2,655 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
Cross-Paced Representation Learning with Partial Curricula for Sketch-based Image Retrieval
In this paper we address the problem of learning robust cross-domain
representations for sketch-based image retrieval (SBIR). While most SBIR
approaches focus on extracting low- and mid-level descriptors for direct
feature matching, recent works have shown the benefit of learning coupled
feature representations to describe data from two related sources. However,
cross-domain representation learning methods are typically cast into non-convex
minimization problems that are difficult to optimize, leading to unsatisfactory
performance. Inspired by self-paced learning, a learning methodology designed
to overcome convergence issues related to local optima by exploiting the
samples in a meaningful order (i.e. easy to hard), we introduce the cross-paced
partial curriculum learning (CPPCL) framework. Compared with existing
self-paced learning methods which only consider a single modality and cannot
deal with prior knowledge, CPPCL is specifically designed to assess the
learning pace by jointly handling data from dual sources and modality-specific
prior information provided in the form of partial curricula. Additionally,
thanks to the learned dictionaries, we demonstrate that the proposed CPPCL
embeds robust coupled representations for SBIR. Our approach is extensively
evaluated on four publicly available datasets (i.e. CUFS, Flickr15K, QueenMary
SBIR and TU-Berlin Extension datasets), showing superior performance over
competing SBIR methods
A finite point method for compressible flow
This is the accepted version of the following article: [Löhner, R. , Sacco, C. , Oñate, E. and Idelsohn, S. (2002), A finite point method for compressible flow. Int. J. Numer. Meth. Engng., 53: 1765-1779. doi:10.1002/nme.334], which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.334A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge-based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh-based finite volume or finite element techniques, making the present finite point method competitive.Peer ReviewedPostprint (author's final draft
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