Related papers: Quantum XYZ Product Codes
We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
We introduce rainbow codes, a novel class of quantum error correcting codes generalising colour codes and pin codes. Rainbow codes can be defined on any $D$-dimensional simplicial complex that admits a valid $(D + 1)$-colouring of its…
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for the code dimension, depending on the two classical codes…
A code is called a $q$-query locally decodable code (LDC) if there is a randomized decoding algorithm that, given an index $i$ and a received word $w$ close to an encoding of a message $x$, outputs $x_i$ by querying only at most $q$…
We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Z\'emor, and all families of toric codes on $m$-dimensional hypercubic lattices. Similar to the latter,…
Quantum low-density parity-check (QLDPC) codes with asymptotically non-zero rates are prominent candidates for achieving fault-tolerant quantum computation, primarily due to their syndrome-measurement circuit's low operational depth.…
We give a framework for generalizing LDPC code constructions that use Transversal Designs or related structures such as mutually orthogonal Latin squares. Our construction offers a broader range of code lengths and codes rates. Similar…
We study linear codes that maximize minimum distance subject to arbitrary support constraints on the parity-check matrix. Such constraints arise naturally in the design of LDPC codes, locally repairable codes, and hardware-constrained…
In the last three decades, several constructions of quantum error-correcting codes were presented in the literature. Among these codes, there are the asymmetric ones, i.e., quantum codes whose $Z$-distance $d_z$ is different from its…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed,…
Quantum hardware rarely suffers equal amounts of bit-flip ($X$) and phase-flip ($Z$) errors; one type is often much more common than the other. A code that is ``bias-tailored'' can exploit this imbalance, lowering the fault-tolerance…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable…
We construct a three-dimensional Calderbank-Shor-Steane (CSS) stabilizer code on the Face-Centered Cubic (FCC) lattice. Physical qubits reside on the edges of the lattice (coordination $K=12$); X-stabilizers act on octahedral voids and…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
Generalized low-density parity-check (GLDPC) codes, where single parity-check constraints on the code bits are replaced with generalized constraints (an arbitrary linear code), are a promising class of codes for low-latency communication.…
Hypergraph product codes are a class of quantum low density parity check (LDPC) codes discovered by Tillich and Z\'emor. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold.…
Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct…