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Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
Single-shot error correction outperforms conventional approaches by requiring only one round of stabilizer measurements for decoding, even in the presence of measurement errors. This capability relates to the confinement property of codes,…
$ \newcommand{\Z}{\mathbb{Z}} \newcommand{\eps}{\varepsilon} \newcommand{\cc}[1]{\mathsf{#1}} \newcommand{\NP}{\cc{NP}} \newcommand{\problem}[1]{\mathrm{#1}} \newcommand{\BDD}{\problem{BDD}} $Bounded Distance Decoding $\BDD_{p,\alpha}$ is…
Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many of them utilize belief propagation (BP) decoding in some…
Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…
We introduce a decoding framework for correlated errors in quantum LDPC codes under circuit-level noise. The core of our approach is a graph augmentation and rewiring for interference (GARI) method, which modifies the correlated detector…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require…
An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements…
A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special…
The concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum…
We consider quantum two-block group algebra (2BGA) codes, a previously unstudied family of smallest lifted-product (LP) codes. These codes are related to generalized-bicycle (GB) codes, except a cyclic group is replaced with an arbitrary…
In realistic stabiliser-based quantum error correction there are many ways in which real physical systems deviate from simple toy models of error. Stabiliser measurements may not always be deterministic or may suffer from erasure errors,…
We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the…
We prove by construction that the Bravyi-Poulin-Terhal bound on the spatial density of stabilizer codes does not generalize to stabilizer circuits. To do so, we construct a fault tolerant quantum computer with a coding rate above 5% and…
Quantum error-correcting codes with translation symmetry and local checks have been studied extensively, leading to a wide variety of fracton codes in three or more dimensions which lack a complete unifying picture. Recently, the study of…