Showing papers on "Quantum computer published in 1995"

Scheme for reducing decoherence in quantum computer memory

Abstract: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits---techniques that may become the key to practical quantum computing on a large scale.

Quantum Computations with Cold Trapped Ions.

Abstract: A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams. Quantum gates involving any pair, triplet, or subset of ions can be realized by coupling the ions through the collective quantized motion. In this system decoherence is negligible, and the measurement (readout of the quantum register) can be carried out with a high efficiency.

Demonstration of a Fundamental Quantum Logic Gate

Abstract: We demonstrate the operation of a two-bit "controlled-NOT" quantum logic gate, which, in conjunction with simple single-bit operations, forms a universal quantum logic gate for quantum computation. The two quantum bits are stored in the internal and external degrees of freedom of a single trapped atom, which is first laser cooled to the zero-point energy. Decoherence effects are identified for the operation, and the possibility of extending the system to more qubits appears promising.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Abstract: A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Decoherence, Continuous Observation, and Quantum Computing: A Cavity QED Model

Abstract: We use the theory of continuous measurement to analyze the effects of decoherence on a realistic model of a quantum computer based on cavity QED. We show how decoherence affects the computation, and methods to prevent it.

Maintaining coherence in quantum computers

Abstract: The effects of the inevitable coupling to external degrees of freedom of a quantum computer are examined. It is found that for quantum calculations (in which the maintenance of coherence over a large number of states is important), not only must the coupling be small, but the time taken in the quantum calculation must be less than the thermal time scale \ensuremath{\Elzxh}/${\mathit{k}}_{\mathit{B}}$T. For longer times the condition on the strength of the coupling to the external world becomes much more stringent.

Quantum measurements and the Abelian Stabilizer Problem

Abstract: We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor’s results [7]. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary finite Abelian group. The paper also contains a rather detailed introduction to the theory of quantum computation.

Universality in Quantum Computation

Abstract: We show that in quantum computation 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.

Simple quantum computer.

Abstract: We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail quantum-bit representation as a simple form of error correction, our machine can tolerate some amount of decoherence and still give the correct result with high probability. The design that we employ also demonstrates a signature for quantum parallelism which unambiguously distinguishes the desired quantum behavior from the merely classical. The experimental demonstration of our proposal using quantum optical components calls for the development of several key technologies common to single photonics.

Quantum tunneling of magnetization - QTM '94

Abstract: Preface. I: General Introduction. Macroscopic Quantum Effects in Magnetic Systems: An Overview A.J. Leggett. II: Particles (Theory). Theory of Mesoscopic Quantum Tunneling in Magnetism: A WKB Approach J.L. van Hemmen, A. Sutoe. Quantum Spin-Tunneling: A Path Integral Approach R. Schilling. Quantum Tunneling in Small Particles E.M. Chudnovsky. Macroscopic Quantum Tunneling in Ferromagnets and Antiferromagnets H. Simanjuntak. Monte-Carlo Simulations on Reversal Magnetization of Small Clusters P.A. Serena, N. Garcia. III: QTM in Magnetic Relaxation (Experiment). Quantum Tunneling of Magnetization J. Tejada, X. Zhang. Relaxation and Mesoscopic Quantum Tunneling of Magnetization in Amorphous Rare-Earth Alloys J.I. Arnaudas, et. al. Linear Response and Thermal Equilibrium Noise of Magnetic Materials at Low Temperature: Logarithmic Relaxation, VF Noise, Activation and Tunnelling S. Vitale, et al. AC Susceptibility Relaxation Studies on a Manganese Organic Cluster Compound: MN12Ac M.A. Novak, R. Sessoli. Evidence for Quantum Tunnelling of the Magnetization in Mn12Ac C. Paulsen, J.-G. Park. Acoustic and Magnetic Properties of Rare-Earth-Ion-Doped Glasses: Elastic and Magnetic Tunnelling States G. Bellessa, et al. DC- Squid Magnetization Measurements of Single Magnetic Particles W. Wernsdorfer, et al. IV: Macroscopic Coherence of Magnetization (Experiment). Macroscopic Quantum Tunnelling of Magnetization in Natural and Artificially Engineered Ferritin S. Gider, D.D. Awschalom. V: Quantum Tunnelling of Domain Walls (Experiment). Domain Wall Tunnelling in a One Dimensional Ferromagnet K. Hong, N. Giordano. VI: Dissipation inQTM (Theory). Nuclear Spin Dissipation in Magnetic Macroscopic Quantum Phenomena A. Garg. Macroscopic Quantum Tunnelling and Dissipation of Domain Wall in Ferromagnetic Metals G. Tatara, H. Fukuyama. The Collective Coordinate Method and Bloch Wall Motion A.O. Caldeira. VII: Spin Parity Effects in QTM (Theory). Spin Parity Effects and Macroscopic Quantum Coherence of Bloch Walls H.-B. Braun, D. Loss. Spin Environments and the Suppression of Quantum Coherence N.V. Prokofev, P.C.E. Stamp. Unconventional Environments P.C.E. Stamp. VIII: QTM & Electron-Electron Interactions (Theory). Particle Tunneling and Magnetization Tunneling in the Presence of Electron-Electron Interaction J.M.P. Carmelo, F. Guinea. IX: Comments on Theory and Experiment. On the Search for Quantum Tunneling of Magnetization L. Gunther. X: Macroscopic Quantum Tunneling in Superconductors (Experiment). Quantum Tunneling of Vortices in High-Tc Superconductors: Magnetic Relaxation Experiments in T1BaCACuO Compounds D. Fiorani, et al. Crossover from Thermal to Quantum Regime in Vortex Motion in Conventional Type II Superconductors: Slow Magnetic Relaxation and Abrupt Flux Jumps M. Uehara. Flux Motion by Quantum Tunneling A.C. Mota. Macroscopic Quantum Tunneling in Long Josephson Junctions O.G. Symko. XI: Quantum Computers (Theory). Quantum Computing and Spin Physics D.P. DiVincenzo. XII: Scientific Summary of Workshop. B. Barbara, L. Gunther, A.J. Leggett. Index.

Quantum Computers, Factoring, and Decoherence

Abstract: It is known that quantum computers can dramatically speed up the task of finding factors of large numbers, a problem of practical significance for cryptographic applications. Factors of an L -digit number can be found in ∼ L 2 time [compared to ∼exp( L 1/3 ) time] by a quantum computer, which simultaneously follows all paths corresponding to distinct classical inputs, obtaining the solution from the coherent quantum interference of the alternatives. Here it is shown how the decoherence process degrades the interference pattern that emerges from the quantum factoring algorithm. For a quantum computer performing logical operations, an exponential decay of quantum coherence is inevitable. However, even in the presence of exponential decoherence, quantum computation can be useful as long as a sufficiently low decoherence rate can be achieved to allow meaningful results to be extracted from the calculation.

A Universal Two-Bit Gate for Quantum Computation

Abstract: We prove the existence of a class of two-input, two-output gates any one of which is universal for quantum computation. This is done by explicitly constructing the three-bit gate introduced by Deutsch (Proc. R. Soc. Lond. A 425, 73 (1989)) as a network consisting of replicas of a single two-bit gate.

On one-dimensional quantum cellular automata

Abstract: Since Richard Feynman introduced the notion of quantum computation in 1982, various models of "quantum computers" have been proposed (R. Feynman, 1992). These models include quantum Turing machines and quantum circuits. We define another quantum computational model, one dimensional quantum cellular automata, and demonstrate that any quantum Turing machine can be efficiently simulated by a one dimensional quantum cellular automaton with constant slowdown. This can be accomplished by consideration of a restricted class of one dimensional quantum cellular automata called one dimensional partitioned quantum cellular automata. We also show that any one dimensional partitioned quantum cellular automaton can be simulated by a quantum Turing machine with linear slowdown, but the problem of efficiently simulating an arbitrary one dimensional quantum cellular automaton with a quantum Turing machine is left open. From this discussion, some interesting facts concerning these models are easily deduced.

Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)

Abstract: Recently there has been a great deal of interest in the power of "Quantum Computers" [4, 15, 18]. The driving force is the recent beautiful result of Shor that shows that discrete log and factoring are solvable in random quantum polynomial time [15]. We use a method similar to Shor's to obtain a general theorem about quantum polynomial time. We show that any cryptosystem based on what we refer to as a 'hidden linear form' can be broken in quantum polynomial time. Our results imply that the discrete log problem is doable in quantum polynomial time over any group including Galois fields and elliptic curves. Finally, we introduce the notion of 'junk bits' which are helpful when performing classical computations that are not injective.

Quantum Cryptanalysis of Hidden Linear Functions

Abstract: Recently there has been a great deal of interest in the power of “Quantum Computers” [4, 15, 18]. The driving force is the recent beautiful result of Shor that shows that discrete log and factoring are solvable in random quantum polynomial time [15]. We use a method similar to Shor’s to obtain a general theorem about quantum polynomial time. We show that any cryptosystem based on what we refer to as a ‘hidden linear form’ can be broken in quantum polynomial time. Our results imply that the discrete log problem is doable in quantum polynomial time over any group including Galois fields and elliptic curves. Finally, we introduce the notion of ‘junk bits’ which are helpful when performing classical computations that are not injective.

Learning DNF over the uniform distribution using a quantum example oracle

Abstract: : We generalize the notion of PAC learning from an example oracle to a notion of efficient learning on a quantum computer using a quantum example oracle. This quantum example oracle is a natural extension of the traditional PAC example oracle, and it immediately follows that all PAC-learnable function classes are learnable in the quantum model. Furthermore, we obtain positive quantum learning results for classes that are not known to be PAC learnable. Specifically, we show that DNF is efficiently learnable with respect to the uniform distribution by a quantum algorithm using a quantum example oracle. While it was already known that DNF is uniform-learnable using a membership oracle, the quantum example oracle is provably less powerful than a membership oracle. We also generalize the notion of classification noise to the quantum setting and show that the quantum DNF algorithm learns even in the presence of such noise. This result contrasts with a recent negative result for DNF in the statistical query model of learning from noisy data. Quantum computation, Computational learning theory DNF, (Disjunctive normal form), Quantum example oracle, Classification noise, Statistical query learning

Transparent potentials at fixed energy in dimension two: Fixed energy dispersion relations for the fast decaying potentials

Abstract: For the two-dimensional Schrodinger equation $$[ - \Delta + v(x)]\psi = E\psi , x \in \mathbb{R}^2 , E = E_{fixed} > 0 (*)$$ at a fixed positive energy with a fast decaying at infinity potentialv(x) dispersion relations on the scattering data are given. Under “small norm” assumption using these dispersion relations we give (without a complete proof of sufficiency) a characterization of scattering data for the potentials from the Schwartz classS=C∞(∞)(ℝ2). For the potentials with zero scattering amplitude at a fixed energyEfixed (transparent potentials) we give a complete proof of this characterization. As a consequence we construct a family (parametrized by a function of one variable) of two-dimensional spherically-symmetric real potentials from the Schwartz classS transparent at a given energy. For the two-dimensional case (without assumption that the potential is small) we show that there are no nonzero real exponentially decreasing, at infinity, potentials transparent at a fixed energy. For any dimension greater or equal to 1 we prove that there are no nonzero real potentials with zero forward scattering amplitude at an energy interval. We show that KdV-type equations in dimension 2+1 related with the scattering problem (*) (the Novikov-Veselov equations) do not preserve, in general, these dispersion relations starting from the second one. As a corollary these equations do not preserve, in general, the decay rate faster than |x|−3 for initial data from the Schwartz class.

Event enhanced quantum theory and piecewise deterministic dynamics

Abstract: The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave-function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID-tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment-induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.

On diagonalization in map(m,g)

Abstract: Motivated by some questions in the path integral approach to (topological) gauge theories, we are led to address the following question: given a smooth map from a manifoldM to a compact groupG, is it possible to smoothly “diagonalize” it, i.e. conjugate it into a map to a maximal torusT ofG?

Method for reducing decoherence in quantum computer memory

Abstract: The present invention is a methodology for reducing the rate of decoherence in quantum memory. A procedure is disclosed for storing an arbitrary state of n qubits using expanded groupings of these n qubits in a decoherence-resistant manner. Each qubit of the original n qubits is mapped into a grouping of qubits, and the process will reconstruct the original superposition simultaneously correcting both bit and phase errors if at most one qubit decoheres in each of these groups of qubits. In one preferred embodiment of the present invention, a method is disclosed for decoding a set of N'(2m+1) qubits, wherein the set of N'(2m+1) exposed qubits has undergone possible decoherence from a superposition of states due to exposure to an environment. The method comprises the steps of decoding the set of N'(2m+1) exposed qubits using a repetition decoder to yield a set of N' decoded qubits, applying a first transformation to each decoded qubit in the set of said N' decoded qubits to yield a set of N' transformed decoded qubits, wherein the first transformation is represented as a unitary matrix comprising matrix entries of equal absolute value, and decoding the set of N' transformed decoded qubits using an error correcting decoder to yield a set of n decoded qubits.

Separation of variables in the classicalSL(N) magnetic chain

Abstract: We propose an elementary construction of separation of variables for the classical integrableSL(N) magnetic chain

Universality in Quantum Computation

Abstract: We show that in quantum computation 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.

Quantum and biological computation

Abstract: Ubiquitous internal measurement of material origin and conservation laws, when combined together, uphold biological computation as a specific mode of quantum computation. Internal measurement supplemented by conservation laws can reproduce quantum mechanics or the uncertainty principle in particular. Furthermore, biological computation founded upon internal measurement provides an irreversible enhancement of organization and quantum coherency through non-algorithmic and non-programmable procedures of generating variations in accordance with the operation of the uncertainty principle.

A quantum jump in computer science

Abstract: Classical and quantum information are very different. Together they can perform feats that neither could achieve alone. These include quantum computing, quantum cryptography and quantum teleportation. This paper surveys some of the most striking new applications of quantum mechanics to computer science. Some of these applications are still theoretical but others have been implemented.

On universal Vassiliev invariants

Abstract: Using properties of ordered exponentials and the definition of the Drinfeld associator as a monodromy operator for the Knizhnik-Zamolodchikov equations, we prove that the analytic and the combinatorial definitions of the universal Vassiliev invariants of links are equivalent.

Quantum Error Correction by Coding

Abstract: Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We propose a new technique based on the use of coding in order to detect and correct errors due to imperfect transmission lines in quantum cryptography or memories in quantum computers. We give a particular example of how to detect a decohered qubit in order to transmit or preserve with high fidelity the original qubit.

Mesoscopic coherences in cavity QED

Abstract: The principles of cavity QED experiments are described, in which fields exhibiting coherences between different mesoscopic states are generated and studied. These experiments, based on the Ramsey method of atomic interferometry, are presently under way at Ecole Normale Superieure, Paris. They will constitute tests of the quantum measurement theory and could open the way to interesting applications in quantum computing and cryptology.

Molecular quantum computer of neuron

Abstract: Living cells are controlled by quantum regulators in which the price of action of elementary operations approaches Planck's constant. The description of such systems is based on four principles: (1) minimal price of action principle for control; (2) principle of optimality; (3) minimum irreversibility principle; and (4) the principle of causality.

Physics and the New Computation

Abstract: New computation devices increasingly depend on particular physical properties rather than on logical organization alone as used to be the case in conventional technologies. This has impact on the synthesis and analysis of algorithms and the computation models on which they are to run. Therefore, scientists working in these areas will have to understand and apply physical law in their considerations. We discuss three cases in some detail: interconnect length and communication in massive multicomputers which depend on the geometry of space and speed of light; energy dissipation and reversible (adiabatic) computation which depend on thermodynamics; and quantum coherent parallel computing which depends on quantum mechanics.