203 research outputs found
Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds) such that each model can be obtained from the dual of the other after freezing k spins on large-degree sites. Such a pair of Ising models can be interpreted as a two-chain complex with k being the rank of the first homology group. Our focus is on the case where k is extensive, that is, scales linearly with the number of bonds n. Flipping any of these additional spins introduces a homologically nontrivial defect (generalized domain wall). In the presence of bond disorder, we prove the existence of a low-temperature weak-disorder region where additional summation over the defects has no effect on the free energy density f(T) in the thermodynamical limit and of a high-temperature region where an extensive homological defect does not affect f(T). We also discuss the convergence of the high- and low-temperature series for the free energy density, prove the analyticity of limiting f(T) at high and low temperatures, and construct inequalities for the critical point(s) where analyticity is lost. As an application, we prove multiplicity of the conventionally defined critical points for Ising models on all { f, d} tilings of the infinite hyperbolic plane, where df/(d + f) \u3e 2. Namely, for these infinite graphs, we show that critical temperatures with free and wired boundary conditions differ, Tc(f)T(f)
Coding scheme for 3D vertical flash memory
Recently introduced 3D vertical flash memory is expected to be a disruptive
technology since it overcomes scaling challenges of conventional 2D planar
flash memory by stacking up cells in the vertical direction. However, 3D
vertical flash memory suffers from a new problem known as fast detrapping,
which is a rapid charge loss problem. In this paper, we propose a scheme to
compensate the effect of fast detrapping by intentional inter-cell interference
(ICI). In order to properly control the intentional ICI, our scheme relies on a
coding technique that incorporates the side information of fast detrapping
during the encoding stage. This technique is closely connected to the
well-known problem of coding in a memory with defective cells. Numerical
results show that the proposed scheme can effectively address the problem of
fast detrapping.Comment: 7 pages, 9 figures. accepted to ICC 2015. arXiv admin note: text
overlap with arXiv:1410.177
A linear-time benchmarking tool for generalized surface codes
Quantum information processors need to be protected against errors and faults. One of the most widely considered fault-tolerant architecture is based on surface codes. While the general principles of these codes are well understood and basic code properties such as minimum distance and rate are easy to characterize, a code's average performance depends on the detailed geometric layout of the qubits. To date, optimizing a surface code architecture and comparing different geometric layouts relies on costly numerical simulations. Here, we propose a benchmarking algorithm for simulating the performance of surface codes, and generalizations thereof, that runs in linear time. We
implemented this algorithm in a software that generates performance reports and allows to quickly compare different architectures
Numerical and analytical bounds on threshold error rates for hypergraph-product codes
We study analytically and numerically decoding properties of finite rate
hypergraph-product quantum LDPC codes obtained from random (3,4)-regular
Gallager codes, with a simple model of independent X and Z errors. Several
non-trival lower and upper bounds for the decodable region are constructed
analytically by analyzing the properties of the homological difference, equal
minus the logarithm of the maximum-likelihood decoding probability for a given
syndrome. Numerical results include an upper bound for the decodable region
from specific heat calculations in associated Ising models, and a minimum
weight decoding threshold of approximately 7%.Comment: 14 pages, 5 figure
Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
We consider pairs of few-body Ising models where each spin enters a bounded
number of interaction terms (bonds), such that each model can be obtained from
the dual of the other after freezing spins on large-degree sites. Such a
pair of Ising models can be interpreted as a two-chain complex with being
the rank of the first homology group. Our focus is on the case where is
extensive, that is, scales linearly with the number of bonds . Flipping any
of these additional spins introduces a homologically non-trivial defect
(generalized domain wall). In the presence of bond disorder, we prove the
existence of a low-temperature weak-disorder region where additional summation
over the defects have no effect on the free energy density in the
thermodynamical limit, and of a high-temperature region where in the
ferromagnetic case an extensive homological defect does not affect . We
also discuss the convergence of the high- and low-temperature series for the
free energy density, prove the analyticity of limiting at high and low
temperatures, and construct inequalities for the critical point(s) where
analyticity is lost. As an application, we prove multiplicity of the
conventionally defined critical points for Ising models on all
tilings of the hyperbolic plane, where . Namely, for these infinite
graphs, we show that critical temperatures with free and wired boundary
conditions differ, .Comment: 18 pages, 6 figure
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