Related papers: Improved decoding algorithms for surface codes und…
We present an approach to showing that a linear code is resilient to random errors. We use this approach to obtain decoding results for both transitive codes and Reed-Muller codes. We give three kinds of results about linear codes in…
Minimum-weight perfect matching (MWPM) has been been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108,…
Minimum Weight Cycle (MWC) is the problem of finding a simple cycle of minimum weight in a graph $G=(V,E)$. This is a fundamental graph problem with classical sequential algorithms that run in $\tilde{O}(n^3)$ and $\tilde{O}(mn)$ time where…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…
The performance of short polar codes under successive cancellation (SC) and SC list (SCL) decoding is analyzed for the case where the decoder messages are coarsely quantized. This setting is of particular interest for applications requiring…
We present adaptive on-line schemes for lossy encoding of individual sequences under the conditions of the Wyner-Ziv (WZ) problem. In the first part of this article, a set of fixed-rate scalar source codes with zero delay is presented. We…
In magnetic-recording systems, consecutive sections experience different signal to noise ratios (SNRs). To perform error correction over these systems, one approach is to use an individual block code for each section. However, the…
As improved versions of successive cancellation (SC) decoding algorithm, successive cancellation list (SCL) decoding and successive cancellation stack (SCS) decoding are used to improve the finite-length performance of polar codes. Unified…
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
We introduce an efficient decoder of the color code in $d\geq 2$ dimensions, the Restriction Decoder, which uses any $d$-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the…
We present a method, called matching synthesis, for decoding quantum codes that produces an enhanced assignment of errors from an ensemble of decoders. We apply matching synthesis to develop a decoder named Libra, and show in simulations…
Monotone chain polar codes generalize classical polar codes to multivariate settings, offering a flexible approach for achieving the entire admissible rate region in the distributed lossless coding problem. However, this flexibility also…
In the Maximum Weight Independent Set of Rectangles (MWISR) problem we are given a set of n axis-parallel rectangles in the 2D-plane, and the goal is to select a maximum weight subset of pairwise non-overlapping rectangles. Due to many…
We describe a computationally-efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding minimal surface given its boundary (curve) in any hypercubic lattice of dimension $D>2$. We…
With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up…
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
Ultra-reliable low-latency communications (URLLC) operate with short packets, where finite-blocklength effects make near-maximum-likelihood (near-ML) decoding desirable but often too costly. This paper proposes a two-stage near-ML decoding…