195 research outputs found
Dynamical fidelity of a solid-state quantum computation
In this paper we analyze the dynamics in a spin-model of quantum computer.
Main attention is paid to the dynamical fidelity (associated with dynamical
errors) of an algorithm that allows to create an entangled state for remote
qubits. We show that in the regime of selective resonant excitations of qubits
there is no any danger of quantum chaos. Moreover, in this regime a modified
perturbation theory gives an adequate description of the dynamics of the
system. Our approach allows to explicitly describe all peculiarities of the
evolution of the system under time-dependent pulses corresponding to a quantum
protocol. Specifically, we analyze, both analytically and numerically, how the
fidelity decreases in dependence on the model parameters.Comment: 9 pages, 6 figures, submitted to PR
General-Purpose Parallel Simulator for Quantum Computing
With current technologies, it seems to be very difficult to implement quantum
computers with many qubits. It is therefore of importance to simulate quantum
algorithms and circuits on the existing computers. However, for a large-size
problem, the simulation often requires more computational power than is
available from sequential processing. Therefore, the simulation methods using
parallel processing are required.
We have developed a general-purpose simulator for quantum computing on the
parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We
have performed Shor's factorization and Grover's database search by using the
simulator, and we analyzed robustness of the corresponding quantum circuits in
the presence of decoherence and operational errors. The corresponding results,
statistics and analyses are presented.Comment: 15 pages, 15 figure
Solid-State Nuclear Spin Quantum Computer Based on Magnetic Resonance Force Microscopy
We propose a nuclear spin quantum computer based on magnetic resonance force
microscopy (MRFM). It is shown that an MRFM single-electron spin measurement
provides three essential requirements for quantum computation in solids: (a)
preparation of the ground state, (b) one- and two- qubit quantum logic gates,
and (c) a measurement of the final state. The proposed quantum computer can
operate at temperatures up to 1K.Comment: 16 pages, 5 figure
A Quantum Full Adder for a Scalable Nuclear Spin Quantum Computer
We demonstrate a strategy for implementation a quantum full adder in a spin
chain quantum computer. As an example, we simulate a quantum full adder in a
chain containing 201 spins. Our simulations also demonstrate how one can
minimize errors generated by non-resonant effects.Comment: 15 pages RevTex including 2 figure
Perturbation Theory for Quantum Computation with Large Number of Qubits
We describe a new and consistent perturbation theory for solid-state quantum
computation with many qubits. The errors in the implementation of simple
quantum logic operations caused by non-resonant transitions are estimated. We
verify our perturbation approach using exact numerical solution for relatively
small (L=10) number of qubits. A preferred range of parameters is found in
which the errors in processing quantum information are small. Our results are
needed for experimental testing of scalable solid-state quantum computers.Comment: 8 pages RevTex including 2 figure
Quantum Breaking Time Scaling in the Superdiffusive Dynamics
We show that the breaking time of quantum-classical correspondence depends on
the type of kinetics and the dominant origin of stickiness. For sticky dynamics
of quantum kicked rotor, when the hierarchical set of islands corresponds to
the accelerator mode, we demonstrate by simulation that the breaking time
scales as with the transport exponent
that corresponds to superdiffusive dynamics. We discuss also other
possibilities for the breaking time scaling and transition to the logarithmic
one with respect to
Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem of Electron Localization
When an ion confined in a linear ion trap interacts with a coherent laser
field, the internal degrees of freedom, related to the electron transitions,
couple to the vibrational degree of freedom of the ion. As a result of this
interaction, quantum dynamics of the vibrational degree of freedom becomes
complicated, and in some ranges of parameters even chaotic. We analyze the
vibrational ion dynamics using a formal analogy with the solid-state problem of
electron localization. In particular, we show how the resonant approximation
used in analysis of the ion dynamics, leads to a transition from a
two-dimensional (2D) to a one-dimensional problem (1D) of electron
localization. The localization length in the solid-state problem is estimated
in cases of weak and strong interaction between the cites of the 2D cell by
using the methods of resonance perturbation theory, common in analysis of 1D
time-dependent dynamical systems.Comment: 18 pages RevTe
Single-Pulse Preparation of the Uniform Superpositional State used in Quantum Algorithms
We examine a single-pulse preparation of the uniform superpositional wave
function, which includes all basis states, in a spin quantum computer. The
effective energy spectrum and the errors generated by this pulse are studied in
detail. We show that, in spite of the finite width of the energy spectrum
bands, amplitude and phase errors can be made reasonably small.Comment: RevTex, 5 pages, 7 eps figure
Quantum computation in a Ising spin chain taking into account second neighbor couplings
We consider the realization of a quantum computer in a chain of nuclear spins
coupled by an Ising interaction. Quantum algorithms can be performed with the
help of appropriate radio-frequency pulses. In addition to the standard
nearest-neighbor Ising coupling, we also allow for a second neighbor coupling.
It is shown, how to apply the 2\pi k method in this more general setting, where
the additional coupling eventually allows to save a few pulses. We illustrate
our results with two numerical simulations: the Shor prime factorization of the
number 4 and the teleportation of a qubit along a chain of 3 qubits. In both
cases, the optimal Rabi frequency (to suppress non-resonant effects) depends
primarily on the strength of the second neighbor interaction.Comment: 19 pages, 6 figure
Two Qubit Quantum Computing in a Projected Subspace
A formulation for performing quantum computing in a projected subspace is
presented, based on the subdynamical kinetic equation (SKE) for an open quantum
system. The eigenvectors of the kinetic equation are shown to remain invariant
before and after interaction with the environment. However, the eigenvalues in
the projected subspace exhibit a type of phase shift to the evolutionary
states. This phase shift does not destroy the decoherence-free (DF) property of
the subspace because the associated fidelity is 1. This permits a universal
formalism to be presented - the eigenprojectors of the free part of the
Hamiltonian for the system and bath may be used to construct a DF projected
subspace based on the SKE. To eliminate possible phase or unitary errors
induced by the change in the eigenvalues, a cancellation technique is proposed,
using the adjustment of the coupling time, and applied to a two qubit computing
system. A general criteria for constructing a DF projected subspace from the
SKE is discussed. Finally, a proposal for using triangulation to realize a
decoherence-free subsystem based on SKE is presented. The concrete formulation
for a two-qubit model is given exactly. Our approach is novel and general, and
appears applicable to any type of decoherence. Key Words: Quantum Computing,
Decoherence, Subspace, Open System PACS number: 03.67.Lx,33.25.+k,.76.60.-kComment: 24 pages. accepted by Phys. Rev.
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