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Distributed architectures are a route to scalable quantum computing, but the performance of fault-tolerant operations across noisy inter-module links remains poorly characterized. We present circuit-level simulations of two key distributed…
Low-density parity-check (LDPC) codes are specified by graphs, and are the error correction technique of choice in many communications and data storage contexts. Message passing decoders diffuse information carried by parity bits into the…
We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight…
Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…
The Extended Min-Sum (EMS) algorithm for non-binary low-density parity-check (LDPC) defined over an alphabet of size $q$ operates on truncated messages of length $q'$ to achieve a complexity of the order $q'^2$. In contrast, Walsh-Hadamard…
Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes.…
The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g.…
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…
Quantum low-density parity-check (qLDPC) codes have emerged as a promising approach for realizing low-overhead logical quantum memories. Recent theoretical developments have established shift automorphisms as a fundamental building block…
Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of…
A method to construct girth-12 (3,L) quasi-cyclic low-density parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes…
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
LDPC (Low Density Parity Check) codes are among the most powerful and widely adopted modern error correcting codes. The iterative decoding algorithms required for these codes involve high computational complexity and high processing…
We can design efficient quantum error-correcting (QEC) codes by tailoring them to our choice of quantum architecture. Useful tools for constructing such codes include Clifford deformations and appropriate gauge fixings of compass codes. In…
We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by…
In this paper, we propose a novel decoding method for Quantum Low-Density Parity-Check (QLDPC) codes based on Graph Neural Networks (GNNs). Similar to the Belief Propagation (BP)-based QLDPC decoders, the proposed GNN-based QLDPC decoder…
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in…
Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices…