3,705 research outputs found
Tailoring surface codes for highly biased noise
The surface code, with a simple modification, exhibits ultra-high error
correction thresholds when the noise is biased towards dephasing. Here, we
identify features of the surface code responsible for these ultra-high
thresholds. We provide strong evidence that the threshold error rate of the
surface code tracks the hashing bound exactly for all biases, and show how to
exploit these features to achieve significant improvement in logical failure
rate. First, we consider the infinite bias limit, meaning pure dephasing. We
prove that the error threshold of the modified surface code for pure dephasing
noise is , i.e., that all qubits are fully dephased, and this threshold
can be achieved by a polynomial time decoding algorithm. We demonstrate that
the sub-threshold behavior of the code depends critically on the precise shape
and boundary conditions of the code. That is, for rectangular surface codes
with standard rough/smooth open boundaries, it is controlled by the parameter
, where and are dimensions of the surface code lattice. We
demonstrate a significant improvement in logical failure rate with pure
dephasing for co-prime codes that have , and closely-related rotated
codes, which have a modified boundary. The effect is dramatic: the same logical
failure rate achievable with a square surface code and physical qubits can
be obtained with a co-prime or rotated surface code using only
physical qubits. Finally, we use approximate maximum likelihood decoding to
demonstrate that this improvement persists for a general Pauli noise biased
towards dephasing. In particular, comparing with a square surface code, we
observe a significant improvement in logical failure rate against biased noise
using a rotated surface code with approximately half the number of physical
qubits.Comment: 18+4 pages, 24 figures; v2 includes additional coauthor (ASD) and new
results on the performance of surface codes in the finite-bias regime,
obtained with beveled surface codes and an improved tensor network decoder;
v3 published versio
Parameter likelihood of intrinsic ellipticity correlations
Subject of this paper are the statistical properties of ellipticity
alignments between galaxies evoked by their coupled angular momenta. Starting
from physical angular momentum models, we bridge the gap towards ellipticity
correlations, ellipticity spectra and derived quantities such as aperture
moments, comparing the intrinsic signals with those generated by gravitational
lensing, with the projected galaxy sample of EUCLID in mind. We investigate the
dependence of intrinsic ellipticity correlations on cosmological parameters and
show that intrinsic ellipticity correlations give rise to non-Gaussian
likelihoods as a result of nonlinear functional dependencies. Comparing
intrinsic ellipticity spectra to weak lensing spectra we quantify the magnitude
of their contaminating effect on the estimation of cosmological parameters and
find that biases on dark energy parameters are very small in an
angular-momentum based model in contrast to the linear alignment model commonly
used. Finally, we quantify whether intrinsic ellipticities can be measured in
the presence of the much stronger weak lensing induced ellipticity
correlations, if prior knowledge on a cosmological model is assumed.Comment: 14 pages, 8 figures, submitted to MNRA
On the Design of Cryptographic Primitives
The main objective of this work is twofold. On the one hand, it gives a brief
overview of the area of two-party cryptographic protocols. On the other hand,
it proposes new schemes and guidelines for improving the practice of robust
protocol design. In order to achieve such a double goal, a tour through the
descriptions of the two main cryptographic primitives is carried out. Within
this survey, some of the most representative algorithms based on the Theory of
Finite Fields are provided and new general schemes and specific algorithms
based on Graph Theory are proposed
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