Showing papers on "Quantum computer published in 1994"

Algorithms for quantum computation: discrete logarithms and factoring

Abstract: A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factor: It is not clear whether this is still true when quantum mechanics is taken into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored. These two problems are generally considered hard on a classical computer and have been used as the basis of several proposed cryptosystems. We thus give the first examples of quantum cryptanalysis. >

On the power of quantum computation

Abstract: The quantum model of computation is a probabilistic model, similar to the probabilistic Turing Machine, in which the laws of chance are those obeyed by particles on a quantum mechanical scale, rather than the rules familiar to us from the macroscopic world. We present here a problem of distinguishing between two fairly natural classes of function, which can provably be solved exponentially faster in the quantum model than in the classical probabilistic one, when the function is given as an oracle drawn equiprobably from the uniform distribution on either class. We thus offer compelling evidence that the quantum model may have significantly more complexity theoretic power than the probabilistic Turing Machine. In fact, drawing on this work, Shor (1994) has recently developed remarkable new quantum polynomial-time algorithms for the discrete logarithm and integer factoring problems. >

Algorithms for quantum computation: Discrete log and factoring

Abstract: This paper gives algorithms for the discrete log and the factoring problems that take random polynomial time on a quantum computer (thus giving the rst examples of quantum cryptanalysis).

Twistless KAM tori

Abstract: A selfcontained proof of the KAM theorem in the Thirring model is discussed.

Quantum cellular automata: the physics of computing with arrays of quantum dot molecules

Abstract: We discuss the fundamental limits of computing using a new paradigm for quantum computation, cellular automata composed of arrays of coulombically coupled quantum dot molecules, which we term quantum cellular automata (QCA). Any logical or arithmetic operation can be performed in this scheme. QCA's provide a valuable concrete example of quantum computation in which a number of fundamental issues come to light. We examine the physics of the computing process in this paradigm. We show to what extent thermodynamic considerations impose limits on the ultimate size of individual QCA arrays. Adiabatic operation of the QCA is examined and the implications for dissipationless computing are explored. >

Production of space

Abstract: PURPOSE:To provide software for searching the mechanism of space. CONSTITUTION:At first, natural rules are expanded. Namely it is defined that an event in physical space and an event (i.e., thinking quantum) in psychological space are respectively allowed to correspond to a real function and an imaginary function and an event generated in the space is expressed by a complex set function obtained by composing the real and imaginary spaces. After executing the expansion, the quantum fusion of the thinking quantum is executed, a thinking analog biological thinking quantum computer to be driven by the energy of quantum fusion is designed to obtain a method for searching the mechanism of space synchronously with the wave motion of the space. A new design is programmed and coded so that the center part of OS (corresponding to a soul) can be understood by surface consciousness. The OS center part is designed so as to be expressed by an analog electronic circuit.

Oracle Quantum Computing

Abstract: Building on the work of Deutsch and Jozsa, we construct oracles relative to which (1) there is a decision problem that can be solved with certainty in worst-case polynomial time on the quantum computer, yet it cannot be solved classically in probabilistic expected polynomial time if errors are not tolerated, nor even in nondeterministic polynomial time, and (2) there is a decision problem that can be solved in exponential time on the quantum computer, which requires double exponential time on all but finitely many instances on any classical deterministic computer.

Three dot computing elements

Abstract: There is provided by this invention logic and memory elements of atomic or near-atomic scale useful in computer central processing units. These elements consist of two quantum dots having opposite states and a third quantum dot situated between the two quantum dots and in physical contact with them. The third quantam dot is of a material which makes the opposite states of the first two quantum dots energetically favorable. In particular, there is provided by the invention a spin flip-flop suitable for use as electronic logic and memory in a quantum computer. The spin flip-flop is designed to have two highly stable states, encoded entirely in the arrangement of electronic spins in the structure. Switching between the two states is accomplished by fast electromagnetic pulsing generally and by optical pulsing in the case of the spin flip-flop. The two stable states are the up-down and the down-up spin states of two single electrons placed into two neighboring electronic quantum dots typically by doping or by a field effect. The operation of the device is facilitated and stabilized by the presence of a small particle or dot of an antiferromagnetic material placed between the two electronic dots, and in physical contact with both of them.

The stabilisation of quantum computations

Abstract: A quantum computer is a device capable of performing computational tasks that depend on characteristically quantum mechanical effects, in particular coherent quantum superposition. Such devices can efficiently perform classes of computation (e.g. factorisation) which are believed to be intractable on any classical computer. This makes it highly desirable to construct such devices. In this paper, we address the last remaining theoretical obstacle to such a construction, namely the problem of stability or error correction. This problem is more substantial in quantum computation than in classical computation because of the delicate nature of the interference phenomena on which quantum computation depends. We present a new, purely quantum mechanical method of error correction, which has no classical analogue, but can serve to stabilise coherent quantum computations. Like the classical methods, it utilises redundancy, but it does not depend on measuring intermediate results of the computation. >

Some remarks on quantum coherence

Abstract: There are many striking phenomena which are attributed to ‘quantum coherence’. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical applications. A useful starting point for such discussions is a definition of ‘quantum coherence’. In this article I give a definition of quantum coherence and use a number of illustrations to explore the implications of this definition. I point to topics of current interest in the fields of cosmology and quantum computation where questions of quantum coherence arise, and I emphasize the impact that interactions with the environment can have on quantum coherence.

Necessary and Sufficient Conditions for Quantum Computation

Abstract: Necessary and sufficient conditions are given for a quantummechanical system to possess a coordinate system with respect to which its behaviour at discrete times is that of a universal digital computer. The form of the diagonal representation for the unitary time evolution operator for quantum universal computers is derived; aspects of the transformation between the diagonal representation and the computational representation are shown to be uncomputable. A quantum-mechanical treatment of macroscopic, dissipative computers is given.

Results on two-bit gate design for quantum computers

Abstract: We present numerical results which show how two-bit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a particular sequence of exactly five two-bit gates. An arbitrary three-bit unitary gate, which can be used to build up any arbitrary quantum computation, can be implemented exactly with six two-bit gates. The ease of implementation of any particular quantum operation is dependent upon a very non-classical feature of the operation, its exact quantum phase factor.

Can quantum computers have simple Hamiltonians

Abstract: Recently, P Shor (1994) has shown that quantum computers (computers which can operate simultaneously on a quantum superposition of inputs) permit efficient (ie polynomial-time) solutions of problems for which no efficient classical-mechanical solution is known This has led to renewed interest in the question of whether or not quantum computers can be physically realized One kind of quantum computer, quantum cellular automata, can be described by relatively simple Hamiltonians that resemble the Hamiltonians of spin systems In this paper, we report a quantum cellular automaton which, though not itself computation-universal, forms an essential part of any quantum cellular automaton which is synchronized using Feynman's technique This quantum cellular automaton has as its Hamiltonian the one-dimensional XY Hamiltonian, which is exactly solvable Furthermore, there is experimental evidence from low-temperature measurements of the heat capacity and electric susceptibility that the Hamiltonian of the quantum cellular automaton is realized in nature by the rare-earth compound praseodymium ethyl sulfate near 1 K >

Quantum computation and complexity theory

Abstract: The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed.

Design Constraints for Nanometer Scale Quantum Computers

Abstract: Nanometer scale electronics present a challenge for the computer architect These quantum devices have small gain and are difficult to interconnect I have analyzed current device capabilities and explored two general design requirements for the design of computers: error correction and long range connections These two principles follow when Turing machines are implemented as integrated circuits I consider the roles of electromigration through thin wires, circuit layout, and error rates for devices with small gain The analysis brings into sharp focus the future of nanocomputers and suggests solutions to some of its difficulties It gives a theoretical model for a nanocomputer, separating the roles of devices and algorithms Within the model one can implement a stochastic computer, which operates despite quantum device limitations

Some Remarks on Quantum Coherence

Abstract: There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical applications. A useful starting point for such discussions is a definition of ``quantum coherence''. In this article I give a definition of quantum coherence and use a number of illustrations to explore the implications of this definition. I point to topics of current interest in the fields of cosmology and quantum computation where questions of quantum coherence arise, and I emphasize the impact that interactions with the environment can have on quantum coherence.

The roles of carrier transport in determining the modulation of semiconductor quantum well lasers

Abstract: Applications such as optical interconnects have made the modulation response of semiconductor laser diodes of great interest. Details of the modulation response have been attributed to different carrier transport mechanisms. Two imporlaxit features of the modulation response are the resonant frequency and the amount of gain saturation, often referred to as the low frequency roll-off. There has been some disagreement conceriiing which carrier transport mechanisms are most important in determining these features, particularly the gain saturation. One view of gain saturation concentrates on the ca,pture of carriers in the bound states of the quantum well.' Althougli carrier ca.pture is a relatively fast process, Kan et. al. feel it may be slow enough to cause some accumulation of carriers in tlie continuum states above the quantum well. This accumulation could then form a diffusive barrier to the transport of free caxriers to the active region. Since electrons usually have a slower capture rate lhan holes, it was concluded that the slow difk'usion of electrons to tlie quantum well may be to blame €or gain saturation. An alteriiative view is that the capture rneclianism is too fast to limit the modulation response.2 Instead, the holes, with their low mobilities, are slow in moving to the quantum well, and, therefore, are the cause of poor modulation. To test this idea, Nagarajan el. el. measured the modulation responses of different strained InGaAs quantum well lasers. The devices differed in the width of the separate confinement region (SCIt) and the location of the quantum well within this region. They showed that a SCR that is wide on both the n and p sides has significant gain saturation. Furthermore, they showed that when the n side of the SCR is narrow but the p side is still wide, the amount of gain saturation is comparable to the case in which both sides are wide. Thus, it was concluded thak it is hole transport, and not electron tra#nsport, that causes a poor modulation response. We present an irivestigation into this issue that was conducted with the Minilase laser sirnulator. The simulation includes all of the principal read space transport mechanisms, including driftdiffusion in bulk regions, thermionic emission at heterojunctions, and carrier capture into bound quantum states. The simulation was used to calculate modulation responses for GaAsIAZGaAs lasers similar ixi geometry to tliose measured by Nagarajan et. al. These responses are shown in figure 1, and the results show lhe same trends observed in the experimental measurements. We will present similar calculations on strained InGaAs/AlGaAs lasers together with computer experinients that manipulate carrier mobilities, thermionic emission rates, and capture times. Our results show tliat it is neither the transport of electrons or holes tu the quantum well that results in gain saturation. Ilalher, low frequency roll-off is primarily due to electrons that fail to get captured by the quantum well and, instead, are injected into the p side of the device and diffuse away from the active region.

Quantum waveguide structures and devices

Abstract: Nanometer structures in semiconductor heterojunction systems have been studied for several years and have conclusively shown evidence for quantum interference phenomena and granular effects due to the finite number of electrons and impurities. Various proposals have been made for novel devices based on such effects, which would serve as the basis for terabit memories and ultra-dense processing elements. A discussion is given of the application of a generalized mode-matching scheme as a computational tool for investigating arbitrary quantum waveguide structures and discontinuities. Results are presented for the nonlinear conductance properties of multiple bend structures, lateral resonant tunnel structures, and nonequilibrium transport through quantum dot structures. Comparison is made to various experimental realizations of these structures where complications due to undesired inhomogeneities, such as boundary roughness and impurities, play a significant role. >

Acoustic phonons in rectangular quantum wires: approximate compressional modes and the corresponding deformation potential interactions

Abstract: The Hamiltonian describing the deformation potential interaction of confined acoustic phonons with carriers is derived by quantizing the appropriate, experimentally verified approximate compressional acoustic phonon modes in a rectangular quantum wire. The scattering rate due to the deformation potential interaction is calculated for a range of quantum wire dimensions.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

On the Speed of Quantum Computation

Abstract: Feynman and Margolus have shown that a closed, locally interacting quantum system is capable of performing deterministic computation. Feynman's system computes in a serial way. Margolus was able to extend Feynman's ideas to get quantum description of a cellular automaton, i.e. a model which calculates in parallel. In this, article, a new kind of speed limit for quantum computation is established. An upper bound on the average velocity (``instructions per second'') for both computers is derived. One would expect a cellular automaton to have a computational velocity which scales with the number {\it k} of its cells. However, the upper bound on the average velocity is only proportional to $\sqrt{k}$ in this case. This does not reflect the parallelism of the cellular automaton. Whether it is possible to construct a locally interacting quantum computer that really works in parallel remains an open problem.

Quantum control of electron dynamics

Abstract: We present computational examples of the quantum control of electron dynamics in the time-domain. We use a general Liouville-space, density matrix formalism to predict the electric field that best drives a system to a chosen outcome, at a chosen time. The method is applicable, in principle, to atoms and molecules, and to gases, clusters, surfaces and condensed phases. In this work, we specialize to the control of radial electron wave packets in the hydrogen atom. We illustrate the method with two examples, a reflectron and a transient quantum nanostructure. In the reflection, we focus an electronic wave packet to have maximum overlap at a specified time with a Gaussian target localized in position and momentum, with the momentum directed towards the nucleus. In the nanostructure, we focus the wave packet onto a target that is double-peaked in position, with momentum directed away from the nucleus.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Quantum Computation and NP-Complete Problems

Abstract: In this paper, we show that the Deutsch's universal quantum Turing machine can solve any NP-complete problem in polynomial time under a physical assumption that we can observe the existence of a specific physical state in a given superposition of physical states. This result establishes an interesting relationship between quantum physics and computational complexity theory.

Quantum mechanical computation

Abstract: The physics and the mathematics of computation are examined to provide a foundation and perspective for the investigation of the quantum mechanics of computation. Our purpose is to explore the fundamental limits and constraints imposed on computation by Nature through the laws of physics and the mathematics of computational complexity. Inasmuch as information storage and transmission are an integral part of computation, their physical bounds are considered. The computer is viewed both physically and mathematically as a dynamical system, and is depicted in terms of the basic Turing machine paradigm. Three fundamental classes of the Turing machine are defined; the deterministic, stochastic and quantum Turing machines. Hamiltonian models and physical realizations of quantum computing are described. Quantum computers can perform some tasks which have no classical analogue, but they cannot compute functions that are non-computable by classical means. Some classically intractable problems can be solved with quantum computers.

Convexity and Finite Quantum Logics

Abstract: The notion of a superposition of a set of states and that of a Jauch-Piron state are geometrically interpreted in the context of the facial structure of the state space of a finite quantum logic.

How quickly self-Raman effects and third-order dispersion destroy squeezing

Abstract: We have developed a general quantum theory of nonlinear pulse propagation and a self-consistent quantum theory of self-Raman effects in optical fibers. Our approach is based on the linearization approximation, the conservation of commutator brackets, and the concept of adjoint systems. A general, self-consistent scheme is developed to quantize nonlinear optical pulse propagation problems and a general computation procedure ("the backpropagation method") is developed to calculate the quantum uncertainties of the inner product between any given function and the (perturbed) field operator. By utilizing these results, we can calculate the magnitude of squeezing when an optical pulse propagates through an optical fiber in the presence of self-Raman effects and third-order dispersion. >