1,589 research outputs found
Quantum Metropolis Sampling
The original motivation to build a quantum computer came from Feynman who
envisaged a machine capable of simulating generic quantum mechanical systems, a
task that is believed to be intractable for classical computers. Such a machine
would have a wide range of applications in the simulation of many-body quantum
physics, including condensed matter physics, chemistry, and high energy
physics. Part of Feynman's challenge was met by Lloyd who showed how to
approximately decompose the time-evolution operator of interacting quantum
particles into a short sequence of elementary gates, suitable for operation on
a quantum computer. However, this left open the problem of how to simulate the
equilibrium and static properties of quantum systems. This requires the
preparation of ground and Gibbs states on a quantum computer. For classical
systems, this problem is solved by the ubiquitous Metropolis algorithm, a
method that basically acquired a monopoly for the simulation of interacting
particles. Here, we demonstrate how to implement a quantum version of the
Metropolis algorithm on a quantum computer. This algorithm permits to sample
directly from the eigenstates of the Hamiltonian and thus evades the sign
problem present in classical simulations. A small scale implementation of this
algorithm can already be achieved with today's technologyComment: revised versio
Optimal and Efficient Decoding of Concatenated Quantum Block Codes
We consider the problem of optimally decoding a quantum error correction code
-- that is to find the optimal recovery procedure given the outcomes of partial
"check" measurements on the system. In general, this problem is NP-hard.
However, we demonstrate that for concatenated block codes, the optimal decoding
can be efficiently computed using a message passing algorithm. We compare the
performance of the message passing algorithm to that of the widespread
blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit
and Steane's code on a depolarizing channel demonstrate significant advantages
of the message passing algorithms in two respects. 1) Optimal decoding
increases by as much as 94% the error threshold below which the error
correction procedure can be used to reliably send information over a noisy
channel. 2) For noise levels below these thresholds, the probability of error
after optimal decoding is suppressed at a significantly higher rate, leading to
a substantial reduction of the error correction overhead.Comment: Published versio
Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs
Belief propagation -- a powerful heuristic method to solve inference problems
involving a large number of random variables -- was recently generalized to
quantum theory. Like its classical counterpart, this algorithm is exact on
trees when the appropriate independence conditions are met and is expected to
provide reliable approximations when operated on loopy graphs. In this paper,
we benchmark the performances of loopy quantum belief propagation (QBP) in the
context of finite-tempereture quantum many-body physics. Our results indicate
that QBP provides reliable estimates of the high-temperature correlation
function when the typical loop size in the graph is large. As such, it is
suitable e.g. for the study of quantum spin glasses on Bethe lattices and the
decoding of sparse quantum error correction codes.Comment: 5 pages, 4 figure
Quantum communication using a bounded-size quantum reference frame
Typical quantum communication schemes are such that to achieve perfect
decoding the receiver must share a reference frame with the sender. Indeed, if
the receiver only possesses a bounded-size quantum token of the sender's
reference frame, then the decoding is imperfect, and we can describe this
effect as a noisy quantum channel. We seek here to characterize the performance
of such schemes, or equivalently, to determine the effective decoherence
induced by having a bounded-size reference frame. We assume that the token is
prepared in a special state that has particularly nice group-theoretic
properties and that is near-optimal for transmitting information about the
sender's frame. We present a decoding operation, which can be proven to be
near-optimal in this case, and we demonstrate that there are two distinct ways
of implementing it (corresponding to two distinct Kraus decompositions). In
one, the receiver measures the orientation of the reference frame token and
reorients the system appropriately. In the other, the receiver extracts the
encoded information from the virtual subsystems that describe the relational
degrees of freedom of the system and token. Finally, we provide explicit
characterizations of these decoding schemes when the system is a single qubit
and for three standard kinds of reference frame: a phase reference, a Cartesian
frame (representing an orthogonal triad of spatial directions), and a reference
direction (representing a single spatial direction).Comment: 17 pages, 1 figure, comments welcome; v2 published versio
Foliated quantum error-correcting codes
We show how to construct a large class of quantum error-correcting codes, known as Calderbank-Steane-Shor codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error-correction codes and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate Calderbank-Steane-Shor codes known as turbo codes, finding that they perform well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation
Liquid Crystals in Electric Field
We present a general theory of electric field effects in liquid crystals
where the dielectric tensor depends on the orientation order. As applications,
we examine (i) the director fluctuations in nematic states in electric field
for arbitrary strength of the dielectric anisotropy and (ii) deformation of the
nematic order around a charged particle. Some predictions are made for these
effects.Comment: 9pages, 2figure
Higher harmonics of ac voltage response in narrow strips of YBa2Cu3O7 thin films: Evidence for strong thermal fluctuations
We report on measurements of higher harmonics of the ac voltage response in
strips of YBa2Cu3O7 thin films as a function of temperature, frequency and ac
current amplitude. The third (fifth) harmonic of the local voltage is found to
exhibit a negative (positive) peak at the superconducting transition
temperature and their amplitudes are closely related to the slope (derivative)
of the first (Ohmic) harmonic. The peaks practically do not depend on frequency
and no even (second or fourth) harmonics are detected. The observed data can be
interpreted in terms of ac current induced thermal modulation of the sample
temperature added to strong thermally activated fluctuations in the transition
region.Comment: 9 pages, 4 figures (PDF file
Development and characterization of 16 microsatellite markers for the Louisiana pine snake, Pituophis ruthveni, and two congeners of conservation concern
We isolated and characterized 16 microsatellite loci from the Louisiana pine snake, Pituophis ruthveni. Loci were screened in 24 individuals from locations throughout its distribution in Louisiana and Texas. The number of alleles per locus ranged from 4 to 12, observed heterozygosity ranged from 0.200 to 0.875, and the probability of identity ranged from 0.043 to 0.298. We examined cross-species amplification at these loci in P. catenifer (bullsnakes and gopher snakes) and P. melanoleucus (pine snakes). These new markers provide tools for examining the conservation genetics of this species complex. Louisiana pine snakes face numerous threats: population densities are extremely low and their natural habitat has been severely altered and fragmented. In southern Canada, P. catenifer is at the northern extreme of its range and limited by the availability of suitable over-wintering sites. Hence, for these two species reduction of heterozygosity, potential for inbreeding, and increased effects of genetic drift are all of considerable conservation concern
On compatibility and improvement of different quantum state assignments
When Alice and Bob have different quantum knowledges or state assignments
(density operators) for one and the same specific individual system, then the
problems of compatibility and pooling arise. The so-called first
Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in
terms of possessed or sharp (i. e., probability one) properties. The second BFM
condition is shown to be generally invalid in an infinite-dimensional state
space. An argument leading to a procedure of improvement of one state
assifnment on account of the other and vice versa is presented.Comment: 8 page
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