5,541 research outputs found
Efficient Discrete Approximations of Quantum Gates
Quantum compiling addresses the problem of approximating an arbitrary quantum
gate with a string of gates drawn from a particular finite set. It has been
shown that this is possible for almost all choices of base sets and furthermore
that the number of gates required for precision epsilon is only polynomial in
log 1/epsilon. Here we prove that using certain sets of base gates quantum
compiling requires a string length that is linear in log 1/epsilon, a result
which matches the lower bound from counting volume up to constant factor.Comment: 7 pages, no figures, v3 revised to correct major error in previous
version
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
A Lorentz-invariant look at quantum clock synchronization protocols based on distributed entanglement
Recent work has raised the possibility that quantum information theory
techniques can be used to synchronize atomic clocks nonlocally. One of the
proposed algorithms for quantum clock synchronization (QCS) requires
distribution of entangled pure singlets to the synchronizing parties. Such
remote entanglement distribution normally creates a relative phase error in the
distributed singlet state which then needs to be purified asynchronously. We
present a fully relativistic analysis of the QCS protocol which shows that
asynchronous entanglement purification is not possible, and, therefore, that
the proposed QCS scheme remains incomplete. We discuss possible directions of
research in quantum information theory which may lead to a complete, working
QCS protocol.Comment: 5 pages; typeset in RevTe
Quantum computation with linear optics
We present a constructive method to translate small quantum circuits into
their optical analogues, using linear components of present-day quantum optics
technology only. These optical circuits perform precisely the computation that
the quantum circuits are designed for, and can thus be used to test the
performance of quantum algorithms. The method relies on the representation of
several quantum bits by a single photon, and on the implementation of universal
quantum gates using simple optical components (beam splitters, phase shifters,
etc.). The optical implementation of Brassard et al.'s teleportation circuit, a
non-trivial 3-bit quantum computation, is presented as an illustration.Comment: LaTeX with llncs.cls, 11 pages with 5 postscript figures, Proc. of
1st NASA Workshop on Quantum Computation and Quantum Communication (QCQC 98
Angular distribution of photoluminescence as a probe of Bose Condensation of trapped excitons
Recent experiments on two-dimensional exciton systems have shown the excitons
collect in shallow in-plane traps. We find that Bose condensation in a trap
results in a dramatic change of the exciton photoluminescence (PL) angular
distribution. The long-range coherence of the condensed state gives rise to a
sharply focussed peak of radiation in the direction normal to the plane. By
comparing the PL profile with and without Bose Condensation we provide a simple
diagnostic for the existence of a Bose condensate. The PL peak has strong
temperature dependence due to the thermal order parameter phase fluctuations
across the system. The angular PL distribution can also be used for imaging
vortices in the trapped condensate. Vortex phase spatial variation leads to
destructive interference of PL radiation in certain directions, creating nodes
in the PL distribution that imprint the vortex configuration.Comment: 4 pages, 3 figure
Polarization state of a biphoton: quantum ternary logic
Polarization state of biphoton light generated via collinear
frequency-degenerate spontaneous parametric down-conversion is considered. A
biphoton is described by a three-component polarization vector, its arbitrary
transformations relating to the SU(3) group. A subset of such transformations,
available with retardation plates, is realized experimentally. In particular,
two independent orthogonally polarized beams of type-I biphotons are
transformed into a beam of type-II biphotons. Polarized biphotons are suggested
as ternary analogs of two-state quantum systems (qubits)
Theory of quantum dot spin-lasers
We formulate a model of a semiconductor Quantum Dot laser with injection of
spin-polarized electrons. As compared to higher-dimensionality structures, the
Quantum-Dot-based active region is known to improve laser properties, including
the spin-related ones. The wetting layer, from which carriers are captured into
the active region, acts as an intermediate level that strongly influences the
lasing operation. The finite capture rate leads to an increase of lasing
thresholds, and to saturation of emitted light at higher injection. In spite of
these issues, the advantageous threshold reduction, resulting from spin
injection, can be preserved. The "spin-filtering" effect, i.e., circularly
polarized emission at even modest spin-polarization of injection, remains
present as well. Our rate-equations description allows to obtain analytical
results and provides transparent guidance for improvement of spin-lasers.Comment: 7 pages, 3 figure
Quantum Bit Regeneration
Decoherence and loss will limit the practicality of quantum cryptography and
computing unless successful error correction techniques are developed. To this
end, we have discovered a new scheme for perfectly detecting and rejecting the
error caused by loss (amplitude damping to a reservoir at T=0), based on using
a dual-rail representation of a quantum bit. This is possible because (1)
balanced loss does not perform a ``which-path'' measurement in an
interferometer, and (2) balanced quantum nondemolition measurement of the
``total'' photon number can be used to detect loss-induced quantum jumps
without disturbing the quantum coherence essential to the quantum bit. Our
results are immediately applicable to optical quantum computers using single
photonics devices.Comment: 4 pages, postscript only, figures available at
http://feynman.stanford.edu/qcom
Factoring in a Dissipative Quantum Computer
We describe an array of quantum gates implementing Shor's algorithm for prime
factorization in a quantum computer. The array includes a circuit for modular
exponentiation with several subcomponents (such as controlled multipliers,
adders, etc) which are described in terms of elementary Toffoli gates. We
present a simple analysis of the impact of losses and decoherence on the
performance of this quantum factoring circuit. For that purpose, we simulate a
quantum computer which is running the program to factor N = 15 while
interacting with a dissipative environment. As a consequence of this
interaction randomly selected qubits may spontaneously decay. Using the results
of our numerical simulations we analyze the efficiency of some simple error
correction techniques.Comment: plain tex, 18 pages, 8 postscript figure
- …