9,492 research outputs found
Full-revivals in 2-D Quantum Walks
Recurrence of a random walk is described by the Polya number. For quantum
walks, recurrence is understood as the return of the walker to the origin,
rather than the full-revival of its quantum state. Localization for two
dimensional quantum walks is known to exist in the sense of non-vanishing
probability distribution in the asymptotic limit. We show on the example of the
2-D Grover walk that one can exploit the effect of localization to construct
stationary solutions. Moreover, we find full-revivals of a quantum state with a
period of two steps. We prove that there cannot be longer cycles for a
four-state quantum walk. Stationary states and revivals result from
interference which has no counterpart in classical random walks
CFD Model of a Specific Fire Scenario
Flashover is a complex and potentially very dangerous phenomenon. The NSW Fire Brigade currently conducts training courses in flashover and backdraft using a test cell made from a shipping container where chipboard is set alight in the test cell and the fire is allowed to develop into flashover. As part of a collaborative project with the NSWFB, computational models are being developed to aid in the training procedure. CFD models of the test cell in advancing flashover scenarios, using the code FDS are compared with qualitative experimental data, with good agreement shown for the fire behaviour. Models with different configurations of the test cell were also compared, with particular consideration on the effect on time to flashover and temperature trends
Electronic structure of periodic curved surfaces -- topological band structure
Electronic band structure for electrons bound on periodic minimal surfaces is
differential-geometrically formulated and numerically calculated. We focus on
minimal surfaces because they are not only mathematically elegant (with the
surface characterized completely in terms of "navels") but represent the
topology of real systems such as zeolites and negative-curvature fullerene. The
band structure turns out to be primarily determined by the topology of the
surface, i.e., how the wavefunction interferes on a multiply-connected surface,
so that the bands are little affected by the way in which we confine the
electrons on the surface (thin-slab limit or zero thickness from the outset).
Another curiosity is that different minimal surfaces connected by the Bonnet
transformation (such as Schwarz's P- and D-surfaces) possess one-to-one
correspondence in their band energies at Brillouin zone boundaries.Comment: 6 pages, 8 figures, eps files will be sent on request to
[email protected]
Quantum walks in higher dimensions
We analyze the quantum walk in higher spatial dimensions and compare
classical and quantum spreading as a function of time. Tensor products of
Hadamard transformations and the discrete Fourier transform arise as natural
extensions of the quantum coin toss in the one-dimensional walk simulation, and
other illustrative transformations are also investigated. We find that
entanglement between the dimensions serves to reduce the rate of spread of the
quantum walk. The classical limit is obtained by introducing a random phase
variable.Comment: 6 pages, 6 figures, published versio
Estimating the Expected Value of Partial Perfect Information in Health Economic Evaluations using Integrated Nested Laplace Approximation
The Expected Value of Perfect Partial Information (EVPPI) is a
decision-theoretic measure of the "cost" of parametric uncertainty in decision
making used principally in health economic decision making. Despite this
decision-theoretic grounding, the uptake of EVPPI calculations in practice has
been slow. This is in part due to the prohibitive computational time required
to estimate the EVPPI via Monte Carlo simulations. However, recent developments
have demonstrated that the EVPPI can be estimated by non-parametric regression
methods, which have significantly decreased the computation time required to
approximate the EVPPI. Under certain circumstances, high-dimensional Gaussian
Process regression is suggested, but this can still be prohibitively expensive.
Applying fast computation methods developed in spatial statistics using
Integrated Nested Laplace Approximations (INLA) and projecting from a
high-dimensional into a low-dimensional input space allows us to decrease the
computation time for fitting these high-dimensional Gaussian Processes, often
substantially. We demonstrate that the EVPPI calculated using our method for
Gaussian Process regression is in line with the standard Gaussian Process
regression method and that despite the apparent methodological complexity of
this new method, R functions are available in the package BCEA to implement it
simply and efficiently
The quantum to classical transition for random walks
We look at two possible routes to classical behavior for the discrete quantum
random walk on the line: decoherence in the quantum ``coin'' which drives the
walk, or the use of higher-dimensional coins to dilute the effects of
interference. We use the position variance as an indicator of classical
behavior, and find analytical expressions for this in the long-time limit; we
see that the multicoin walk retains the ``quantum'' quadratic growth of the
variance except in the limit of a new coin for every step, while the walk with
decoherence exhibits ``classical'' linear growth of the variance even for weak
decoherence.Comment: 4 pages RevTeX 4.0 + 2 figures (encapsulated Postscript). Trimmed for
length. Minor corrections + one new referenc
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
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
Entanglement-assisted quantum low-density parity-check codes
This paper develops a general method for constructing entanglement-assisted
quantum low-density parity-check (LDPC) codes, which is based on combinatorial
design theory. Explicit constructions are given for entanglement-assisted
quantum error-correcting codes (EAQECCs) with many desirable properties. These
properties include the requirement of only one initial entanglement bit, high
error correction performance, high rates, and low decoding complexity. The
proposed method produces infinitely many new codes with a wide variety of
parameters and entanglement requirements. Our framework encompasses various
codes including the previously known entanglement-assisted quantum LDPC codes
having the best error correction performance and many new codes with better
block error rates in simulations over the depolarizing channel. We also
determine important parameters of several well-known classes of quantum and
classical LDPC codes for previously unsettled cases.Comment: 20 pages, 5 figures. Final version appearing in Physical Review
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