7,075 research outputs found
Quantum Computers, Factoring, and Decoherence
In a quantum computer any superposition of inputs evolves unitarily into the
corresponding superposition of outputs. It has been recently demonstrated that
such computers can dramatically speed up the task of finding factors of large
numbers -- a problem of great practical significance because of its
cryptographic applications. Instead of the nearly exponential (, for a number with digits) time required by the fastest classical
algorithm, the quantum algorithm gives factors in a time polynomial in
(). This enormous speed-up is possible in principle because quantum
computation can simultaneously follow all of the paths corresponding to the
distinct classical inputs, obtaining the solution as a result of coherent
quantum interference between the alternatives. Hence, a quantum computer is
sophisticated interference device, and it is essential for its quantum state to
remain coherent in the course of the operation. In this report we investigate
the effect of decoherence on the quantum factorization algorithm and establish
an upper bound on a ``quantum factorizable'' based on the decoherence
suffered per operational step.Comment: 7 pages,LaTex + 2 postcript figures in a uuencoded fil
Deutsch-Jozsa algorithm as a test of quantum computation
A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a
refined algorithm, which reduces the size of the register and simplifies the
function evaluation, is proposed. The refined version allows a simpler analysis
of the use of entanglement between the qubits in the algorithm and provides
criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful
test of quantum computation.Comment: 10 pages, 2 figures, RevTex, Approved for publication in Phys Rev
Approximate quantum error correction can lead to better codes
We present relaxed criteria for quantum error correction which are useful
when the specific dominant noise process is known. These criteria have no
classical analogue. As an example, we provide a four-bit code which corrects
for a single amplitude damping error. This code violates the usual Hamming
bound calculated for a Pauli description of the error process, and does not fit
into the GF(4) classification.Comment: 7 pages, 2 figures, submitted to Phys. Rev.
Where are the Hedgehogs in Nematics?
In experiments which take a liquid crystal rapidly from the isotropic to the
nematic phase, a dense tangle of defects is formed. In nematics, there are in
principle both line and point defects (``hedgehogs''), but no point defects are
observed until the defect network has coarsened appreciably. In this letter the
expected density of point defects is shown to be extremely low, approximately
per initially correlated domain, as result of the topology
(specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)
Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
The Schur basis on n d-dimensional quantum systems is a generalization of the
total angular momentum basis that is useful for exploiting symmetry under
permutations or collective unitary rotations. We present efficient (size
poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur
transform, which is the change of basis between the computational and the Schur
bases. These circuits are based on efficient circuits for the Clebsch-Gordan
transformation. We also present an efficient circuit for a limited version of
the Schur transform in which one needs only to project onto different Schur
subspaces. This second circuit is based on a generalization of phase estimation
to any nonabelian finite group for which there exists a fast quantum Fourier
transform.Comment: 4 pages, 3 figure
Topological twisted sigma model with H-flux revisited
In this paper we revisit the topological twisted sigma model with H-flux. We
explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian
geometry. we show that the resulting action consists of a BRST exact term and
pullback terms, which only depend on one of the two generalized complex
structures and the B-field. We then discuss the topological feature of the
model.Comment: 16 pages. Appendix adde
Decoherence Free Subspaces for Quantum Computation
Decoherence in quantum computers is formulated within the Semigroup approach.
The error generators are identified with the generators of a Lie algebra. This
allows for a comprehensive description which includes as a special case the
frequently assumed spin-boson model. A generic condition is presented for
error-less quantum computation: decoherence-free subspaces are spanned by those
states which are annihilated by all the generators. It is shown that these
subspaces are stable to perturbations and moreover, that universal quantum
computation is possible within them.Comment: 4 pages, no figures. Conditions for decoherence-free subspaces made
more explicit, updated references. To appear in PR
NMR quantum computation with indirectly coupled gates
An NMR realization of a two-qubit quantum gate which processes quantum
information indirectly via couplings to a spectator qubit is presented in the
context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive
NMR implementation of the Deutsch-Jozsa algorithm for functions with three
argument bits and demonstrates a technique essential for multi-qubit quantum
computation.Comment: 9 pages, 2 figures. 10 additional figures illustrating output spectr
Prevention of dissipation with two particles
An error prevention procedure based on two-particle encoding is proposed for
protecting an arbitrary unknown quantum state from dissipation, such as phase
damping and amplitude damping. The schemes, which exhibits manifestation of the
quantum Zeno effect, is effective whether quantum bits are decohered
independently or cooperatively. We derive the working condition of the scheme
and argue that this procedure has feasible practical implementation.Comment: 12 pages, Late
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