8,026 research outputs found
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 logic operations and creation of entanglement in a scalable superconducting quantum computer with long-range constant interaction between qubits
We consider a one-dimensional chain of many superconducting quantum
interference devices (SQUIDs), serving as charge qubits. Each SQUID is coupled
to its nearest neighbors through constant capacitances. We study the quantum
logic operations and implementation of entanglement in this system.
Arrays with two and three qubits are considered in detail. We show that the
creation of entanglement with an arbitrary number of qubits can be implemented,
without systematic errors, even when the coupling between qubits is not small.
A relatively large coupling constant allows one to increase the clock speed of
the quantum computer. We analytically and numerically demonstrate the creation
of the entanglement for this case, which can be a good test for the
experimental implementation of a relatively simple quantum protocol with many
qubits. We discuss a possible application of our approach for implementing
universal quantum logic for more complex algorithms by decreasing the coupling
constant and, correspondingly, decreasing the clock speed. The errors
introduced by the long-range interaction for the universal logic gates are
estimated analytically and calculated numerically. Our results can be useful
for experimental implementation of quantum algorithms using controlled magnetic
fluxes and gate voltages applied to the SQUIDs. The algorithms discussed in
this paper can be implemented using already existing technologies in
superconducting systems with constant inter-qubit coupling.Comment: 24 page
Non-Resonant Effects in Implementation of Quantum Shor Algorithm
We simulate Shor's algorithm on an Ising spin quantum computer. The influence
of non-resonant effects is analyzed in detail. It is shown that our ``''-method successfully suppresses non-resonant effects even for relatively
large values of the Rabi frequency.Comment: 11 pages, 13 figure
Survival of quantum effects for observables after decoherence
When a quantum nonlinear system is linearly coupled to an infinite bath of
harmonic oscillators, quantum coherence of the system is lost on a decoherence
time-scale . Nevertheless, quantum effects for observables may still
survive environment-induced decoherence, and be observed for times much larger
than the decoherence time-scale. In particular, we show that the Ehrenfest
time, which characterizes a departure of quantum dynamics for observables from
the corresponding classical dynamics, can be observed for a quasi-classical
nonlinear oscillator for times . We discuss this observation in
relation to recent experiments on quantum nonlinear systems in the
quasi-classical region of parameters.Comment: submitted to PR
Limiting phase trajectories and the origin of energy localization in nonlinear oscillatory chains
We demonstrate that the modulation instability of the zone boundary mode in a
finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient
condition for the efficient energy transfer by localized excitations. This
transfer results from the exclusion of complete energy exchange between
spatially different parts of the chain, and the excitation level corresponding
to that turns out to be twice more than threshold of zone boundary mode's
instability. To obtain this result one needs in far going extension of the
beating concept to a wide class of finite oscillatory chains. In turn, such an
extension leads to description of energy exchange and transition to energy
localization and transfer in terms of 'effective particles' and Limiting Phase
Trajectories. The 'effective particles' appear naturally when the frequency
spectrum crowding ensures the resonance interaction between zone boundary and
two nearby nonlinear normal modes, but there are no additional resonances. We
show that the Limiting Phase Trajectories corresponding to the most intensive
energy exchange between 'effective particles' can be considered as an
alternative to Nonlinear Normal Modes, which describe the stationary process
Avoiding Quantum Chaos in Quantum Computation
We study a one-dimensional chain of nuclear spins in an external
time-dependent magnetic field. This model is considered as a possible candidate
for experimental realization of quantum computation. According to the general
theory of interacting particles, one of the most dangerous effects is quantum
chaos which can destroy the stability of quantum operations. According to the
standard viewpoint, the threshold for the onset of quantum chaos due to an
interaction between spins (qubits) strongly decreases with an increase of the
number of qubits. Contrary to this opinion, we show that the presence of a
magnetic field gradient helps to avoid quantum chaos which turns out to
disappear with an increase of the number of qubits. We give analytical
estimates which explain this effect, together with numerical data supportingComment: RevTex, 5 pages including 3 eps-figure
Solid-State Quantum Computer Based on Scanning Tunneling Microscopy
We propose a solid-state nuclear spin quantum computer based on application
of scanning tunneling microscopy (STM) and well-developed silicon technology.
It requires the measurement of tunneling current modulation caused by the
Larmor precession of a single electron spin.
Our envisioned STM quantum computer would operate at the high magnetic field
(T) and at low temperature K.Comment: 3pages RevTex including 2 figure
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
- …