information from oracle to computer.

We show that mere observation of a quantum system can turn its dynamics from a very simple one into a universal quantumcomputation. This effect, which occurs if the system is regularly observed at short time intervals, can be rephrased as a modern version of Plato's Cave allegory. More precisely, while in the original version of the myth, the reality perceived within the Cave is described by the projected shadows of some more fundamental dynamics which is intrinsically more complex, we found that in the quantum world the situation changes drastically as the "projected" reality perceived through sequences of measurements can be more complex than the one that originated it. After discussing examples we go on to show that this effect is generally to be expected: almost any quantum dynamics will become universal once "observed" as outlined above. Conversely, we show that any complex quantum dynamics can be "purified" into a simpler one in larger dimensions.

Daniel Burgarth; Paolo Facchi; Vittorio Giovannetti; Hiromichi Nakazato; Saverio Pascazio; Kazuya Yuasa

This effort examines the intersection of the emerging field of quantumcomputing and the more established field of evolutionary computation. The goal is to understand what benefits quantumcomputing might offer to computational intelligence and how computational intelligence paradigms might be implemented as quantum programs to be run on a future quantumcomputer. We critically examine proposed algorithms and methods for implementing computational intelligence paradigms, primarily focused on heuristic optimization methods including and related to evolutionary computation, with particular regard for their potential for eventual implementation on quantumcomputing hardware.

When coherent states of the electromagnetic field are used to drive the evolution of a quantumcomputer, a decoherence results due to the back reaction from the qubits onto the fields. We show how to calculate this effect. No assumptions about the environment are necessary, so this represents a useful model to test the fidelity of quantum error correcting codes. We examine two cases of interest. First, the decoherence from the Walsh-Hadamard transformations in Grover's search algorithm is found [Phys. Rev. Lett. 79, 325 (1997)]. Interference effects, and decoherence-dependent phases, are present that could be useful in reducing the decoherence. Second, Shor's fault-tolerant controlled-NOT gate is examined, utilizing frequency-selective pulses [Proceedings, 35th Annual Symposium on Foundations of Computer Science (IEEE Press, New York, 1994), pp. 56-65]. This implementation is found not to be optimal in regards to fault-tolerant quantumcomputation.

We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantumcomputer based on only 3 qubits.

Quantum Teleportation Computational Non-Linear and Quantum Optics Further information:- nikhil are encapsulated in quantum teleportation. 1 Quantum Teleportation? 4 Entangled States 5 How teleportation works (cont ) Quantum teleportation does not involve the transfer of matter from one location to another

We propose a scheme to implement quantum controlled SWAP gates by directing single-photon pulses to a two-sided cavity with a single trapped atom. The resultant gates can be used to realize quantum fingerprinting and universal photonic quantumcomputation. The performance of the scheme is characterized under realistic experimental noise with the requirements well within the reach of the current technology.

Majorana fermionic quantumcomputation (MFQC) was proposed by S. B. Bravyi and A. Yu. Kitaev [Ann. Phys. (NY) 298, 210 (2002), 10.1006/aphy.2002.6254], who indicated that a (nontopological) fault-tolerant quantumcomputer built from Majorana fermions may be more efficient than that built from distinguishable two-state systems. However, until now scientists have not known how to realize a MFQC in a physical system. In this paper we propose a possible realization of MFQC. We find that the end of a line defect of a p-wave superconductor or superfluid in a honeycomb lattice traps a Majorana zero mode, which becomes the starting point of MFQC. Then we show how to manipulate Majorana fermions to perform universal MFQC, which possesses possibilities for high-level local controllability through individually addressing the quantum states of individual constituent elements by using timely cold-atom technology.

In theory, quantumcomputers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantumcomputers must operate with noisy devices called ``gates'' that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantumcomputing is to compute accurately even when gates have a high probability of error each time they are used. Here we give evidence that accurate quantumcomputing is possible with error probabilities above 3% per gate, which is significantly higher than what was previously thought possible. However, the resources required for computing at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantumcomputations at error probabilities as high as 1% per gate.

We study effects of the physical realization of quantumcomputers on their logical operation. Through simulation of physical models of quantumcomputer hardware, we analyze the difficulties that are encountered in programming physical realizations of quantumcomputers. Examples of logically identical implementations of the controlled-NOT operation and Grover's database search algorithm are used to demonstrate that the results of a quantumcomputation are unstable with respect to the physical realization of the quantumcomputer. We discuss the origin of these instabilities and discuss possibilities to overcome this, for practical purposes, fundamental limitation of quantumcomputers.

Hans De Raedt; Kristel Michielsen; Anthony Hams; Seiji Miyashita; Keiji Saito

We study numerically the imperfection effects in the quantumcomputing of the kicked rotator model in the regime of quantum chaos. It is shown that there are two types of physical characteristics: for one of them the quantumcomputation errors grow exponentially with the number of qubits in the computer while for the other the growth is polynomial. Certain similarity between classical and quantumcomputing errors is also discussed.

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.

M. -H. Yung; J. Casanova; A. Mezzacapo; J. McClean; L. Lamata; A. Aspuru-Guzik; E. Solano

We show that certain computational algorithms can be simulated on a quantumcomputer with exponential efficiency and be insensitive to phase errors. Our explicit algorithm simulates accurately the classical chaotic dynamics for exponentially many orbits even when the quantum fidelity drops to zero. Such phase-insensitive algorithms open new possibilities for computation on realistic quantumcomputers.

Theory of QuantumComputing and Communication A report from the NSF sponsored workshop held January quantum mechanics fundamentally changes the way we must consider computation, communication of Computer-Communications Research (C- CR) develop a new initiative in "Theory of QuantumComputing

QuantumComputation: Towards the Construction of a `Between Quantum and Classical Computer the possibility to construct a `between quantum and classical' computer. In this view, the pure quantumcomputer and the classical Turing machine can be seen as two special cases of our general computer. We have shown in earlier

987DNA, QUANTUM, AND MOLECULAR COMPUTING #12;988 DNA, QUANTUM, AND MOLECULAR COMPUTING #12;DNA and QuantumComputers Russell Deaton Computer Science and Engineering Dept. The University of Arkansas Fayetteville, AR 72701 rdeaton@uark.edu 501-575-5590 Abstract Both DNA and quantumcomputers have the potential

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 quantumtechnologies. Here, important control techniques are reviewed and presented in a unified frame covering quantumcomputational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems. PMID:22946034

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 quantumtechnologies. Here, important control techniques are reviewed and presented in a unified frame covering quantumcomputational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems. PMID:22946034

Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantumcomputing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via one and two bit gate operations. Previous explanations of decoherence-free operations have used an environment-induced quantum Zeno effect. In this paper a purely dynamical explanation is given for why the scheme based on atoms inside an {\\em optical cavity} works. In addition, we show how spontaneous emission by the atoms can be highly suppressed. Because the system behaves very similarly to three-level atoms exhibiting macroscopic dark periods the proposed scheme can be called ``quantumcomputing in the dark.''

Tregenna, B; Knight, P L; Tregenna, Ben; Beige, Almut; Knight, Peter L.

The prime factorization can be efficiently solved on a quantumcomputer. This result was given by Shor in 1994. In the first half of this article, a review of Shor's algorithm with mathematical setups is given. In the second half of this article, the prime number theorem which is an essential tool to understand the distribution of prime numbers is given.

Recent experimental advances have demonstrated technologies capable of supporting scalable quantumcomputation. A critical next step is how to put those technologies together into a scalable, fault-tolerant system that is also feasible. We propose a Quantum Logic Array (QLA) microarchitecture that forms the foundation of such a system. The QLA focuses on the communication resources necessary to efficiently support fault-tolerant

Tzvetan S. Metodi; Darshan D. Thaker; Andrew W. Cross; Frederic T. Chong; Isaac L. Chuang

We show that universal quantum logic can be achieved using only linear optics and a quantum shutter device. With these elements, we design a quantum memory for any number of qubits and a CNOT gate which are the basis of a universal quantumcomputer. An interaction-free model for a quantum shutter is given.

Juan Carlos Garcia-Escartin; Pedro Chamorro-Posada

The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any "classical" computer, including any potential non-quantumtechnologies the future may bring. However, the fragility of quantum states poses a challenging obstacle for realization of a fault-tolerant quantumcomputer. The topological approach to quantumcomputation proposes to surmount this obstacle by using special physical systems -- non-Abelian topologically ordered phases of matter -- that would provide intrinsic fault-tolerance at the hardware level. The so-called "Ising-type" non-Abelian topological order is likely to be physically realized in a number of systems, but it can only provide a universal gate set (a requisite for quantumcomputation) if one has the ability to perform certain dynamical topology-changing operations on the system. Until now, practical methods of implementing thes...

This paper presents a new technology program, within the fundamental physics, focusing on four quantumtechnology areas: quantum atomics, quantum optics, space superconductivity and quantum sensor technology, and quantum field based sensor and modeling technology.

This paper presents a new technology program, within the fundamental physics research program, focusing on four quantumtechnology areas: quantum atomics, quantum optics, space superconductivity and quantum sensor technology, and quantum fluid based sensor and modeling technology.

Quantumcomputation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantumcomputer design that performs universal quantumcomputation within a single non-degenerate ground state protected from decohering noise by an energy gap that we argue is system-size-independent. Closely analogous to a traditional electric circuit, it substantially changes the requirements for quantumcomputer construction, easing measurement, timing, and heating problems. Using the standard adiabatic condition, we present evidence that this design permits "quantum concurrent processing" distributing a quantumcomputation among extra qubits to perform a quantum algorithm of N gates in an amount of time that scales with the square root of N. One consequence of our work is a fixed gap version of adiabatic quantumcomputation, which several arguments hinted could be impossible.

This paper examines whether unitary evolution alone is sufficient to explain emergence of the classical world from the perspective of computability theory. Specifically, it looks at the problem of how the choice related to the measurement is made by the observer viewed as a quantum system. In interpretations where the system together with the observers is completely described by unitary transformations, the observer cannot make any choices and so measurement is impossible. From the perspective of computability theory, a quantum machine cannot halt and so it cannot observe the computed state, indicating that unitarity alone does not explain all matter processes. Further it is argued that the consideration of information and observation requires an overarching system of knowledge and expectations about outcomes.

Graph search represents a cornerstone in computer science and is employed when the best algorithmic solution to a problem consists in performing an analysis of a search space representing computational possibilities. Typically, in such problems it is crucial to determine the sequence of transitions performed that led to certain states. In this work we discuss how to adapt generic quantum search procedures, namely quantum random walks and Grover's algorithm, in order to obtain computational paths. We then compare these approaches in the context of tree graphs. In addition we demonstrate that in a best-case scenario both approaches differ, performance-wise, by a constant factor speedup of two, whilst still providing a quadratic speedup relatively to their classical equivalents. We discuss the different scenarios that are better suited for each approach.

The first generation quantumcomputer will be implemented in the cloud style, since only few groups will be able to access such an expensive and high-maintenance machine. How the privacy of the client can be protected in such a cloud quantumcomputing? It was theoretically shown [A. Broadbent, J. F. Fitzsimons, and E. Kashefi, Proceedings of the 50th Annual IEEE Symposium on Foundation of Computer Science, 517 (2009)], and experimentally demonstrated [S. Barz, E. Kashefi, A. Broadbent, J. F. Fitzsimons, A. Zeilinger, and P. Walther, Science {\\bf335}, 303 (2012)] that a client who can generate randomly-rotated single qubit states can delegate her quantumcomputing to a remote quantum server without leaking any privacy. The generation of a single qubit state is not too much burden for the client, and therefore we can say that "almost classical client" can enjoy the secure cloud quantumcomputing. However, isn't is possible to realize a secure cloud quantumcomputing for a client who is completely free from any quantumtechnology? Here we show that perfectly-secure cloud quantumcomputing is impossible for a completely classical client unless classical computing can simulate quantumcomputing, or a breakthrough is brought in classical cryptography.

quantum key distribution (QKD), quantum teleportation, quantumcomputing, quantum networks, quantum-error correction, using the same technology. Two basic circuits required in quantum teleportation systems are Bell quantum circuit needed in the quantum teleportation system is the Bell states preparation circuit. Because

1 Date January 18, 2007 Title Topological QuantumComputing Speaker Chetan Nayak (Station Q) Abstract The computational power of a quantum-mechanical Hilbert space is potentially far greater than and QuantumComputation (CSQC) University of California, Santa Barbara, CA 93106-6105 Phone: 805

Thoughts on Noise and QuantumComputation Gil Kalai Hebrew University of Jerusalem and Yale models of quantumcomputation on n qubits subject to noise operators that are obtained as products of this pa- per is that these properties of noise are sufficient to reduce quantumcomputation

Quantumcomputers, besides offering substantial computational speedups, are also expected to provide the possibility of preserving the privacy of a computation. Here we show the first such experimental demonstration of blind quantumcomputation where the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantumcomputation that enables a client to delegate a computation to a quantum server. We demonstrate various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover algorithms. Remarkably, the client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for future unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantumcomputers widely available.

Barz, Stefanie; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip

Quantumcomputers, besides offering substantial computational speedups, are also expected to provide the possibility of preserving the privacy of a computation. Here we show the first such experimental demonstration of blind quantumcomputation where the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantumcomputation that enables a client to delegate a computation to a quantum server. We demonstrate various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover algorithms. Remarkably, the client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for future unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantumcomputers widely available.

Stefanie Barz; Elham Kashefi; Anne Broadbent; Joseph F. Fitzsimons; Anton Zeilinger; Philip Walther

Digital Technology Group 1/20 Computer Laboratory Digital Technology Group Computer Laboratory William R Carson Building on the presentation by Francisco Monteiro Matlab #12;Digital Technology Group 2/20 Computer Laboratory Digital Technology Group Computer Laboratory The product: MATLABÂ® - The Language

Quantum Cryptographic Network based on Quantum Memories Eli Biham Computer Science Department, Switzerland Tal Mor Department of Physics Technion Haifa 32000, Israel (September 24, 1996) Abstract Quantum transmission of information. We present a quantum cryptographic system, in which users store particles

Candidates for quantumcomputing which offer only restricted control, e.g., due to lack of access to individual qubits, are not useful for general purpose quantumcomputing. We present concrete proposals for the use of systems with such limitations as RISQ - reduced instruction set quantumcomputers and devices - for simulation of quantum dynamics, for multi-particle entanglement and squeezing of collective spin variables. These tasks are useful in their own right, and they also provide experimental probes for the functioning of quantum gates in pre-mature proto-types of quantumcomputers.

A concise introduction to quantum probability, quantum mechanics, and quantumcomputation Greg called "non-commutative probability". Recently quantumcomputation has entered as a new reason for both mathematicians and computer scientists to learn the precepts of quantum mechan- ics. Just as randomized

Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly entangled quantum systems efficiently, and we hope to hasten the day when well controlled quantum systems can perform tasks surpassing what can be done in the classical world. One way to achieve such "quantum supremacy" would be to run an algorithm on a quantumcomputer which solves a problem with a super-polynomial speedup relative to classical computers, but there may be other ways that can be achieved sooner, such as simulating exotic quantum states of strongly correlated matter. To operate a large scale quantumcomputer reliably we will need to overcome the debilitating effects of decoherence, which might be done using "standard" quantum hardware protected by quantum error-correcting codes, or by exploiting the nonabelian quantum statistics of anyons realized in solid state sy...

We show that the Knill Laflamme Milburn method of quantumcomputation with linear optics gates can be interpreted as a one-way, measurement based quantumcomputation of the type introduced by Briegel and Rausendorf. We also show that the permanent state of n n-dimensional systems is a universal state for quantumcomputation.

The QuantumComputer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantumcomputers. In this paper we apply the QCC to the problem of fluctuations and systematic errors in the values of characteristic parameters in realistic systems. We show that fault-tolerant quantumcomputation is possible despite variations in these

Gerald Gilbert; Michael Hamrick; F. Javier Thayer; Yaakov S. Weinstein

referred to as SLAM or Simultaneous Localization and Mapping [1] [2] [3], and is considered of motions used by the robot to map the environment. Keywords: SLAM, topological word, explorationProcedia Information Technology & Computer Science 00 (2013) 000-000 3rd World Conference

We propose a scheme to implement quantumcomputation in graphene nanoribbon (GNR). It is shown that an electron or hole can be naturally localized in each zigzag region for a GNR with a sequence of Z-shaped structures, without using confined gates. A one-dimensional graphene quantum dot chain is formed in such a GNR, where an electron or hole spin can be used as a qubit. The coupling interaction between neighboring qubits is found to be of the always-on Heisenberg type. By exploiting the bang-bang control strategy and the decoherence-free subspaces encoding method, universal quantum gates are argued to be realizable with the present techniques.

Quantumcomputers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantumcomputation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantumcomputation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology. PMID:11343107

Inventors Document: P1337 Category: ComputingTechnologies, Hardware License Status: Available to License Texas Industry Cluster: Information and ComputerTechnologyQuantum dot applications for flash design using a protein-templated array of quantum dots reduces failure rates. When combined with a new

Determining the quantum circuit complexity of a unitary operation is an important problem in quantumcomputation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantumcomputation 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. PMID:24005379

A quantumcomputer is a hypothetical device in which the laws of quantum mechanics are used to introduce a degree of parallelism into computations and which could therefore significantly improve on the computational speed of a classical computer at certain tasks. Cluster state quantumcomputing (recently proposed by Raussendorf and Briegel) is a new paradigm in quantum information processing and is a departure from the conventional model of quantumcomputation. The cluster state quantumcomputer begins by creating a highly entangled multi-particle state (the cluster state) which it uses as a quantum resource during the computation. Information is processed in the computer via selected measurements on individual qubits that form the cluster state. We describe in detail how a scalable quantumcomputer can be constructed using microwave cavity QED and, in a departure from the traditional understanding of a computer as a fixed array of computational elements, we show that cluster state quantumcomputing is well suited to atomic beam experiments. We show that all of the necessary elements have been individually realised, and that the construction of a truly scalable atomic beam quantumcomputer may be an experimental reality in the near future.

Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the exponential speed-up of quantumcomputations possess their classical counterparts for the hybrid digital-analog computer. It is argued that the measurement errors which cannot be fully corrected make the computation not efficient for both models.

A quantumcomputer (QC) can operate in parallel on all its possible inputs at once, but the amount of information that can be extracted from the result is limited by the phenomenon of wave function collapse. We present a new computational model, which differs from a QC only in that the result of a measurement is the expectation value of the observable, rather than a random eigenvalue thereof. Such an expectation value QC can solve nondeterministic polynomial-time complete problems in polynomial time. This observation is significant precisely because the computational model can be realized, to a certain extent, by NMR spectroscopy on macroscopic ensembles of quantum spins, namely molecules in a test tube. This is made possible by identifying a manifold of statistical spin states, called pseudo-pure states, the mathematical description of which is isomorphic to that of an isolated spin system. The result is a novel NMR computer that can be programmed much like a QC, but in other respects more closely resembles a DNA computer. Most notably, when applied to intractable combinatorial problems, an NMR computer can use an amount of sample, rather than time, which grows exponentially with the size of the problem. Although NMR computers will be limited by current technology to exhaustive searches over only 15 to 20 bits, searches over as much as 50 bits are in principle possible, and more advanced algorithms could greatly extend the range of applicability of such machines. PMID:9050830

It has been claimed that quantumcomputers 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. Quantumcomputers 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 quantumcomputer, 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. PMID:22652702

The previously proposed Heisenberg-type relation $ E_c t_c >> \\hbar {\\cal C}$ for the energy used by a quantumcomputer, the total computation time and the logical ("classical") complexity of the problem is verified for the following examples of quantumcomputations: preparation of the input state, two Hamiltonian versions of the Grover's algorithm, a model of "quantum telephone directory", a quantum-optical device factorizing numbers and the Shor's algorithm.

We propose an approach to optical quantumcomputation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beamsplitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantumcomputing proposal of Knill, Laflamme and Milburn [Nature 409 (6816), 46 (2001)], and the abstract cluster-state model of quantumcomputation proposed by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)].

A quantumcomputer is a machine that can perform certain calculations much\\u000afaster than a classical computer by using the laws of quantum mechanics.\\u000aQuantumcomputers do not exist yet, because it is extremely difficult to\\u000acontrol quantum mechanical systems to the necessary degree. What is more, we do\\u000aat this moment not know which physical system is the best

Accurate prediction of chemical and material properties from first principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantumcomputation offer a route towards 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 quantumcomputation. 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 provide numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantumcomputers.

Jarrod R. McClean; Ryan Babbush; Peter J. Love; Alán Aspuru-Guzik

Accurate prediction of chemical and material properties from first principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantumcomputation offer a route towards 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 quantumcomputation. 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 provide numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantumcomputers.

McClean, Jarrod R; Love, Peter J; Aspuru-Guzik, Alán

As quantumcomputingtechnology improves and quantumcomputers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantumcomputers gains importance. One frequently mentioned application is Feynman's original proposal of simulating quantum systems, and in particular the electronic structure of molecules and materials. In this paper, we analyze the computational requirements for one of the standard algorithms to perform quantum chemistry on a quantumcomputer. We focus on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly. We find that while such a problem requires about a ten-fold increase in the number of qubits over current technology, the required increase in the number of gates that can be coherently executed is many orders of magnitude larger. This suggests that for quantumcomputation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed.

Dave Wecker; Bela Bauer; Bryan K. Clark; Matthew B. Hastings; Matthias Troyer

We introduce a generalized method of holonomic quantumcomputation (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.

I provide an alternative way of seeing quantumcomputation. First, I describe an idealized classical problem solving machine\\u000a whose coordinates are submitted to a nonfunctional relation representing all the problem constraints; moving an input part,\\u000a reversibly and nondeterministically produces a solution through a many body interaction. The machine can be considered the\\u000a many body generalization of another perfect machine, the

Standard quantumcomputation is based on sequences of unitary quantum logic gates which process qubits. The one-way quantumcomputer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantumcomputation 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 quantumcomputation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement a one-way quantumcomputer is irreversible. In the one-way quantumcomputer 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 fully characterize the quantum state by implementing the first experimental four-qubit quantum state tomography. Using this cluster state we demonstrate the feasibility of one-way quantumcomputing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantumcomputation is ideally suited for such tasks.

P. Walther; K. J. Resch; T. Rudolph; E. Schenck; H. Weinfurter; V. Vedral; M. Aspelmeyer; A. Zeilinger

QUANTUM TUNNELING, QUANTUMCOMPUTING, AND HIGH TEMPERATURE SUPERCONDUCTIVITY A Dissertation by QIAN WANG Submitted to the O?ce of Graduate Studies of Texas A&M University in partial ful?llment of the requirements for the degree of DOCTOR... OF PHILOSOPHY December 2003 Major Subject: Physics QUANTUM TUNNELING, QUANTUMCOMPUTING, AND HIGH TEMPERATURE SUPERCONDUCTIVITY A Dissertation by QIAN WANG Submitted to Texas A&M University in partial ful?llment of the requirements for the degree of DOCTOR...

We present numerical and analytical studies of a quantumcomputer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantumcomputer hardware are identified as a function of magnetic field gradient and dipole-dipole couplings between qubits on a square lattice. It is shown that a strong magnetic field gradient leads to suppression of quantum chaos.

We consider stability of a general quantum algorithm with respect to a fixed but unknown residual interaction between qubits, and show a surprising fact, namely that the average fidelity of quantumcomputation increases by decreasing average time correlation function of the perturbing operator in sequences of consecutive quantum gates. Our thinking is applied to the quantum Fourier transformation where an alternative 'less regular' quantum algorithm is devised which is qualitatively more robust against static random residual n-qubit interaction.

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…

It is shown in the paper that the unitary quantum dynamics in quantum mechanics is the universal quantum driving force to speed up a quantumcomputation. This assertion supports strongly in theory that the unitary quantum dynamics is the fundamental and universal principle in nature. On the other hand, the symmetric structure of Hilbert space of a composite quantum system is the quantum-computing resource that is not owned by classical computation. A new quantum-computing speedup theory is set up on the basis of the unitary quantum dynamics. Both the unitary quantum dynamics and the symmetric structure and property of the Hilbert space of the quantum system are mainly responsible for an exponential quantum-computing speedup for a general efficient quantum algorithm. The inherent importance for the unitary quantum dynamics to speed up a quantumcomputation lies in the unique ability of the unitary quantum dynamics to build the effective interaction between the symmetric structure of the Hilbert space of the quantum system and the mathematical symmetric structure of a problem to be solved on the quantum system. This unique ability could result in an essential difference of computational power between quantum and classical computations by combining the symmetric structure and property of the Hilbert space. The new quantum-computing speedup theory also provides reasonable mechanisms for exponential quantum-computing speedup for the existing efficient quantum algorithms based on the quantum parallel principle. These existing quantum algorithms including the hidden-subgroup-problem quantum algorithms and conventional quantum search algorithms have the common character that the symmetric structure of the Hilbert space does not have any effective effect on these quantum algorithms. This could be the main reason why these quantum algorithms are quite special and considered to be semiclassical.

An implementation of the topological cluster-state quantumcomputer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for nonlinear devices to create a lattice of entangled photons. Whereas the thresholds found for computational errors are quite satisfactory (above 10{sup -3}), the estimates of the minimum efficiencies needed for the detectors and quantum dots are beyond current technology's reach. This is because we rely heavily on probabilistic entangling gates, which introduces loss into the scheme irrespective of detector and quantum-dot efficiencies.

Herrera-Marti, David A.; Jennings, David; Rudolph, Terry [Institute for Mathematical Sciences, Imperial College London, London SW7 2BW (United Kingdom); Fowler, Austin G. [Centre for Quantum Computer Technology, University of Melbourne, Victoria (Australia)

A lambda calculus for quantumcomputation with classical control is to develop a functional programming language for quantumcomputers. We develop a lambda calculus a functional programming language for* * quan- tum computers. Quantumcomputing is a theory of computation

We propose an approach to optical quantumcomputation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beam splitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantumcomputing proposal of Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)

Quantumcomputation promises solution to problems that are hard to solve by classical computers. The efficient construction of quantum circuits that can solve interesting tasks is a fundamental challenge in the field. Such efficient construction also reduces decoherence losses in physical implementations of quantum algorithms by reducing interaction time with the environment. Therefore, finding time-optimal ways to synthesize unitary transformations

The quantum circuit model is the most widely used model of quantumcomputation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantumcomputers. However, several other models of quantumcomputation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantumcomputers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantumcomputation. Then, I present three results relating to various models of quantumcomputation: a scheme for improving the intrinsic fault tolerance of adiabatic quantumcomputers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be directly simulated using 2-body interactions. Lastly, I discuss general principles regarding quantumcomputation that I learned in the course of my research, and using these principles I propose directions for future research.

The computation of the ground state (i.e. the eigenvector related to the smallest eigenvalue) is an important task in the simulation of quantum many-body systems. As the dimension of the underlying vector space grows exponentially in the number of particles, one has to consider appropriate subsets promising both convenient approximation properties and efficient computations. The variational ansatz for this numerical approach leads to the minimization of the Rayleigh quotient. The Alternating Least Squares technique is then applied to break down the eigenvector computation to problems of appropriate size, which can be solved by classical methods. Efficient computations require fast computation of the matrix-vector product and of the inner product of two decomposed vectors. To this end, both appropriate representations of vectors and efficient contraction schemes are needed. Here approaches from many-body quantum physics for one-dimensional and two-dimensional systems (Matrix Product States and Projected Entangled Pair States) are treated mathematically in terms of tensors. We give the definition of these concepts, bring some results concerning uniqueness and numerical stability and show how computations can be executed efficiently within these concepts. Based on this overview we present some modifications and generalizations of these concepts and show that they still allow efficient computations such as applicable contraction schemes. In this context we consider the minimization of the Rayleigh quotient in terms of the {\\sc parafac} (CP) formalism, where we also allow different tensor partitions. This approach makes use of efficient contraction schemes for the calculation of inner products in a way that can easily be extended to the mps format but also to higher dimensional problems.

Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantumcomputation. Nevertheless the model is not always optimal (e.g. concerning the number of computational steps) and it neglects physical systems which cannot follow the "standard circuit model" analysis. We propose a computational scheme which overcomes the notion of the transposition from classical circuits providing a computation scheme with the least possible number of Hamiltonians in order to minimize the physical resources needed to perform quantumcomputation and to succeed a minimization of the computational procedure (minimizing the number of computational steps needed to perform an arbitrary unitary transformation). It is a general scheme of construction, independent of the specific system used for the implementation of the quantumcomputer. The open problem of controllability in Lie groups is directly related and rises to prominence in an effort to perform universal quantumcomputation.

K. Ch. Chatzisavvas; C. Daskaloyannis; C. P. Panos

The accelerated development of quantumtechnology has reached a pivotal point. Early in 2014, several results were published demonstrating that several experimental technologies are now accurate enough to satisfy the requirements of fault-tolerant, error corrected quantumcomputation. While there are many technological and experimental issues that still need to be solved, the ability of experimental systems to now have error rates low enough to satisfy the fault-tolerant threshold for several error correction models is a tremendous milestone. Consequently, it is now a good time for the computer science and classical engineering community to examine the {\\em classical} problems associated with compiling quantum algorithms and implementing them on future quantum hardware. In this paper, we will review the basic operational rules of a topological quantumcomputing architecture and outline one of the most important classical problems that need to be solved; the decoding of error correction data for a large-scale quantumcomputer. We will endeavour to present these problems independently from the underlying physics as much of this work can be effectively solved by non-experts in quantum information or quantum mechanics.

Because of the rapid development of quantumcomputation and of quantumtechnologies in general, computer scientists and electrical engineers will have to learn quantum mechanics (QM) in the near future. Although the teaching methods of QM are well established in both undergraduate and graduate physics courses, an effective method for teaching QM to computer scientists and electrical engineers is still

We present a solid state implementation of quantumcomputation, which improves previously proposed optically driven schemes. Our proposal is based on vertical arrays of quantum dots embedded in a mesoporous material which can be fabricated with present technology. The redundant encoding typical of the chosen hardware protects the computation against gate errors and the effects of measurement induced noise. The system parameters required for quantumcomputation applications are calculated for II-VI and III-V materials and found to be within the experimental range. The proposed hardware may help minimize errors due to polydispersity of dot sizes, which is at present one of the main problems in relation to quantum dot-based quantumcomputation.

Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve using existing computers for even modestly large systems. Here I will show that quantumcomputers can sometimes be used to address such problems and that quantumcomputer science can assign formal complexities to learning facts about nature. Hence, computer science should not only be regarded as an applied science; it is also of central importance to the foundations of science.

A detailed understanding of catalytic mechanisms and surface chemistry is critical to chemical processes. These mechanisms are typically controlled by the detailed structural, electronic, and thermo-chemical properties and interactions of molecules and materials.Computational techniques offer unique solutions in catalysis and surface chemistry, providing an in-depth knowledge of the reaction mechanisms and the role of the individual reaction components.Accelrys offers leading

Xenophon Krokidis; Jan W. Andzelm; Niranjan Govind; V. Milman

This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).

I describe a quantum cellular automaton capable of performing universal quantumcomputation. The automaton has an elementary transition function that acts on Margolus cells of $2\\times 2$ qubits, and both the ``quantum input'' and the program are encoded in the initial state of the system.

Advice is supplementary information that enhances the computational power of an underlying computation. This paper focuses on advice that is given in the form of a pure quantum state and examines the influence of such advice on the behaviors of an underlying polynomial-time quantumcomputation with bounded-error probability.

An outstanding problem in quantumcomputing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that such a device can be trained to calculate the entanglement of an input state, something neither an algorithmic quantumcomputer nor a classical neural net can do.

E. C. Behrman; V. Chandrashekar; Z. Wang; C. K. Belur; J. E. Steck; S. R. Skinner

This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantumcomputer to perform computations while continually monitoring and actively correcting the hardware faults. We discuss parallels and differences with similar methods for ordinary digital computation, we discuss some of the noise models used in designing and analyzing noisy quantum circuits, and we sketch the logic of some of the central results in this area of research.

The paper is devoted to a new idea of simulation of accounting by quantumcomputing. We expose the actual accounting principles in a pure mathematics language. After that we simulated the accounting principles on quantumcomputers. We show that all arbitrary accounting actions are exhausted by the described basic actions. The main problem of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation we use our constructed quantum Gau\\ss-Jordan Elimination to solve the problem and the time of quantumcomputing is some square root order faster than the time in classical computing.

Quantumcomputers promise dramatic advantages over their classical counterparts, but the answer to the most basic question "What is the source of the power in quantumcomputing?" has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantumcomputation via magic state distillation. This is a conceptually satisfying link because contextuality provides one of the fundamental characterizations of uniquely quantum phenomena and, moreover, magic state distillation is the leading model for experimentally realizing fault-tolerant quantumcomputation. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the nonlocality of quantum theory is a particular kind of contextuality and nonlocality 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 quantumcomputation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantumcomputation and bounding the overhead cost for the classical simulation of quantum algorithms.

Mark Howard; Joel J. Wallman; Victor Veitch; Joseph Emerson

Because of its geometric nature, holonomic quantumcomputation is fault tolerant against certain types of control errors. Although proposed more than a decade ago, the experimental realization of holonomic quantumcomputation is still an open challenge. In this Letter, we report the first experimental demonstration of nonadiabatic holonomic quantumcomputation in a liquid NMR quantum information processor. Two noncommuting one-qubit holonomic gates, rotations about x and z axes, and the two-qubit holonomic CNOT gate are realized by evolving the work qubits and an ancillary qubit nonadiabatically. The successful realizations of these universal elementary gates in nonadiabatic holonomic quantumcomputation demonstrates the experimental feasibility of this quantumcomputing paradigm. PMID:23705695

In the present paper methods and algorithms of modeling quantum operations for quantumcomputer integrated circuits design are developed. We examine different ways of quantum operation descriptions, including operator-sums, unitary representations, Choi-Jamiolkowski state representations and the corresponding chi-matrices, as well as quantum system evolution operators. The results of modeling of practically important quantum gates: SQiSW (square root of i-SWAP gate), controlled-NOT (CNOT), and controlled Z-transform (CZ) subject to different decoherence mechanisms are presented. These mechanisms include analysis of depolarizing quantum noise and processes of amplitude and phase relaxation. Finally, we consider error correction of phase flip, and the tasks of creating and maintaining the entanglement, as well as its breaking for two- and multi-qubit realizations of quantum operations. Importance of the present analysis for the quality and efficiency of quantum information technologies in practical applications is discussed.

Yu. I. Bogdanov; A. Yu. Chernyavskiy; A. S. Holevo; V. F. Luckichev; S. A. Nuyanzin; A. A. Orlikovsky

We define formally decohered quantumcomputers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantumcomputers, or quantum Turing machines(QTM), and (2) parallel quantumcomputers, or quantum circuits. This paper shows that the computational power of decohered quantumcomputers depends strongly on the amount of parallelism in the computation. The expected slowdown of the simulation of a QTM is polynomial in time and space of the quantumcomputation, for any non zero decoherence rate. This means that a QTM subjected to any amount of noise is worthless. For decohered quantum circuits, the situation is more subtle and depends on the decoherence rate, eta. We find that our simulation is efficient for circuits with decoherence rate higher than some constant, but exponential for general circuits with decoherence rate lower than some other constant. Using computer experiments, we show that the transition from exponential cost to polynomial cost happens in a short range of decoherence rates, and exhibit the phase transitions in various quantum circuits.

Chapter 51. Algorithms and Architectures for QuantumComputers 51-1 Algorithms and Architectures for QuantumComputers RLE Group Quanta Research Group Academic and Research Staff Professor Isaac Chuang physics. Two fundamental questions motivate our work: (1) How can a large-scale, reliable quantumcomputer

Recently Shor showed how to perform fault tolerant quantumcomputation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantumcomputation when the error probability is smaller than some constant threshold. The cost is polylogarithmic in time and space, and no measurements are used during the quantumcomputation. The result holds also for quantum circuits which operate on nearest neighbors only. To achieve this noise resistance, we use concatenated quantum error correcting codes. The scheme presented is general, and works with all quantum codes that satisfy some restrictions, namely that the code is ``proper''. We present two explicit classes of proper quantum codes. The first example of proper quantum codes generalizes classical secret sharing with polynomials. The second uses a known class of quantum codes and converts it to a proper code. This class is defined over a field with p elements, so the elementary quantum particle is not a qubit but a ``qupit''. With our codes, the threshold is about 10^(-6). Hopefully, this paper motivates a search for proper quantum codes with higher thresholds, at which point quantumcomputation becomes practical.

The spin network simulator model represents a bridge between (generalised) circuit schemes for standard quantumcomputation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the fiber space structure underlying the model which exhibits combinatorial properties closely related to SU(2) state sum models, widely employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.

REVIEWS Quantumcomputers 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 information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer

The quantumcomputer 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…

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantumcomputation.

David Collins; K. W. Kim; W. C. Holton; H. Sierzputowska-Gracz; E. O. Stejskal

A one-way quantumcomputer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantumcomputer. On the other hand, the network model of quantumcomputation cannot explain all ways of processing quantum information possible with the one-way quantumcomputer. In this paper, two examples of the non-network character of the one-way quantumcomputer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantumcomputer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)

Robert Raussendorf; Daniel E. Browne; Hans J. Briegel

This publication provides materials to help adult educators use computertechnology in their teaching. Section 1, Computer Basics, contains activities and materials on these topics: increasing computer literacy, computer glossary, parts of a computer, keyboard, disk care, highlighting text, scrolling and wrap-around text, setting up text,…

Slider, Patty; Hodges, Kathy; Carter, Cea; White, Barbara

Accounting for resources is the central issue in computational efficiency. We point out physical constraints implicit in information readout that have been overlooked in classical computing. The basic particle-counting mode of read-out sets a lower bound on the resources needed to implement a quantumcomputer. As a consequence, computers based on classical waves are as efficient as those based on single quantum particles.

Quantumcomputers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantumcomputers requires new ways of thinking beyond those in the familiar classical world. To help in this thinking, we give a description of the foundational ideas that hold in all of our successful physical models, including quantum theory. Our emphasis will be on the proper interpretation of our theories, and not just their statements. Our tact will be to build on the concept of information, which lies central to the operation of not just computers, but the Universe. For application to quantumcomputing, the essence of quantum theory is given, together with special precautions and limitations.

The Internet Archive has gathered up this excellent audio collection featuring interviews, discussions, and musings about computers, technology, and science. All told, there are over 700 audio files here, including the popular Groks Science Radio Show and Podcast and Textfiles BBS Audio. This last collection contains a varied set of audio files assembled by Jason Scott, curator of textfiles.com. Here, visitors can learn about the days of ASCII and Dial-up Bulletin Board Systems (BBS) that were popular from the 1970s to the early 1990s. To get started, first-time visitors can look over the Most Downloaded Items for a few suggestions, or simply find out more via the About the Archive area.

A new model of quantumcomputation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantumcomputation, e. g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the "quantum switch", which can be programmed to switch the order of two channels with a single use of each one.

Timoteo Colnaghi; Giacomo Mauro D'Ariano; Paolo Perinotti; Stefano Facchini

A new model of quantumcomputation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantumcomputation, e.g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the quantum switch, which can be programmed to switch the order of two channels with a single use of each one.

Colnaghi, Timoteo; D'Ariano, Giacomo Mauro; Facchini, Stefano; Perinotti, Paolo

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantumtechnologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantumtechnologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects. PMID:24851858

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantumtechnologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantumtechnologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantumtechnologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantumtechnologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects. PMID:24851858

We discuss the issues surrounding the implementation of quantumcomputation in rare-earth-ion doped solids. We describe a practical scheme for two qubit gate operations which utilise experimentally available interactions between the qubits. Possibilities for a scalable quantumcomputer are discussed.

A two-dimensional quantum system with anyonic excitations can be considered as a quantumcomputer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.

We explain how to combine holonomic quantumcomputation (HQC) with fault tolerant quantum error correction. This establishes the scalability of HQC, putting it on equal footing with other models of computation, while retaining the inherent robustness the method derives from its geometric nature.

We develop a non-adiabatic generalization of holonomic quantumcomputation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $\\Lambda$ configuration. Our scheme opens up for universal holonomic quantumcomputation on qubits characterized by short coherence times.

Erik Sjöqvist; D. M. Tong; L. Mauritz Andersson; Björn Hessmo; Markus Johansson; Kuldip Singh

quantumcomputers by simulating quantum spin models representing quantumcomputer hardware. ExamplesQuantumComputation and Quantum Spin Dynamics Hans De Raedt, Kristel Michielsen, and Anthony Hams@yuragi.t.u-tokyo.ac.jp, saitoh@spin.t.u-tokyo.ac.jp We analyze the stability of quantumcomputations on physically realiz- able

Quantum cryptographic network based on quantum memories Eli Biham Computer Science Department that these complexity assumptions may not hold for a quantumcomputer for example, a quantumcomputer should enable fast , may be broken by quantumcomputers. These developments enhanced the interest in quantum cryptography

and femtocell technology. Next Generation Networks: RU6 research in this area deals with the latest. . . . . . . . . ComputerTechnology Institute & Press "DIOPHANTUS" Research Unit 6 http://ru6.cti.gr Networks, Telematics and New Services 2014 #12;ComputerTechnology Institute & Press "Diophantus

In the measurement-based quantumcomputing, 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 byproduct operators. If we respect the no-signaling principle, byproduct operators cannot be avoided. In this paper, we study the possibility of acausal measurement-based quantumcomputing by using the process matrix framework [O. Oreshkov, F. Costa, and C. Brukner, Nature Communications {\\bf3}, 1092 (2012)]. We construct a resource process matrix for acausal measurement-based quantumcomputing. The resource process matrix is an analog of the resource state of the causal measurement-based quantumcomputing. We find that 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 quantumcomputing.

One-way quantumcomputing is an important and novel approach to quantumcomputation. By exploiting the existing particle-particle interactions, we report an experimental realization of the complete process of deterministic one-way quantum Deutsch-Josza algorithm in NMR, including graph state preparation, single-qubit measurements, and feed-forward corrections. The findings in our experiment may shed light on the future scalable one-way quantumcomputation.

Ju, Chenyong; Zhu Jing; Peng Xinhua; Chong Bo; Zhou Xianyi; Du Jiangfeng [Heifei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, 230026 Hefei (China)

A one-way quantumcomputer (QCC) works by performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the QCC. On the other hand, the network model of quantumcomputation cannot explain all ways of processing quantum information

Robert Raussendorf; Daniel E. Browne; Hans J. Briegel

The unique capability of quantum mechanics to evolve alternative possibilities in parallel is appealing and over the years a number of quantum algorithms have been developed offering great computational benefits. Systems coupled to the environment lose quantum coherence quickly and realization of schemes based on unitarity might be impossible. Recent discovery of room temperature quantum coherence in light harvesting complexes opens up new possibilities to borrow concepts from biology to use quantum effects for computational purposes. While it has been conjectured that light harvesting complexes such as the Fenna-Matthews-Olson (FMO) complex in the green sulfur bacteria performs an efficient quantum search similar to the quantum Grover's algorithm the analogy has yet to be established. In this work we show that quantum dissipation plays an essential role in the quantum search performed in the FMO complex and it is fundamentally different from known algorithms. In the FMO complex not just the optimal level of phase breaking is present to avoid both quantum localization and Zeno trapping but it can harness quantum dissipation as well to speed the process even further up. With detailed quantum calculations taking into account both phase breaking and quantum dissipation we show that the design of the FMO complex has been evolutionarily optimized and works faster than pure quantum or classical-stochastic algorithms. Inspired by the findings we introduce a new computational concept based on decoherent quantum evolution. While it is inspired by light harvesting systems, the new computational devices can also be realized on different material basis opening new magnitude scales for miniaturization and speed.

The QuantumComputer Condition (QCC) provides a rigorous and completely\\u000ageneral framework for carrying out analyses of questions pertaining to\\u000afault-tolerance in quantumcomputers. In this paper we apply the QCC to the\\u000aproblem of fluctuations and systematic errors in the values of characteristic\\u000aparameters in realistic systems. We show that fault-tolerant quantum\\u000acomputation is possible despite variations in these

Gerald Gilbert; Michael Hamrick; F. Javier Thayer; Yaakov S. Weinstein

AN INTRODUCTION TO QUANTUMCOMPUTING NOSON S. YANOFSKY Abstract.QuantumComputing is a new and exciting field at the intersecti* *on of mathematics, computer science and physics. It concerns a utilization* * of quantum mechanics to improve

In communication networks many different channels must share a limited amount of resources. In order to allow for multiple simultaneous communications, multiple access techniques are routinely employed. With quantum communication, it is possible to share a new kind of resource. All of the system channels can be accommodated into a single channel in a larger Hilbert space. In the scheme, a single line combines the information of all the users, and, at the receiver, the original quantum channels are recovered. The given multiplexer/demultiplexer circuit can perform this n qubits to qudit transformation. Connections with superdense coding and classical multiple access schemes are discussed.

Juan Carlos Garcia-Escartin; Pedro Chamorro-Posada

The QuantumComputer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantumcomputers. In this paper we apply the QCC to the problem of fluctuations and systematic errors in the values of characteristic parameters in realistic systems. We show that fault-tolerant quantumcomputation is possible despite variations in these parameters. We also use the QCC to explicitly show that reliable classical computation can be carried out using as input the results of fault-tolerant, but imperfect, quantumcomputation. Finally, we consider the advantages and disadvantages of the superoperator and diamond norms in connection with application of the QCC to various quantum information-theoretic problems.

Gilbert, G; Thayer, F J; Weinstein, Yu S; Gilbert, Gerald; Hamrick, Michael; Weinstein, Yaakov S.

The QuantumComputer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantumcomputers. In this paper we apply the QCC to the problem of fluctuations and systematic errors in the values of characteristic parameters in realistic systems. We show that fault-tolerant quantumcomputation is possible despite variations in these parameters. We also use the QCC to explicitly show that reliable classical computation can be carried out using as input the results of fault-tolerant, but imperfect, quantumcomputation. Finally, we consider the advantages and disadvantages of the superoperator and diamond norms in connection with application of the QCC to various quantum information-theoretic problems.

Gerald Gilbert; Michael Hamrick; F. Javier Thayer; Yaakov S. Weinstein

AN INTRODUCTION TO QUANTUMCOMPUTING NOSON S. YANOFSKY Abstract. QuantumComputing is a new of quantum mechanics to improve the e#ciency of computation. Here we present a gentle introduction to some of the ideas in quantumcomputing. The paper begins by motivating the central ideas of quantum mechanics

Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage of the localization of quantum states into wave packets occupying small regions of classical phase space. Following and extending the original proposal of Percival, Alber and Steimle, we show that MQSD can provide a further gain over ordinary QSD and other quantum trajectory methods of many orders of magnitude in computational space and time. Because of these gains, it is even possible to calculate an open quantum system trajectory when the corresponding isolated system is intractable. MQSD is particularly advantageous where classical or semiclassical dynamics provides an adequate qualitative picture but is numerically inaccurate because of significant quantum effects. The principles are illustrated by computations for the quantum Duffing oscillator and for second harmonic generation in quantum optics. Potential applications in atomic and molecular dynamics, quantum circuits and quantumcomputation are suggested.

Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly entangled quantum systems efficiently, and we hope to hasten the day when well controlled quantum systems can perform tasks surpassing what can be done in the classical world. One way to achieve such "quantum supremacy" would be to run an algorithm on a quantumcomputer which solves a problem with a super-polynomial speedup relative to classical computers, but there may be other ways that can be achieved sooner, such as simulating exotic quantum states of strongly correlated matter. To operate a large scale quantumcomputer reliably we will need to overcome the debilitating effects of decoherence, which might be done using "standard" quantum hardware protected by quantum error-correcting codes, or by exploiting the nonabelian quantum statistics of anyons realized in solid state systems, or by combining both methods. Only by challenging the entanglement frontier will we learn whether Nature provides extravagant resources far beyond what the classical world would allow.

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 quantumcomputation. 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

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 quantumcomputation. 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

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 quantumcomputation. 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.

We propose a method to achieve scalable quantumcomputation based on fast quantum gates on an array of trapped ions, without the requirement of ion shuttling. Conditional quantum gates are obtained for any neighboring ions through spin-dependent acceleration of the ions from periodic photon kicks. The gates are shown to be robust to influence of all the other ions in the array and insensitive to the ions' temperature.

Blind quantumcomputation is a new secure quantumcomputing protocol which enables Alice (who does not have sufficient quantumtechnology) to delegate her quantumcomputation to Bob (who has a full-fledged quantumcomputer) 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.

Blind quantumcomputation is a new secure quantumcomputing protocol where a client, who does not have enough quantumtechnologies at her disposal, can delegate her quantumcomputation to a server, who has a fully fledged quantumcomputer, 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 quantumcomputing.

Postselected quantumcomputation is distinguished from regular quantumcomputation by accepting the output only if measurement outcomes satisfy predetermined conditions. The output must be accepted with nonzero probability. Methods for implementing postselected quantumcomputation with noisy gates are proposed. These methods are based on error-detecting codes. Conditionally on detecting no errors, it is expected that the encoded computation can be made to be arbitrarily accurate. Although the probability of success of the encoded computation decreases dramatically with accuracy, it is possible to apply the proposed methods to the problem of preparing arbitrary stabilizer states in large error-correcting codes with local residual errors. Together with teleported error-correction, this may improve the error tolerance of non-postselected quantumcomputation.

In the graph isomorphism (GI) problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G ?G'. If yes, then G and G' are said to be isomorphic; otherwise they are nonisomorphic. The GI problem is an important problem in computer science and is thought to be of comparable difficulty to integer factorization. In this paper we present a quantum algorithm that solves arbitrary instances of GI and which also provides an approach to determining all automorphisms of a given graph. We show how the GI problem can be converted to a combinatorial optimization problem that can be solved using adiabatic quantum evolution. We numerically simulate the algorithm's quantum dynamics and show that it correctly (i) distinguishes nonisomorphic graphs; (ii) recognizes isomorphic graphs and determines the permutation(s) that connect them; and (iii) finds the automorphism group of a given graph G. We then discuss the GI quantum algorithm's experimental implementation, and close by showing how it can be leveraged to give a quantum algorithm that solves arbitrary instances of the NP-complete subgraph isomorphism problem. The computational complexity of an adiabatic quantum algorithm is largely determined by the minimum energy gap ? (N) separating the ground and first-excited states in the limit of large problem size N ?1. Calculating ? (N) in this limit is a fundamental open problem in adiabatic quantumcomputing, and so it is not possible to determine the computational complexity of adiabatic quantum algorithms in general, nor consequently, of the specific adiabatic quantum algorithms presented here. Adiabatic quantumcomputing has been shown to be equivalent to the circuit model of quantumcomputing, and so development of adiabatic quantum algorithms continues to be of great interest.

A Knill-Laflamme-Milburn (KLM) type quantumcomputation with bosonic neutral atoms or bosonic ions is suggested. Crucially, as opposite to other quantumcomputation schemes involving atoms (ions), no controlled interactions between atoms (ions) involving their internal levels are required. Versus photonic KLM computation this scheme has the advantage that single atom (ion) sources are more natural than single photon sources, and single atom (ion) detectors are far more efficient than single photon ones.

Dopants in crystalline silicon such as phosphorus (Si:P) have electronic and nuclear spins with exceptionally long coherence times making them promising platforms for quantumcomputing and quantum sensing. The demonstration of single-spin single-shot readout brings these ideas closer to implementation. Progress in fabricating atomic-scale Si:P structures with scanning tunnelling microscopes offers a powerful route to scale up this work, taking advantage of techniques developed by the computing industry. The experimental and theoretical sides of this emerging quantumtechnology are reviewed with a focus on the period from 2009 to mid-2014.

Quantumcomputation has revolutionary potential for speeding computational tasks such as factoring and simulating quantum systems, but the task of constructing a quantumcomputer is daunting. Adiabatic quantumcomputation and other ``hands-off" approaches relieve the need for rapid, precise pulsing to control the system, inspiring at least one high-profile effort to realize a hands-off quantumcomputing device. But is hands-off incompatible with fault-tolerant? Concerted effort and many innovative ideas have not resolved this question but have instead deepened it, linking it to fundamental problems in quantum complexity theory. Here we present a hands-off approach that is provably (a) capable of scalable universal quantumcomputation in a non-degenerate ground state and (b) fault-tolerant against an analogue of the usual local stochastic fault model. A satisfying physical and numerical argument indicates that (c) it is also fault-tolerant against thermal excitation below a threshold temperature independent of the computation size.

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

Quantumcomputation and simulation with trapped ions using dissipation Dissertation zur Erlangung and computer science. A quantumcomputer promises to solve certain problems more efficient than classical computers. But building such a quantumcomputer is a cumbersome task as the quantum system needs

Quantum measurement is universal for quantumcomputation. Two models for performing measurement-based quantumcomputation exist: the one-way quantumcomputer was introduced by Briegel and Raussendorf, and quantumcomputation via projective measurements only by Nielsen. The more recent development of this second model is based on state transfers instead of teleportation. From this development, a finite but approximate quantum universal family of observables is exhibited, which includes only one two-qubit observable, while others are one-qubit observables. In this article, an infinite but exact quantum universal family of observables is proposed, including also only one two-qubit observable. The rest of the paper is dedicated to compare these two models of measurement-based quantumcomputation, i.e. one-way quantumcomputation and quantumcomputation via projective measurements only. From this comparison, which was initiated by Cirac and Verstraete, closer and more natural connections appear between these two models. These close connections lead to a unified view of measurement-based quantumcomputation.

In certain approaches to quantumcomputing the operations between qubits are nondeterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should be assumed to be failure prone. In the ultimate limit of this architecture each component contains only one qubit. Here we derive thresholds for fault-tolerant quantumcomputation under this extreme paradigm. We find that computation is supported for remarkably high failure rates (exceeding 90%) providing that failures are heralded; meanwhile the rate of unknown errors should not exceed 2 in 10(4) operations. PMID:21231569

Li, Ying; Barrett, Sean D; Stace, Thomas M; Benjamin, Simon C

It is well known that a parallel quantumcomputer 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 quantumcomputation. 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 quantumcomputation 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.

It is well known that a parallel quantumcomputer 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 quantumcomputation. 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 quantumcomputation 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.

It is well known that a parallel quantumcomputer 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 quantumcomputation. 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 quantumcomputation 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

In this Brief Report, we propose a potential scheme to implement one-way quantumcomputation 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 quantumcomputation.

Wu Chunwang; Han Yang; Chen Pingxing; Li Chengzu [College of Science, National University of Defense Technology, Changsha 410073 (China); Zhong Xiaojun [China Satellite Maritime Tracking and Control Department, Jiangyin 214400 (China)

such as biological systems, quantum phenomena, nanoscale science and engineering, and other novel computing concepts. To bring fundamental changes to software, hardware and architectural design aspects of future computingEmerging Models and Technologies for Computation (EMT) Program Solicitation NSF 07-523 Replaces

Exploring Tuning Strategies for Quantum Chemistry Computations Lakshminarasimhan Seshagiri1 , Meng-initio molecular quantum chemistry calculations, uses NICAN for dynamically making adaptations so as to improve this adaptation mechanism by analyzing the GAMESS performance through the use of fine-grained data. Key words

Teleportation as a QuantumComputation Frank Rioux Emeritus Professor of Chemistry CSB|SJU This tutorial works through the following teleportation circuit provided by Gilles Brassard in "Teleportation to that used in the other teleportation examples given in this series of tutorials. The necessary quantum bits

-level quantum mechanics is essential. Textbook: Quantum Information and Computation lecture notes by John. Foundations Review of quantum mechanics-Hilbert space, operators, postulates, tensor products, density Information theory - Shannon and Von Neumann entropy, distinction between classical and quantum information

Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantumcomputational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness theorem.

Molecules under the inuence of light can be used to perform quantumcomputational operations when their vibrational or rotational quantum states are coherently controlled. An analysis is presented of quantumcomputation within the vibrational degrees of freedom of a polyatomic molecule. A set of 2n vibrational states covering a range of energies is used to encode n qubits in place of n separate degrees of freedom. Computer simulations are used to demonstrate the capacity of a shaped laser pulse to execute 4-qubit quantumcomputational algorithms with high delity on gas phase thiophosgene. An alternative light-molecule system using terahertz pulses on gas phase D3O+ is also analyzed and found to have the capability of performing 2-qubit operations. Simulations of closed loop experiments in coherent control are presented, and elements of the experimental procedure are tested to demonstrate how intramolecular vibrational relaxation (IVR) may be slowed in the ground state vibrational energy levels of gas phase thiophosgene.

We review an approach to fault-tolerant holonomic quantumcomputation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the information remains protected.

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 communications. We propose a non-classical 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 the information after part of it has left the network node.

Garcia-Escartin, J C; Chamorro-Posada, Pedro; Garcia-Escartin, Juan Carlos

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 communications. We propose a non-classical 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 the information after part of it has left the network node.

Juan Carlos Garcia-Escartin; Pedro Chamorro-Posada

We study concretely how classical signals should be processed in quantum cluster-state computation. Deforming corresponding quantum teleportation circuit, we find a simple rule of a classical signal-flow to obtain correct quantumcomputation results.

We propose a construction of anyon systems associated to quantum tori with real multiplication and the embedding of quantum tori in AF algebras. These systems generalize the Fibonacci anyons, with weaker categorical properties, and are obtained from the basic modules and the real multiplication structure.

In measurement-based quantumcomputing, 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 quantumcomputing 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 quantumcomputing restricting local operations to projective measurements. The resource process matrix is an analog of the resource state of the standard causal measurement-based quantumcomputing. 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 quantumcomputing. We also show that it is possible to consider a causal game whose causal inequality is violated by acausal measurement-based quantumcomputing.

Technological advances and emphasis on time-limited, inexpensive treatment has ushered in counseling through the use of communication via internet. The utilization of technology for health care purposes has increased in popularity and usage in clinical practice. Distance counseling or e-counseling is a method of service delivery with potential to supplement traditional face to face counseling. The challenges of using this

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 quantumcomputing, 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 quantumcomputing 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 quantumcomputing 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 quantumcomputing. As Feynman noted, we could be discussing these diversified issues to study one problem. In our case, this `one problem' is to build quantumcomputers.

Brandt, Howard E.; Kim, Young S.; Man'ko, Margarita A.

Two subjects in the area of quantumcomputation are considered here. In the first chapter I present a universal model for a quantum Robot. Chapters two, three, and four are dedicated to the problem of quantum error correction/protection. A quantum robot is described as a quantum system that moves in, and interacts with, an external environment of quantum systems. Such environments consist of arbitrary numbers and types of particles in two or three dimensional space lattices. I find a set of universal operations that enables the quantum robot to simulate arbitrary quantum dynamics. A computational approach to the quantum error correction problem is presented in chapters two and three. I develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. This theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. I demonstrate via numerical examples that such optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. In the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. I show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block. However, this conclusion breaks down in the presence of an initial entanglement between the encoding and recovery ancillas. Such entanglement assisted error correction procedures are studied in chapter three. I show how entanglement can increase fidelity in the optimized setting by improving the function of the recovery ancillas. In the last chapter quantum error protection methods, decoherence-free subspaces and subsystems, are studied in the framework of linear maps. This framework provides the most general description of open quantum system dynamics.

quantÂph/9809016 8 Sep 1998 An Introduction to QuantumComputing for NonÂPhysicists Eleanor Rieffel more efficiently if it made use of these quantum effects. But building quantumcomputers, computational the quantum effects to speed up computation, the field developed slowly. It wasn't until 1994, when Peter Shor

QuantumComputers: Noise Propagation and Adversarial Noise Models Gil Kalai Hebrew University that will fail quantum error correction and fault-tolerant quantumcomputation. We describe known results;1 Introduction The feasibility of computationally superior quantumcomputers is one of the most fascinating

A lower bound on the amount of energy needed to carry out an elementary logical operation on a quantumcomputer, with a given accuracy and in a given time, is derived. The bound arises from the requirement that the controls used to manipulate the qubits, which ultimately are themselves quantum mechanical systems, must nonetheless be classical to a sufficiently good approximation; it is expected to hold under a wide variety of conditions, and independently of the nature of the physical systems used to encode the qubits. This could have important consequences for very large-scale quantumcomputations.

Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information, and the coherent conversion of quantum information between atomic and optical degrees of freedom. In a landmark paper, Duan et al. (DLCZ) [1] showed that atomic ensembles could be used as nodes of a quantum repeater network capable of sharing pairwise quantum entanglement between systems separated by arbitrarily large distances. In recent years, a number of promising experiments have demonstrated key aspects of this proposal [2-7]. Here, we describe a scheme for full scale quantumcomputing with atomic ensembles. Our scheme uses similar methods to those already demonstrated experimentally, and yet has information processing capabilities far beyond those of a quantum repeater.

The quantumcomputer is supposed to process information by applying unitary transformations to 2N complex amplitudes defining the state of N qubits. A useful machine needing N 103 or more, the number of continuous parameters describing the state of a quantumcomputer at any given moment is at least 21000 10300 which is much greater than the number of protons in the Universe. However, the theorists believe that the feasibility of large-scale quantumcomputing has been proved via the “threshold theorem”. Like for any theorem, the proof is based on a number of assumptions considered as axioms. However, in the physical world none of these assumptions can be fulfilled exactly. Any assumption can be only approached with some limited precision. So, the rather meaningless “error per qubit per gate” threshold must be supplemented by a list of the precisions with which all assumptions behind the threshold theorem should hold. Such a list still does not exist. The theory also seems to ignore the undesired free evolution of the quantumcomputer caused by the energy differences of quantum states entering any given superposition. Another important point is that the hypothetical quantumcomputer will be a system of 103 -106 qubits PLUS an extremely complex and monstrously sophisticated classical apparatus. This huge and strongly nonlinear system will generally exhibit instabilities and chaotic behavior.

Syllabus MCS 590, Spring 2014 Introduction to QuantumComputation and Quantum Information LCD-0-7503-0983-7. Supplementary TEXT: [2] Michael A. Nielsen and Isaac L. Chuang, QuantumComputation and Quantum Infor- mation) or its equiva- lent. 1 Introduction Quantumcomputing (QC) and information (QI) are rapidly developing

We present a scheme to perform universal quantumcomputation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB linear array of group-V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state S=3/2. Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automaton is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum-cellular-automata quantumcomputing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automaton operation and obtain a rough figure of merit for the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantumcomputer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes toward meeting the fifth criterion: qubit readout.

Twamley, J. [Department of Mathematical Physics, National University of Ireland Maynooth, Maynooth, County Kildare (Ireland)

We develop a formal model for distributed measurement-based quantumcomputations, adopting an agent-based view, such that computations are described locally where possible. Because the network quantum state is in general entangled, we need to model it as a global structure, reminiscent of global memory in classical agent systems. Local quantumcomputations are described as measurement patterns. Since measurement-based quantumcomputation is inherently distributed, this allows us to extend naturally several concepts of the measurement calculus, a formal model for such computations. Our goal is to define an assembly language, i.e. we assume that computations are well-defined and we do not concern ourselves with verification techniques. The operational semantics for systems of agents is given by a probabilistic transition system, and we define operational equivalence in a way that it corresponds to the notion of bisimilarity. With this in place, we prove that teleportation is bisimilar to a direct quantum channel, and this also within the context of larger networks.

Vincent Danos; Ellie D'Hondt; Elham Kashefi; Prakash Panangaden

The expanding networks of computer hardware, software, and organizations for controlling them and the institutional data bases they access are described. Improvements are making the data sources accessible but raise some new problems for data managers and institutional researchers. (Author/LBH)

Shell Oil Company used a COSMIC program, called VISCEL to insure the accuracy of the company's new computer code for analyzing polymers, and chemical compounds. Shell reported that there were no other programs available that could provide the necessary calculations. Shell produces chemicals for plastic products used in the manufacture of automobiles, housewares, appliances, film, textiles, electronic equipment and furniture.

Manin, Feynman, and Deutsch have viewed quantumcomputing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum logic circuit model, developed by Feynman and Deutsch, has been more prominent in the research literature than Deutsch's quantum Turing machines. Quantum Turing machines form a class closely related to deterministic and probabilistic Turing machines and one might hope to find a universal machine in this class. A universal machine is the basis of a notion of programmability. The extent to which universality has in fact been established by the pioneers in the field is examined and this key notion in theoretical computer science is scrutinised in quantumcomputing by distinguishing various connotations and concomitant results and problems.

Willem Fouche'; Johannes Heidema; Glyn Jones; Petrus H. Potgieter

The actual (classical) Brain-Computer Interface attempts to use brain signals to drive suitable actuators performing the actions corresponding to subject's intention. However this goal is not fully reached, and when BCI works, it does only in particular situations. The reason of this unsatisfactory result is that intention cannot be conceived simply as a set of classical input-output relationships. It is therefore necessary to resort to quantum theory, allowing the occurrence of stable coherence phenomena, in turn underlying high-level mental processes such as intentions and strategies. More precisely, within the context of a dissipative Quantum Field Theory of brain operation it is possible to introduce generalized coherent states associated, within the framework of logic, to the assertions of a quantum metalanguage. The latter controls the quantum-mechanical computing corresponding to standard mental operation. It thus become possible to conceive a Quantum Cyborg in which a human mind controls, through a quantum metalanguage, the operation of an artificial quantumcomputer.

We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantumcomputers. We show that for a given detector efficiency, there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gates and estimate the efficiency and noise levels required for the linear optical quantumcomputer to function properly.

Scott Glancy; J. M. LoSecco; H. M. Vasconcelos; C. E. Tanner

Matchgates are a family of two-qubit gates associated with noninteracting fermions. They are classically simulatable if acting only on nearest neighbors but become universal for quantumcomputation if we relax this restriction or use swap gates [Jozsa and Miyake, Proc. R. Soc. A 464, 3089 (2008)]. We generalize this result by proving that any nonmatchgate parity-preserving unitary is capable of extending the computational power of matchgates into universal quantumcomputation. We identify the single local invariant of parity-preserving unitaries responsible for this, and discuss related results in the context of fermionic systems.

Brod, Daniel J.; Galvao, Ernesto F. [Instituto de Fisica, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Gragoata, Niteroi, RJ, 24210-340 (Brazil)

We show that universal quantumcomputation can be achieved in the standard pure-state circuit model while the entanglement entropy of every bipartition is small in each step of the computation. The entanglement entropy required for large-scale quantumcomputation even tends to zero. Moreover we show that the same conclusion applies to many entanglement measures commonly used in the literature. This includes e.g., the geometric measure, localizable entanglement, multipartite concurrence, squashed entanglement, witness-based measures, and more generally any entanglement measure which is continuous in a certain natural sense. These results demonstrate that many entanglement measures are unsuitable tools to assess the power of quantumcomputers. PMID:23432229

31 Children and Computers: New Technology-- Old Concerns Ellen A.Wartella Nancy Jennings Abstract concerns about the effect on children's development and well- being. Although we tend to see these issues. With the introduction of each of these technologies, proponents touted the educational benefits for children, while

A lambda calculus for quantumcomputation with classical control Peter Selinger, Beno^it Valiron The objective of this paper is to develop a functional programming language for quantumcomputers. We develop a functional programming language for quan- tum computers. Quantumcomputing is a theory of computation based

A lambda calculus for quantumcomputation with classical control Peter Selinger, Benoâ??ï¿½t Valiron The objective of this paper is to develop a functional programming language for quantumcomputers. We develop a functional programming language for quanÂ tum computers. Quantumcomputing is a theory of computation based

QuantumComputing and Lie Theory Feynman's suggestion that the only effective way to model quantum phe- nomena on a computer would be to build a computer that made use of quantum mechanics was one that a quantumcomputer could, in theory, factor large integers or do discrete logarithms in polynomial time

The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the essentially physical notion of computation. In Quantum mechanics we cannot use the traditional Euclidean geometry but we introduce more sophisticate non Euclidean geometry which include a new kind of information diffuse in the entire universe and that we can represent as Fisher information or active information. We remark that from the Fisher information we can obtain the Bohm and Hiley quantum potential and the classical Schrodinger equation. We can see the quantum phenomena do not affect a limited region of the space but is reflected in a change of the geometry of all the universe. In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics and quantumcomputing. We stress the connection between metric and information as measure of change. Because computation is not restricted to calculus but is the environment changing via physical processes, super-Turing potentialities derive from an incomputable information source embedded into the geometry of the universe in accordance with Bell's constraints. In the general relativity we define the geometry of the space time. In our approach quantum phenomena define the geometry of the parameters of the probability distribution that include also the space time parameters. To study this new approach to the computation we use the new theory of Morphogenic systems.

Progress in manufacturing technology has allowed us to probe the behavior of devices on a smaller and faster scale than ever before. With increasing miniaturization, quantum effects come to dominate the transport properties of these devices, between collisions, carriers undergo ballistic motion under the influence of local electric and magnetic fields. The often surprising propertiesof quantum ballistic transport are currently

Quantumcomputing based on vibrational eigenstates: Pulse area theorem analysis Taiwang Cheng the accuracy of quantum gates in a quantumcomputer based on molecular vibrational eigenstates. The effects.1063/1.2164457 I. INTRODUCTION The field of quantumcomputing1Â3 has emerged as an intriguing and exciting new

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 computationalquantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider the commuting quantum circuits as dynamics of the quantum system. To show intractability of classical simulation above the boundary, we utilize the postselection argument introduced by M. J. Bremner, R. Jozsa, and D. J. Shepherd [Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 465, 1413 (2009).] and crucially strengthen its statement by taking noise effect into account. Classical simulatability below the boundary is shown by taking a projected-entangled-pair-state picture. Not only the separability criteria but also the condition for the entangled pair to become a convex mixture of stabilizer states is developed to show classical simulatability of highly entangling operations. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computationalquantum-classical boundary is tightly given by the dephasing rate required for the magic state distillation.

These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of Monte Carlo studies of classical spin systems, to illustrate finite-size scaling at continuous and first-order phase transitions. Exact diagonalization and quantum Monte Carlo (stochastic series expansion) algorithms and their computer implementations are then discussed in detail. Applications of the methods are illustrated by results for some of the most essential models in quantum magnetism, such as the S=1/2 Heisenberg antiferromagnet in one and two dimensions, as well as extended models useful for studying quantum phase transitions between antiferromagnetic and magnetically disordered states.

??Quantumcomputers offer the possibility of solving some problems more efficiently than their classical counterparts. The current forerunner in the experimental demonstration of quantum algorithms… (more)

We show that the problem of communication in a quantumcomputer reduces to constructing reliable quantum channels by distributing high-fidelity EPR pairs. We develop analytical models of the latency, bandwidth, error rate and resource utilization of such channels, and show that 100s of qubits must be distributed to accommodate a single data communication. Next, we show that a grid of teleportation nodes forms a good substrate on which to distribute EPR pairs. We also explore the control requirements for such a network. Finally, we propose a specific routing architecture and simulate the communication patterns of the Quantum Fourier Transform to demonstrate the impact of resource contention.

Nemanja Isailovic; Yatish Patel; Mark Whitney; John Kubiatowicz

General properties of quantum systems which interact with stochastic environment are studied with a strong emphasis on the role of physical symmetries. The similarity between the fidelity which is used to characterize the stability of such a systems and the Wilson loop in QCD is demonstrated, and the fidelity decay rates are derived. The consequences of existence of the symmetry group on the statistical properties of the system are analyzed for various physical systems - a simple quantum mechanical system, holonomic quantumcomputer and Yang-Mills fields.

We introduce a model of quantumcomputation 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.

Anders, Janet; Browne, Dan E. [Department of Physics and Astronomy, University College London, London WC1E 6BT (United Kingdom); Oi, Daniel K. L. [SUPA, Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom); Kashefi, Elham [School of Informatics, University of Edinburgh, Edinburgh EH8 9AB (United Kingdom); Andersson, Erika [SUPA, Department of Physics, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)

We describe the current state-of-the-art in Trusted ComputingTechnologies - focusing mainly on Intel's Trusted Execution Technology (TXT). This document is based on existing documentation and tests of two existing TXT-based systems: Intel's Trusted Boot and Invisible Things Lab's Qubes OS. We describe what features are lacking in current implementations, describe what a mature system could provide, and present a list of developments to watch. Critical systems perform operation-critical computations on high importance data. In such systems, the inputs, computation steps, and outputs may be highly sensitive. Sensitive components must be protected from both unauthorized release, and unauthorized alteration: Unauthorized users should not access the sensitive input and sensitive output data, nor be able to alter them; the computation contains intermediate data with the same requirements, and executes algorithms that the unauthorized should not be able to know or alter. Due to various system requirements, such critical systems are frequently built from commercial hardware, employ commercial software, and require network access. These hardware, software, and network system components increase the risk that sensitive input data, computation, and output data may be compromised.

We describe an architecture based on a processing "core," where multiple qubits interact perpetually, and a separate "store," where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the core, and free evolution of the core. This enables computation using physical systems where the entangling interactions are "always on." Alternatively, for switchable systems, our model constitutes a prescription for optimizing many-qubit gates. We discuss implementations of the quantum Fourier transform, Hamiltonian simulation, and quantum error correction. PMID:16803291

Ground-state quantumcomputers 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 quantumcomputer design.

ITAMP/HQOC Quantum Sciences Colloquium The Quantum Way of Doing Computations.iqoqi.at In this talk, the basic toolbox of the Innsbruck quantumcomputer based on a string.quantumoptics.at Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences

We show that a set of gates that consists of all one-bit quantum gates [U(2)] and the two-bit exclusive-OR gate [that maps Boolean values (x,y) to (x,x?y)] is universal in the sense that all unitary operations on arbitrarily many bits n [U(2n)] can be expressed as compositions of these gates. We investigate the number of the above gates required to

Adriano Barenco; Charles H. Bennett; Richard Cleve; David P. Divincenzo; Norman Margolus; Peter Shor; Tycho Sleator; John A. Smolin; Harald Weinfurter

Blind quantumcomputing is a new secure quantumcomputing protocol where a client who does not have any sophisticated quantum technlogy can delegate her quantumcomputing to a server without leaking any privacy. It is known that a client who has only a measurement device can perform blind quantumcomputing [T. Morimae and K. Fujii, Phys. Rev. A {\\bf87}, 050301(R) (2013)]. It has been an open problem whether the protocol can enjoy the verification, i.e., the ability of client to check the correctness of the computing. In this paper, we propose a protocol of verification for the measurement-only blind quantumcomputing.

Technical Report No. 2005Â500 Quantumcomputing: Beyond the limits of conventional computation Canada EÂmail: fmarius,aklg@cs.queensu.ca July 22, 2005 Abstract The quantum model of computation measurement capabilities as the quantumcomputational device). A new class of information processing tasks

In this article, a strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantumcomputation and quantum information theory.

Measurement-based quantumcomputation (MBQC) and holonomic quantumcomputation (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 quantumcomputation (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.

Suppression of quantum chaos in a quantumcomputer hardware J. Lages* and D. L. Shepelyansky regimes in the quantumcomputer hardware are identified as a function of magnetic field gradient chaos and melting of quantumcomputer hardware 15Â17 . It has been also shown 18,19 that these static

different potential hardware implemen- tations, quantumcomputer architecture is a rich field with an opTailoring Quantum Architectures to Implementation Style: A QuantumComputer for Mobile University {echi,lyon,mrm}@princeton.edu ABSTRACT In recent years, quantumcomputing (QC) research has moved

How QuantumComputers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation towards a negative answer. The first is a conjecture about physical realizations of quantum codes superior compared to digital computers. The idea was that since computations in quantum physics require

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 0.4 sec (Region Feature) and 0.3 sec (Payoff Feature) on a Intel Core 2 Duo GHz with 2 GB of memory under Windows XP.

For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation can be performed faster than the typical decoherence time of the underlying system. The computational model underlying the one-way quantumcomputer, which has been introduced by Hans Briegel and Robert Raussendorf, provides a suitable concept for a fast implementation of quantum error correcting codes. It is shown explicitly in this article is how encoding and decoding operations for stabilizer codes can be realized on a one-way quantumcomputer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.

Nowadays there are two secure ways of encrypting information, the public key cryptography (PKC), and the symmetric cryptography (SC). With the arrival of the quantumcomputation, both methods become vulnerable, thanks to its exponential-growing calculation capacity. To solve this lack of security, quantum physics nowadays offers us two satisfactory methods which have been proposed successfully from a theoretical point of view: the two non-commuting observables, based on the Bennet and Brassard protocol, and the quantum entanglement combined with the Bell's inequality theorem, based on the Ekert protocol. Since some experiments have demonstrated the viability of the conduction of free space quantum cryptography at the surface of the Earth, we propose that this could be a boost for secure ground-to-satellite or satellite-to-satellite communications.

Delicado, Raquel Fernandez; Cabello, David Bellver; Boada, Ivan Lloro

The quest for quantumcomputers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous framework for classifying the hardness of problems according to the computational resources, most notably time, needed to solve them. Its extension to quantumcomputers allows the

C. R. Laumann; R. Moessner; A. Scardicchio; S. L. Sondhi

"The Stanford Persuasive Technology Lab creates insight into how computing products -- from websites to mobile phone software -- can be designed to change what people believe and what they do." This unusual field of study is called captology, and the subject is explored in detail on the lab's homepage. The Key Concepts section provides a brief overview of captology and links to another page with nine topic papers published by researchers at the lab. In a series of examples demonstrating how computers can be used to influence a person, the site's creators separate instances into macrosuasion and microsuasion. Specific websites and computer programs are highlighted to reveal these interesting marketing or motivational tactics.

We propose an experimentally feasible scheme to achieve quantumcomputation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantumcomputation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, promises a possible way for robust quantumcomputation.

QuantumComputing without Magic Devices Zdzislaw Meglicki The MIT Press Cambridge, Massachusetts, recording, or information storage and retrieval) without permission in writing from the publisher. MIT Press and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Meglicki

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 quantumcomputation. 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 quantumcomputation that are closely related to topological quantumcomputation, but for which the fault tolerance is implemented in software rather than coming from a physical medium.

Koenig, Robert, E-mail: rkoenig@caltech.ed [Institute for Quantum Information, California Institute of Technology, Pasadena, CA 91125 (United States); Kuperberg, Greg [Department of Mathematics, University of California, Davis, CA 95616 (United States); Reichardt, Ben W. [School of Computer Science, Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1 (Canada)

Molecular structures appear to be natural candidates for a quantumtechnology: 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 realising 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.

Simon C Benjamin; Arzhang Ardavan; G Andrew D Briggs; David A Britz; Daniel Gunlycke; John Jefferson; Mark A G Jones; David F Leigh; Brendon W Lovett; Andrei N Khlobystov; S A Lyon; John J L Morton; Kyriakos Porfyrakis; Mark R Sambrook; Alexei M Tyryshkin

Quantum simulation can beat current classical computers with minimally a few tens of qubits and will likely become the first practical use of a quantumcomputer. One promising application of quantum simulation is to attack challenging quantum chemistry problems. Here we report an experimental demonstration that a small nuclear-magnetic-resonance (NMR) quantumcomputer is already able to simulate the dynamics of a prototype chemical reaction. The experimental results agree well with classical simulations. We conclude that the quantum simulation of chemical reaction dynamics not computable on current classical computers is feasible in the near future.

The rapidly increasing demand for greater speed and efficiency on the information superhighway requires significant improvements over conventional electronic logic circuits. Optical interconnections and optical integrated circuits are strong candidates to provide the way out of the extreme limitations imposed on the growth of speed and complexity of nowadays computations by the conventional electronic logic circuits. The new optical technology has increased the demand for high quality optical materials. NASA's recent involvement in processing optical materials in space has demonstrated that a new and unique class of high quality optical materials are processible in a microgravity environment. Microgravity processing can induce improved orders in these materials and could have a significant impact on the development of optical computers. We will discuss NASA's role in processing these materials and report on some of the associated nonlinear optical properties which are quite useful for optical computerstechnology.

Abdeldayem, Hossin A.; Frazier, Donald O.; Penn, Benjamin; Paley, Mark S.; Witherow, William K.; Banks, Curtis; Hicks, Rosilen; Shields, Angela

We review the physics of hybrid optomechanical systems consisting of a mechanical oscillator interacting with both a radiation mode and an additional matter-like system. We concentrate on the cases embodied by either a single or a multi-atom system (a Bose-Einstein condensate, in particular) and discuss a wide range of physical effects, from passive mechanical cooling to the set-up of multipartite entanglement, from optomechanical non-locality to the achievement of non-classical states of a single mechanical mode. The reviewed material showcases the viability of hybridised cavity optomechanical systems as basic building blocks for quantum communication networks and quantum state-engineering devices, possibly empowered by the use of quantum and optimal control techniques. The results that we discuss are instrumental to the promotion of hybrid optomechanical devices as promising experimental platforms for the study of non-classicality at the genuine mesoscopic level.

Benjamin Rogers; Nicola Lo Gullo; Gabriele De Chiara; G. Massimo Palma; Mauro Paternostro

with N legs ( ) ( ) ( ) = jjiijiij yxa , i j Matrix-vector product Â contraction over index i: #12;First and TT: Description Computations/Contractions Normalizations (SVD, DMRG) PEPS, MERA, MPO Eigenvalue Notation ix i Vector (1 leg): ( ) jiija , i j Matrix (2 legs): Niix ...1 ... i1 i2 ... iN General tensor

In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantumcomputer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantumcomputer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also proposed thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function

Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first systematic and comprehensive treatment of this (bipartite) quantum separability problem, focusing on its deterministic (as opposed to randomized) computational complexity. First, I review the one-sided tests for separability, paying particular attention to the semidefinite programming methods. Then, I discuss various ways of formulating the quantum separability problem, from exact to approximate formulations, the latter of which are the paper's main focus. I then give a thorough treatment of the problem's relationship with the complexity classes NP, NP-complete, and co-NP. I also discuss extensions of Gurvits' NP-hardness result to strong NP-hardness of certain related problems. A major open question is whether the NP-contained formulation (QSEP) of the quantum separability problem is Karp-NP-complete; QSEP may be the first natural example of a problem that is Turing-NP-complete but not Karp-NP-complete. Finally, I survey all the proposed (deterministic) algorithms for the quantum separability problem, including the bounded search for symmetric extensions (via semidefinite programming), based on the recent quantum de Finetti theorem; and the entanglement-witness search (via interior-point algorithms and global optimization). These two algorithms have the lowest complexity, with the latter being the best under advice of asymptotically optimal point-coverings of the sphere.

What resources are universal for quantumcomputation? In the standard model, a quantumcomputer consists of a sequence of unitary gates acting coherently on the qubits making up the computer. This paper shows that a very different model involving only projective measurements, quantum memory, and the ability to prepare the |0> state is also universal for quantumcomputation. In particular, no coherent unitary dynamics are involved in the computation.

This thesis explores the use of entangled states in quantumcomputation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable ...

Chung, Hyeyoun, M. Eng. Massachusetts Institute of Technology

. This paper proÂ vides a brief introduction to QC, particularly emphasizing methods for quantum data of auxiliary registers for storage of the input. 1.2 An Introduction to QuantumComputationComputationsQuantum Information Processing: Compression, Coding, and Related Computations John H. Reif

attacker--an attacker equipped with a large quantumcomputer? The power of today's cryptanalytic hardware]. Simulating this quantumcomputer on traditional hardware would make it exponentially slower. The goalCost analysis of hash collisions: Will quantumcomputers make SHARCS obsolete? Daniel J. Bernstein

, given only moderately reliable quantumcomputing hardware. 1991 Mathematics Subject Classi cationDoc. Math.J. DMV 467 QuantumComputing Peter W. Shor Abstract. The Church-Turing thesis says that it entails at most a poly- nomial increase in computation time. This may not be true if quantum mechanics

to study the functioning of QuantumComputer hardware. The latter is modeled by a collection of interactingSimulation of QuantumComputers H. De Raedt1 , K. Michielsen2 , A.H. Hams1 , S. Miyashita3 , and K out by the QuantumComputer. Our simulation software consists of code that solves the time

ARTICLES Fault-tolerant architecture for quantumcomputation using electrically controlled for computation and communication and may yield insights into our understanding of the limits of quantum mechanics an architecture for quantumcomputation using electrically controlled semiconductor spins by extending the Loss

LETTERS Deterministic entanglement swapping with an ion-trap quantumcomputer M. RIEBE1 *, T. MONZ1, including secure communication, teleportation and powerful quantumcomputation. Therefore, a focus repeaters2 or aid in distributing entangled states in ion-trap quantumcomputers3 . Entanglement among

QUBIT-RESONATOR SYSTEM AS AN APPLICATION TO QUANTUMCOMPUTATION Ren-Shou Huang Submitted #12;Abstract Ren-Shou Huang Qubit-Resonator System as an Application to QuantumComputation The recent development of quantumcomputation has inspired lots of interesting ideas in a variety of fields

QUANTUMCOMPUTATION AND REAL MULTIPLICATION MATILDE MARCOLLI AND JOHN NAPP Abstract. We propose, and are obtained from the basic modules and the real multiplication structure. 1. Introduction Quantumcomputation operations on data. It is believed that quantumcomputation is signifi- cantly more powerful than classical

Design of a Superconducting QuantumComputer Prof. John Martinis University of California Date building (Faculty of Materials Science and Engineering) #12;Design of a Superconducting QuantumComputer Superconducting quantumcomputing is now at an important crossroad, where "proof of concept" experiments involving

We propose a different scheme to realize holonomic quantumcomputation with rf superconducting quantum interference device (SQUID) qubits in a microwave cavity. In this scheme associated with the non-Abelian holonomies, the single-qubit gates and a two-qubit controlled-PHASE gate as well as a controlled-NOT gate can be easily constructed by tuning adiabatically the Rabi frequencies of classical microwave pulses coupled to the SQUIDs. The fidelity of these gates is estimated to be possibly higher than 90% with the current technology.

Zhang, P. [Department of Physics, University of Hong Kong, Hong Kong (China); Institute of Theoretical Physics, Chinese Academy of Science, Beijing, 100080 (China); Wang, Z.D.; Sun, J.D. [Department of Physics, University of Hong Kong, Hong Kong (China); Sun, C.P. [Institute of Theoretical Physics, Chinese Academy of Science, Beijing, 100080 (China)

The study of QuantumComputing necessitates careful examination of the most fundamental questions of Quantum Theory, such as the measurement problem, and may lead to important advances in practical applications such as cryptography, search, and optimization. In order for a QuantumComputer to be practically useful, the design must be scalable to hundreds of quantum bits, or qubits, while maintaining quantum coherence. Qubits constructed from superconducting electronics are promising because of their inherent scalability using established nano-fabrication techniques. Superconducting qubits based on the flux degree of freedom are insensitive to noise from charge fluctuations and can be read-out using a Superconducting Quantum Interference Device (SQUID). When properly designed, a superconducting loop interrupted by three Josephson junctions acts as a quantum two-state system. In this Dissertation, an exact calculation of the energy levels of the three junction flux qubit is used to design samples consisting of one or two qubits to investigate coherence properties. Careful attention is given to the system electronics to minimize external sources of noise acting back on the qubit that result in decoherence. We report measurements on two superconducting flux qubits coupled to a readout SQUID. Two on-chip flux bias lines allow independent flux control of any two of the three elements, as illustrated by a two-dimensional qubit flux map. The application of microwaves yields a frequency-flux dispersion curve for 1- and 2-photon driving of the single-qubit excited state and reveals spurious resonances intrinsic to each qubit. Coherent manipulation of the single-qubit state results in Rabi oscillations, Ramsey fringes, and Hahn spin-echos. This information is used to develop a model of the decoherence caused by the interaction of the qubit with its environment. A detailed model for the interaction of a flux qubit with a readout SQUID predicts the resolution of a measurement and its effect on the qubit. Two adjustable inter-qubit coupling systems that can produce bipolar coupling strength are presented. These systems can be used to produce the quantum Controlled-NOT gate, which when combined with single qubit operations forms a basis for Universal QuantumComputation.

A constructive scheme has been devised to enable mapping of any quantumcomputation 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 quantumcomputation 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 that the derivation provides explicit constructions for finding the exchange couplings in the physical basis needed to implement any arbitrary 1-qubit gate. These constructions lead to spintronic encodings of quantum logic that are more efficient than those of a previously published scheme that utilizes a universal but fixed set of gates.

Models of quantumcomputation (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.

Bacon, Dave [Department of Computer Science and Engineering, University of Washington, Seattle, Washington 98195 (United States); Department of Physics, University of Washington, Seattle, Washington 98195 (United States); Flammia, Steven T. [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada)

Topological quantumcomputation (TQC) has emerged as one of the most promising approaches to quantumcomputation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.

Development of silicon, enhancement mode nanostructures for solid-state quantumcomputing will be described. A primary motivation of this research is the recent unprecedented manipulation of single electron spins in GaAs quantum dots, which has been used to demonstrate a quantum bit [1]. Long spin decoherence times are predicted possible in silicon qubits. This talk will focus on silicon enhancement mode quantum dot structures that emulate the GaAs lateral quantum dot qubit [1] but use an enhancement mode field effect transistor (FET) structure. One critical concern for silicon quantum dots that use oxides as insulators in the FET structure is that defects in the metal oxide semiconductor (MOS) stack can produce both detrimental electrostatic and paramagnetic effects on the qubit. Understanding the implications of defects in the Si MOS system is also relevant for other qubit architectures that have nearby dielectric passivated surfaces. Stable, lithographically defined, single-period Coulomb-blockade and single-electron charge sensing in a quantum dot nanostructure using a MOS stack will be presented. A combination of characterization of defects, modeling and consideration of modified approaches that incorporate SiGe or donors provides guidance about the enhancement mode MOS approach for future qubits and quantum circuit micro-architecture. [1] J. Petta et al., Science 309, 2180 (2005) We wish to acknowledge the research funding support provided by the laboratory directed research and development (LDRD) program at Sandia National Laboratories and the Laboratory of Physical Sciences. Sandia National Labs is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

We investigate relations between computational power and correlation in resource states for quantumcomputational tensor network, which is a general framework for measurement-based quantumcomputation. We find that if the size of resource states is finite, not all resource states allow correct projective measurements in the correlation space, which is related to non-vanishing two-point correlations in the resource states. On the other hand, for infinite-size resource states, we can always implement correct projective measurements if the resource state can simulate arbitrary single-qubit rotations, since such a resource state exhibits exponentially-decaying two-point correlations. This implies that a many-body state whose two-point correlation cannot be upperbounded by an exponentially-decaying function cannot simulate arbitrary single-qubit rotations.

Quantum Information processing has several di.erent applications: some of them can be performed controlling only few qubits simultaneously (e.g. quantum teleportation or quantum cryptography) [1]. Usually, the transmission of large amount of information is performed repeating several times the scheme implemented for few qubits. However, to exploit the advantages of quantumcomputation, the simultaneous control of many qubits is unavoidable [2]. This situation increases the experimental di.culties of quantumcomputing: maintaining quantum coherence in a large quantum system is a di.cult task. Indeed a quantumcomputer is a many-body complex system and decoherence, due to the interaction with the external world, will eventually corrupt any quantumcomputation. Moreover, internal static imperfections can lead to quantum chaos in the quantum register thus destroying computer operability [3]. Indeed, as it has been shown in [4], a critical imperfection strength exists above which the quantum register thermalizes and quantumcomputation becomes impossible. We showed such e.ects on a quantumcomputer performing an e.cient algorithm to simulate complex quantum dynamics [5,6].

We study a hybrid quantumcomputing system using a nitrogen-vacancy center ensemble (NVE) as quantum memory, a current-biased Josephson junction (CBJJ) superconducting qubit fabricated in a transmission line resonator (TLR) as the quantumcomputing processor, and the microwave photons in TLR as the quantum data bus. The storage process is seriously treated by considering all kinds of decoherence mechanisms. Such

This Mathematica 7.0/8.0 package upgrades and extends the quantumcomputer simulation code called QDENSITY. Use of the density matrix was emphasized in QDENSITY, although that code was also applicable to a quantum state description. In the present version, the quantum state version is stressed and made amenable to future extensions to parallel computer simulations. The add-on QCWAVE extends QDENSITY in several ways. The first way is to describe the action of one, two and three- qubit quantum gates as a set of small ($2 \\times 2, 4\\times 4$ or $8\\times 8$) matrices acting on the $2^{n_q}$ amplitudes for a system of $n_q$ qubits. This procedure was described in our parallel computer simulation QCMPI and is reviewed here. The advantage is that smaller storage demands are made, without loss of speed, and that the procedure can take advantage of message passing interface (MPI) techniques, which will hopefully be generally available in future Mathematica versions. Another extension of QDENSITY provided here is a multiverse approach, as described in our QCMPI paper. This multiverse approach involves using the present slave-master parallel processing capabilities of Mathematica 7.0/8.0 to simulate errors and error correction. The basic idea is that parallel versions of QCWAVE run simultaneously with random errors introduced on some of the processors, with an ensemble average used to represent the real world situation. Within this approach, error correction steps can be simulated and their efficacy tested. This capability allows one to examine the detrimental effects of errors and the benefits of error correction on particular quantum algorithms.

Quantumcomputers have been shown to efficiently solve a class of problems for which no efficient solution is otherwise known. Physical systems can implement quantumcomputation, but devising realistic schemes is an extremely ...

This Mathematica 5.2 package~\\footnote{QDENSITY is available at http://www.pitt.edu/~tabakin/QDENSITY} is a simulation of a QuantumComputer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in {\\it Qdensity.m} which contains the tools needed in quantum circuits, e.g. multiqubit kets, projectors, gates, etc. Selected examples of the basic commands are presented here and a tutorial notebook, {\\it Tutorial.nb} is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: {\\it QFT.nb}, {\\it Teleportation.nb}, {\\it Grover.nb} and {\\it Shor.nb} where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of ``one way computing" ideas, are included as an additional tool in the notebook {\\it Cluster.nb}. A Mathematica palette containing most commands in QDENSITY is also included: {\\it QDENSpalette.nb} .

Highlights: > Our model is the 2D valence bond solid phase of a quantum antiferromagnet. > Universal quantumcomputation is processed by measurements of quantum correlations. > An intrinsic complexity of strongly-correlated quantum systems could be a resource. - Abstract: Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations artificially. Here we show theoretically that quantum correlations exhibited in the 2D valence bond solid phase of a quantum antiferromagnet, modeled by Affleck, Kennedy, Lieb, and Tasaki (AKLT) as a precursor of spin liquids and topological orders, are sufficiently complex yet structured enough to simulate universal quantumcomputation when every single spin can be measured individually. This unveils that an intrinsic complexity of naturally-occurring 2D quantum systems-which has been a long-standing challenge for traditional computers-could be tamed as a computationally valuable resource, even if we are limited not to create newly entanglement during computation. Our constructive protocol leverages a novel way to herald the correlations suitable for deterministic quantumcomputation through a random sampling, and may be extensible to other ground states of various 2D valence bond phases beyond the AKLT state.

Miyake, Akimasa, E-mail: amiyake@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo Ontario, N2L 2Y5 (Canada)

Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantumcomputing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via one- and two-bit gate operations. How this works can be understood by comparing the system with a three-level atom exhibiting a macroscopic dark period.

Computational Fluid Dynamics (or CFD) methods are very familiar to the research community. Even the general public has had some exposure to CFD images, primarily through the news media. However, very little attention has been paid to CST--Computational Structures Technology. Yet, no important design can be completed without it. During the first half of this century, researchers only dreamed of designing and building structures on a computer. Today their dreams have become practical realities as computational methods are used in all phases of design, fabrication and testing of engineering systems. Increasingly complex structures can now be built in even shorter periods of time. Over the past four decades, computertechnology has been developing, and early finite element methods have grown from small in-house programs to numerous commercial software programs. When coupled with advanced computing systems, they help engineers make dramatic leaps in designing and testing concepts. The goals of CST include: predicting how a structure will behave under actual operating conditions; designing and complementing other experiments conducted on a structure; investigating microstructural damage or chaotic, unpredictable behavior; helping material developers in improving material systems; and being a useful tool in design systems optimization and sensitivity techniques. Applying CST to a structure problem requires five steps: (1) observe the specific problem; (2) develop a computational model for numerical simulation; (3) develop and assemble software and hardware for running the codes; (4) post-process and interpret the results; and (5) use the model to analyze and design the actual structure. Researchers in both industry and academia continue to make significant contributions to advance this technology with improvements in software, collaborative computing environments and supercomputing systems. As these environments and systems evolve, computational structures technology will evolve. By using CST in the design and operation of future structures systems, engineers will have a better understanding of how a system responds and lasts, more cost-effective methods of designing and testing models, and improved productivity. For informational and educational purposes, a videotape is being produced using both static and dynamic images from research institutions, software and hardware companies, private individuals, and historical photographs and drawings. The extensive number of CST resources indicates its widespread use. Applications run the gamut from simpler university-simulated problems to those requiring solutions on supercomputers. In some cases, an image or an animation will be mapped onto the actual structure to show the relevance of the computer model to the structure. Transferring the digital files to videotape presents a number of problems related to maintaining the quality of the original image, while still producing a broadcast quality videotape. Since researchers normally do not create a computer image using traditional composition theories or video production requirements, often the image loses some of its original digital quality and impact when transferred to videotape. Although many CST images are currently available, those that are edited into the final project must meet two important criteria: they must complement the narration, and they must be broadcast quality when recorded on videotape.

Modeling QuantumComputing in Haskell Amr Sabry Department of Computer Science, Indiana University sabry@cs.indiana.edu ABSTRACT The paper develops a model of quantumcomputing from the perspective of functional programming. The model explains the fundamental ideas of quantumcomputing at a level

We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic configuration space), we present an explicit algebraic description of one and two-qubit quantum states together with a MSTA characterization of one and two-qubit quantumcomputational gates. Second, using the above mentioned characterization and the GA description of the Lie algebras SO(3) and SU(2) based on the rotor group Spin+(3, 0) formalism, we reexamine Boykin's proof of universality of quantum gates. We conclude that the MSTA approach does lead to a useful conceptual unification where the complex qubit space and the complex space of unitary operators acting on them become united, with both being made just by multivectors in real space. Finally, the GA approach to rotations based on the rotor group does bring conceptual and computational advantages compared to standard vectorial and matricial approaches.

Model-independent semantic requirements for user specification and interpretation of data before and after quantumcomputations are characterized. Classical computational costs of assigning classical data values to quantum registers and to run-time parameters passed across a classical-to-quantum application programming interface are derived. It is shown that the classical computational costs of data definition equal or exceed the classical computational cost of solving the problem of interest for all applications of quantumcomputing except computations defined over the integers and the simulation of linear systems with linear boundary conditions.

The one-way quantumcomputer (QCc) is a universal scheme of quantumcomputation consisting only of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. The computational model underlying the QCc is different from the quantum logic network model and it is based on different constituents. It has no quantum register and does not consist of quantum gates. The

of the ideas in quantumcomputing. The paper begins by motivating the central ideas of quantum mechanics this situation by presenting the basic ideas of quantumcomputing understandable to anyone who has had a course not need more than the ability to do matrix multiplication in order to understand this paper. To motivate

We describe a paradigm for computing with interacting quantum dots, quantum-dot cellular automata (QCA). We show how arrays of quantum-dot cells could be used to perform useful computations. A new adiabatic switching paradigm is developed which permits clocked control, eliminates metastability problems, and enables a pipelined architecture

Quantumcomputation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantumcomputation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantumcomputation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantumcomputation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

Xu, G. F.; Zhang, J.; Tong, D. M.; Sjöqvist, Erik; Kwek, L. C.

A survey research study profiled foodservices and foodservice managers in health care and educational institutions that applied computertechnology to their operations. The survey also examined the extent to which computers were applied to management and client service functions. Both the size and the type of institution were found to be significantly related to computer usage. The larger the institution, the greater the extent of indicated usage. Educational institutions used computers more than all types of health care institutions. Mainframe systems (time shared internally or externally) were the predominant computers used. Internal mainframe systems and minicomputers were used significantly more by educational institutions than by health care institutions. The manager most likely to use computers was a man of any age with at least a bachelor's degree who was employed full-time within the institution. He had taken at least six business management courses and had at least some understanding of and ability to apply systems management concepts to his daily management practices. Applications were categorized into five functional areas: menu, purchasing/storage, production, client service, and managerial information. Managerial information applications were most frequently reported by all respondents, with large institutions and elementary/secondary schools reporting the greatest usage for those applications. Several purchase/storage and production applications were significantly related to type or to size or to both, with large institutions and college/university foodservices reporting the greatest usage. Menu precosting was the only significant menu function, and that was significant only relative to institutional type. No client service functions were significantly related to either type or size. PMID:3941228

twentieth century to the modern VLSI semiconductor tran- sistors of under 0.1 Âµm in size. Under this impressive progression of technology, we have enjoyed an exponential growth in computing power in density every year or two. But this growth will not continue indefinitely. As bits continually shrink

NASA programs for manned space flight are in their 27th year. Scientists and engineers who worked continuously on the development of aerospace technology during that period are approaching retirement. The resulting loss to the organization will be considerable. Although this problem is general to the NASA community, the problem was explored in terms of the institutional memory and technical expertise of a single individual in the Man-Systems division. The main domain of the expert was spacecraft lighting, which became the subject area for analysis in these studies. The report starts with an analysis of the cumulative expertise and institutional memory of technical employees of organizations such as NASA. A set of solutions to this problem are examined and found inadequate. Two solutions were investigated at length: hypertext and expert systems. Illustrative examples were provided of hypertext and expert system representation of spacecraft lighting. These computertechnologies can be used to ameliorate the problem of the loss of invaluable personnel.

Integrated High Performance Turbine Engine Technology Initiative (IHPTET) goals require a strong analytical base. Effective analysis of composite materials is critical to life analysis and structural optimization. Accurate life prediction for all material systems is critical. User friendly systems are also desirable. Post processing of results is very important. The IHPTET goal is to double turbine engine propulsion capability by the year 2003. Fifty percent of the goal will come from advanced materials and structures, the other 50 percent will come from increasing performance. Computer programs are listed.

An obstacle affecting any proposal for a topological quantumcomputer based on Ising anyons is that quasiparticle braiding can only implement a finite (non-universal) set of quantum operations. The computational power of this restricted set of operations (often called stabilizer operations) has been studied in quantum information theory, and it is known that no quantum-computational advantage can be obtained without the help of an additional non-stabilizer operation. Similarly, a bipartite two-qubit system based on Ising anyons cannot exhibit non-locality (in the sense of violating a Bell inequality) when only topologically protected stabilizer operations are performed. To produce correlations that cannot be described by a local hidden variable model again requires the use of a non-stabilizer operation. Using geometric techniques, we relate the sets of operations that enable universal quantumcomputing (UQC) with those that enable violation of a Bell inequality. Motivated by the fact that non-stabilizer operations are expected to be highly imperfect, our aim is to provide a benchmark for identifying UQC-enabling operations that is both experimentally practical and conceptually simple. We show that any (noisy) single-qubit non-stabilizer operation that, together with perfect stabilizer operations, enables violation of the simplest two-qubit Bell inequality can also be used to enable UQC. This benchmarking requires finding the expectation values of two distinct Pauli measurements on each qubit of a bipartite system.

We briefly review the development and theory of an experiment to investigate quantumcomputation with trapped calcium ions. The ion trap, laser and ion requirements are determined, and the parameters required for simple quantum logic operations are described

D. F. V. James; M. S. Gulley; M. H. Holzscheiter; R. J. Hughes; P. G. Kwiat; S. K. Lamoreaux; C. G. Peterson; V. D. Sandberg; M. M. Schauer; C. M. Simmons; D. Tupa; P. Z. Wang; A. G. White

Quantum mechanics presents a more general and potentially more powerful model of computation than classical systems. Quantum bits have many physically different representations which nonetheless share a common need for ...

We present a quantumcomputing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off resonant optical lattice. Raman lasers provide the "Josephson" tunneling, and the collision interaction between atoms represent the "capacitive" couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.

We present a quantumcomputing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off-resonant optical lattice. Raman lasers provide the 'Josephson' tunneling, and the collision interaction between atoms represent the 'capacitive' couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single-qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.

Tian Lin; Zoller, P. [Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria)

Quantum mechanics for everyone: Hands-on activities integrated with technology Dean A. Zollman,a) N approach to higher-level courses. The result is a hands-on approach to learning and teaching quantum interactive instruction and include hands-on activities as well as interactive computer visualiza- tions. Our

many possible routes to quantumcomput- ing have been suggested, but the most promising are solid-intuitive rules of quantum mechanics imply that, unlike classical com- puters, quantumcomputers should per- form be scaled up to generate the massive parallelism required for useful computation. The counter

The one-way quantumcomputer (QCc) is a universal scheme of quantumcomputation consisting only of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. The computational model underlying the QCc is different from the quantum logic network model and it is based on different constituents. It has no quantum register and does not consist of quantum gates. The QCc is nevertheless quantum mechanical since it uses a highly entangled cluster state as the central physical resource. The scheme works by measuring quantum correlations of the universal cluster state.

An open quantum walk formalism for dissipative quantumcomputing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on the open quantum walk formalism are more efficient than the canonical dissipative quantumcomputing approach. In particular, the open quantum walks can be designed to converge faster to the desired steady state and to increase the probability of detection of the outcome of the computation.

Complete characterization of the state of a quantum system made up of subsystems requires determination of relative phase, because of interference effects between the subsystems. For a system of qubits used as a quantumcomputer this is especially vital, because the entanglement, which is the basis for the quantum advantage in computing, depends intricately on phase. We present here a first step towards that determination, in which we use a two-qubit quantum system as a quantum neural network, which is trained to compute and output its own relative phase.

Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation appeared justified when Peter Shor described a polynomial time quantum algorithm for factoring integers. In quantum systems, the computational space increases exponentially with the size of the system which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new non-traditional programming techniques. The aim of this paper is to guide computer scientists and other non-physicists through the conceptual and notational barriers that separate quantumcomputing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantumcomputers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to harnessing the power of quantum parallelism are explained, including Shor's algorithm, Grover's algorithm, and Hogg's algorithms. We conclude with a discussion of quantum error correction.

Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantumcomputing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and manipulating them via one and two bit gate operations. How this works can be understood by comparing the system with a three-level atom exhibiting a macroscopic dark period. In addition, a dynamical explanation is given for a scheme based on atoms inside an optical cavity in the strong coupling regime and we show how spontaneous emission by the atoms can be highly suppressed.

We analyze the performance of adiabatic quantumcomputation (AQC) subject to decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria. PMID:16384441

of QM (the best we can make in non-relativistic atomic physics and quantumcomputation (Mermin 20031 The relation between quantum mechanics and higher brain functions: Lessons from quantumcomputation and neurobiology Christof Koch1,2 and Klaus Hepp1 April 2. 2007 1 Institute for Neuroinformatics

. This architecture is attractive both as a macroscopic analog of atomic physics experiments and for quantumcomputingCavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantumcomputation Alexandre Blais,1 Ren-Shou Huang,1,2 Andreas Wallraff,1 S. M. Girvin,1 and R. J. Schoelkopf1 1

Technological developments sparked by quantum mechanics and wave-particle duality are still gaining ground over a hundred years after the theories were devised. While the impact of the theories in fundamental research, philosophy and even art and literature is widely appreciated, the implications in device innovations continue to breed potential. Applications inspired by these concepts include quantumcomputation and quantum cryptography protocols based on single photons, among many others. In this issue, researchers in Germany and the US report a step towards precisely triggered single-photon sources driven by surface acoustic waves (SAWs) [1]. The work brings technology based on quantum mechanics yet another step closer to practical device reality. Generation of single 'antibunched' photons has been one of the key challenges to progress in quantum information processing and communication. Researchers from Toshiba and Cambridge University in the UK recently reported what they described as 'the first electrically driven single-photon source capable of emitting indistinguishable photons' [2]. Single-photon sources have been reported previously [3]. However the approach demonstrated by Shields and colleagues allows electrical control, which is particularly useful for implementing in compact devices. The researchers used a layer of InAs quantum dots embedded in the intrinsic region of a p-i-n diode to demonstrate interference between single photons. They also present a complete theory based on the interference of photons with a Lorentzian spectrum, which they compare with both continuous-wave and pulsed experiments. The application of SAWs in achieving precisely triggered single-photon sources develops the work of researchers in Germany in the late 1990s [4]. Surface acoustic waves travel like sound waves, but are characterized by an amplitude that typically decays exponentially with depth into the substrate. As Rocke and colleagues demonstrated, they can be used to dissociate an optically excited exciton and spatially separate the electron and hole, thereby increasing the radiative lifetime by orders of magnitude. The interesting behaviour of SAWs has led to studies towards a number of other applications including sensing [5-7], synthesis and nanoassembly [8]. For applications in single-photon sources, the electron-hole pairs are transported by the SAW to a quantum dot where they recombine emitting a single photon. However, so far various limiting factors in the system, such as the low quality of the quantum dots used leading to multiple-exciton recombinations, have hindered potential applications of the system as a single-photon source. Control over high-quality quantum-dot self-assembly is constantly improving. Researchers at the University of California at Berkeley and Harvard University in the US report the ability to successfully position a small number of colloidal quantum dots to within less than 100 nm accuracy on metallic surfaces [9]. They use single-stranded DNA both to act as an anchor to the gold or silver substrates and to selectively bind to the quantum dots, allowing programmed assembly of quantum dots on plasmonic structures. More recently still, researchers in Germany have reported how they can controllably reduce the density of self-assembled InP quantum dots by cyclic deposition with growth interruptions [10]. The impressive control has great potential for quantum emitter use. In this issue, Völk, Krenner and colleagues use an alternative approach to demonstrate how they can improve the performance of single-photon sources using SAWs. They use an optimized system of isolated self-assembled quantum posts in a quantum-well structure and inject the carriers at a distance from the posts where recombination and emission take place [3]. The SAW dissociates the electron-hole pairs and transports them to the quantum posts, so the two carrier types arrive at the quantum post with a set time delay. Other approaches, such as Coulomb blockade ones, have struggled to achieve the sequential injection of the carriers

Mixed state quantumcomputation can perform certain tasks which are believed to be efficiently intractable on a classical computer. For a specific model of mixed state quantumcomputation, namely, {\\it deterministic quantumcomputation with a single qubit} (DQC1), recent investigations suggest that quantum correlations other than entanglement might be responsible for the power of DQC1 model. However, strictly speaking, the role of entanglement in this model of computation was not entirely clear. We provide conclusive evidence that there are instances where quantum entanglement is not present in any part of this model, nevertheless we have advantage over classical computation. This establishes the fact that quantum dissonance (quantum correlations) present in fully separable states provide power to DQC1 model.

Quantumcomputations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantumcomputing, where the graphical syntax directly captures the structure of the entangled states used to represent computations, and show that the notion of information flow within the entangled states gives rise to rewriting strategies for proving the correctness of quantum programs.

Quantumcomputations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantumcomputing, where the graphical syntax directly captures the structure of the entangled states used to represent computations, and show that the notion of information flow within the entangled states gives rise to rewriting strategies for proving the correctness of quantum programs.

We improve the upper bound on the minimal resources required for measurement-based quantumcomputation. Minimizing the resources required for this model is a key issue for experimental realization of a quantumcomputer based on projective measurements. This new upper bound allows also to reply in the negative to the open question about the existence of a trade-off between observable and ancillary qubits in measurement-based quantumcomputation.

We are implementing a new platform for adiabatic quantumcomputation (AQC)footnotetext E. Farhi, et al. Science 292, 472 (2000) based on trapped neutral atoms whose coupling is mediated by the dipole-dipole interactions of Rydberg states. Ground state cesium atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism,footnotetextS. Rolston, et al. Phys. Rev. A, 82, 033412 (2010)^,footnotetextT. Keating, et al. arXiv:1209.4112 (2012) thereby providing the requisite entangling interactions. As a benchmark we study a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model.[4pt] In collaboration with Lambert Parazzoli, Sandia National Laboratories; Aaron Hankin, Center for Quantum Information and Control (CQuIC), University of New Mexico; James Chin-Wen Chou, Yuan-Yu Jau, Peter Schwindt, Cort Johnson, and George Burns, Sandia National Laboratories; Tyler Keating, Krittika Goyal, and Ivan Deutsch, Center for Quantum Information and Control (CQuIC), University of New Mexico; and Andrew Landahl, Sandia National Laboratories.

The quest for quantumcomputers is motivated by their potential for solving\\u000aproblems that defy existing, classical, computers. The theory of computational\\u000acomplexity, one of the crown jewels of computer science, provides a rigorous\\u000aframework for classifying the hardness of problems according to the\\u000acomputational resources, most notably time, needed to solve them. Its extension\\u000ato quantumcomputers allows the

C. R. Laumann; R. Moessner; A. Scardicchio; S. L. Sondhi

In recent years, surface codes have become the preferred method for quantum error correction in large scale computational and communications architectures. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfa...

The Center for Computational Structures Technology (CST) is intended to serve as a focal point for the diverse CST research activities. The CST activities include the use of numerical simulation and artificial intelligence methods in modeling, analysis, sensitivity studies, and optimization of flight-vehicle structures. The Center is located at NASA Langley and is an integral part of the School of Engineering and Applied Science of the University of Virginia. The key elements of the Center are: (1) conducting innovative research on advanced topics of CST; (2) acting as pathfinder by demonstrating to the research community what can be done (high-potential, high-risk research); (3) strong collaboration with NASA scientists and researchers from universities and other government laboratories; and (4) rapid dissemination of CST to industry, through integration of industrial personnel into the ongoing research efforts.

In this presentation are discussed some problems, relevant with application of information technologies in nano-scale systems and devices. Some methods already developed in quantum information technologies may be very useful here. Here are considered two illustrative models: representation of data by quantum bits and transfer of signals in quantum wires.

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 $k$ graphs as input, alignment algorithms use topological information to assign a similarity score to each $k$-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 quantumcomputers. We characterize the accuracy and performance of our method, and show that it can deliver exponential speedups over conventional (non-quantum) methods.

Because the graphic industry demands graduates with computer skills, art students want college programs that include complex computertechnologies. However, students can produce good computer art only if they have mastered traditional drawing and design skills. Discusses designing an art curriculum including both technology and traditional course…

Quantum information processing provides novel methods for pumping heat and refrigerating photons. Devices that obtain and manipulate information at the quantum level can function as quantum 'Maxwell's demons' to cool systems in ways that liquid helium cannot.

The development and theory of an experiment to investigate quantumcomputation with trapped calcium ions is described. The ion trap, laser and ion requirements are determined, and the parameters required for quantum logic operations as well as simple quantum factoring are described.

R. J. Hughes; D. F. V. James; J. J. Gomez; M. S. Gulley; M. H. Holzscheiter; P. G. Kwiat; S. K. Lamoreaux; C. G. Peterson; V. D. Sandberg; M. M. Schauer; C. M. Simmons; C. E. Thorburn; D. Tupa; P. Z. Wang; A. G. White

We demonstrate that locally connected networks of machines that have primitive learning capabilities can be used to perform a deterministic, event-based simulation of quantumcomputation. We present simulation results for basic quantum operations such as the Hadamard and the controlled-NOT gate, and for seven-qubit quantum networks that implement Shor's numbering factoring algorithm.

A quantumcomputer can solve hard problems - such as prime factoring, database searching, and quantum simulation - at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-cycled entangling gates. The gate fidelity requirements are modest: The per-step fidelity threshold is only about 99%. Here, we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity up to 99.4%. This places Josephson quantumcomputing at the fault-tolerant threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger (GHZ) state using the complete circuit and full set of gates. The results demonstrate that Josephson quantumcomputing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

R. Barends; J. Kelly; A. Megrant; A. Veitia; D. Sank; E. Jeffrey; T. C. White; J. Mutus; A. G. Fowler; B. Campbell; Y. Chen; Z. Chen; B. Chiaro; A. Dunsworth; C. Neill; P. O`Malley; P. Roushan; A. Vainsencher; J. Wenner; A. N. Korotkov; A. N. Cleland; John M. Martinis

In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantumcomputation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.

Clare Horsman; Austin G. Fowler; Simon Devitt; Rodney Van Meter

In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantumcomputation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.

Horsman, Clare; Fowler, Austin G.; Devitt, Simon; Van Meter, Rodney

We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We conclude by noting that the lambda-q calculus may be strictly stronger than quantumcomputers because NP-complete problems such as satisfiability are efficiently solvable in the lambda-q calculus but there is a widespread doubt that they are efficiently solvable by quantumcomputers.

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 quantumcomputing. Here, we suggest a circuit-QED approach to nonlinear optics quantumcomputing 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.

Quantumcomputation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantumcomputation 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. PMID:23471401

Describes the nature of modern general-purpose computer systems, including hardware, semiconductor electronics, microprocessors, computer architecture, input output technology, and system control programs. Seven suggested readings are cited. (FM)

Rev. 08/09 GEORGIA INSTITUTE OF TECHNOLOGY College of ComputingComputational Science ______________________________________________ Date _________________________________ List Course Number, Course Title, and Credit Hours by ascending ________________________________________________________________________________________ ___________________________________________________________________________________________________________ Projected Date of Graduation ________________________ _____________________________________________ Student

Cloud computing, a term whose origins have been in existence for more than a decade, has come into fruition due to technological capabilities and marketplace demands. Cloud computing can be defined as a scalable and flexible ...

In this paper we discuss a model of quantumcomputer in which a state is an operator of density matrix and gates are general quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of 4^n-dimensional operator Hilbert space (Liouville space). It allows to use a quantumcomputer model with four-valued logic. The gates of this model are general superoperators which act on n-ququat state. Ququat is a quantum state in a four-dimensional (operator) Hilbert space. Unitary two-valued logic gates and quantum operations for an n-qubit open system are considered as four-valued logic gates acting on n-ququat. We discuss properties of quantum four-valued logic gates. In the paper we study universality for quantum four-valued logic gates.

The simulation of quantum many-body systems is a notoriously hard problem in condensed matter physics, but it could easily be handled by a quantumcomputer [4,1]. There is however one catch: while a quantumcomputer can naturally implement the dynamics of a quantum system --- i.e. solve Schr"odinger's equation --- there was until now no general method to initialize the computer in a low-energy state of the simulated system. We present a quantum algorithm [5] that can prepare the ground state and thermal states of a quantum many-body system in a time proportional to the square-root of its Hilbert space dimension. This is the same scaling as required by the best known algorithm to prepare the ground state of a classical many-body system on a quantumcomputer [3,2]. This provides strong evidence that for a quantumcomputer, preparing the ground state of a quantum system is in the worst case no more difficult than preparing the ground state of a classical system. 1 D. Aharonov and A. Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge, Proc. 35th Annual ACM Symp. on Theo. Comp., (2003), p. 20. F. Barahona, On the computational complexity of ising spin glass models, J. Phys. A. Math. Gen., 15 (1982), p. 3241. C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknessess of quantumcomputing, SIAM J. Comput., 26 (1997), pp. 1510--1523, quant-ph/9701001. S. Lloyd, Universal quantum simulators, Science, 273 (1996), pp. 1073--1078. D. Poulin and P. Wocjan, Preparing ground states of quantum many-body systems on a quantumcomputer, 2008, arXiv:0809.2705.

Measurement-based one-way quantumcomputation using cluster states as resources provides an efficient model to perform computation and information processing of quantum codes. Arbitrary Gaussian quantumcomputation can be implemented sufficiently by long single-mode and two-mode gate sequences. However, continuous variable gate sequences have not been realized so far due to an absence of cluster states larger than four submodes. Here we present the first continuous variable gate sequence consisting of a single-mode squeezing gate and a two-mode controlled-phase gate based on a six-mode cluster state. The quantum property of this gate sequence is confirmed by the fidelities and the quantum entanglement of two output modes, which depend on both the squeezing and controlled-phase gates. The experiment demonstrates the feasibility of implementing Gaussian quantumcomputation by means of accessible gate sequences.

Universal quantum logic gates are important elements for a quantumcomputer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantumcomputations 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

Universal quantum logic gates are important elements for a quantumcomputer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantumcomputations 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.

In their article, "Is the Brain a QuantumComputer,?" Litt, Eliasmith, Kroon, Weinstein, and Thagard (2006) criticize the Penrose-Hameroff "Orch OR" quantumcomputational 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…

A computer is generally considered to be a universalcomputational device; i.e., it is believed able to simulateany physical computational device with a increase in computationtime of at most a polynomial factor. It is notclear whether this is still true when quantum mechanics istaken into consideration. Several researchers, starting withDavid Deutsch, have developed models for quantum mechanicalcomputers and have investigated their