6,915 research outputs found
Influence of qubit displacements on quantum logic operations in a silicon-based quantum computer with constant interaction
The errors caused by qubit displacements from their prescribed locations in
an ensemble of spin chains are estimated analytically and calculated
numerically for a quantum computer based on phosphorus donors in silicon. We
show that it is possible to polarize (initialize) the nuclear spins even with
displaced qubits by using Controlled NOT gates between the electron and nuclear
spins of the same phosphorus atom. However, a Controlled NOT gate between the
displaced electron spins is implemented with large error because of the
exponential dependence of exchange interaction constant on the distance between
the qubits. If quantum computation is implemented on an ensemble of many spin
chains, the errors can be small if the number of chains with displaced qubits
is small
Creation of entanglement in a scalable spin quantum computer with long-range dipole-dipole interaction between qubits
Creation of entanglement is considered theoretically and numerically in an
ensemble of spin chains with dipole-dipole interaction between the spins. The
unwanted effect of the long-range dipole interaction is compensated by the
optimal choice of the parameters of radio-frequency pulses implementing the
protocol. The errors caused by (i) the influence of the environment,(ii)
non-selective excitations, (iii) influence of different spin chains on each
other, (iv) displacements of qubits from their perfect locations, and (v)
fluctuations of the external magnetic field are estimated analytically and
calculated numerically. For the perfectly entangled state the z component, M,
of the magnetization of the whole system is equal to zero. The errors lead to a
finite value of M. If the number of qubits in the system is large, M can be
detected experimentally. Using the fact that M depends differently on the
parameters of the system for each kind of error, varying these parameters would
allow one to experimentally determine the most significant source of errors and
to optimize correspondingly the quantum computer design in order to decrease
the errors and M. Using our approach one can benchmark the quantum computer,
decrease the errors, and prepare the quantum computer for implementation of
more complex quantum algorithms.Comment: 31 page
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 Computation as a Dynamical Process
In this paper, we discuss the dynamical issues of quantum computation. We
demonstrate that fast wave function oscillations can affect the performance of
Shor's quantum algorithm by destroying required quantum interference. We also
show that this destructive effect can be routinely avoided by using
resonant-pulse techniques. We discuss the dynamics of resonant pulse
implementations of quantum logic gates in Ising spin systems. We also discuss
the influence of non-resonant excitations. We calculate the range of parameters
where undesirable non-resonant effects can be minimized. Finally, we describe
the ``-method'' which avoids the detrimental deflection of non-resonant
qubits.Comment: 13 pages, 1 column, no figure
Spin Relaxation Caused by Thermal Excitations of High Frequency Modes of Cantilever Vibrations
We consider the process of spin relaxation in the oscillating
cantilever-driven adiabatic reversals technique in magnetic resonance force
microscopy. We simulated the spin relaxation caused by thermal excitations of
the high frequency cantilever modes in the region of the Rabi frequency of the
spin sub-system. The minimum relaxation time obtained in our simulations is
greater but of the same order of magnitude as one measured in recent
experiments. We demonstrated that using a cantilever with nonuniform
cross-sectional area may significantly increase spin relaxation time.Comment: 12 pages RevTe
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