Related papers: Stabilizer-Assisted Inactivation Decoding of Quant…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
We enhance coarsely quantized LDPC decoding by reusing computed check node messages from previous iterations. Typically, variable and check nodes update and replace old messages every iteration. We show that, under coarse quantization,…
To alleviate the suboptimal performance of belief propagation (BP) decoding of short low-density parity-check (LDPC) codes, a plethora of improved decoding algorithms has been proposed over the last two decades. Many of these methods can be…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
This paper presents a new hybrid classical-quantum approach to solve Mixed Integer Linear Programming (MILP) using neutral atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a…
We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities,…
Layered decoding is well appreciated in Low-Density Parity-Check (LDPC) decoder implementation since it can achieve effectively high decoding throughput with low computation complexity. This work, for the first time, addresses low…
The peeling decoder introduced by Luby, et al. allows analysis of LDPC decoding for the binary erasure channel (BEC). For irregular ensembles, they analyze the decoder state as a Markov process and present a solution to the differential…
In this paper, a simple, general-purpose and effective tool for the design of low-density parity-check (LDPC) codes for iterative correction of bursts of erasures is presented. The design method consists in starting from the parity-check…
Programmable optical tweezer arrays of molecules are an emerging platform for quantum simulation and quantum information science. For these applications, reducing and mitigating errors that arise during initial state preparation and…
This paper tackles two problems that fall under the study of coding for insertions and deletions. These problems are motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm,…
We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…
We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Quantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of…
Quantum information needs to be protected by quantum error-correcting codes due to imperfect physical devices and operations. One would like to have an efficient and high-performance decoding procedure for the class of quantum stabilizer…