Related papers: Decoding quantum Tanner codes
We investigate the coboundary expansion property of tensor product codes, known as product expansion, which plays an important role in recent constructions of good quantum LDPC codes and classical locally testable codes. Prior research has…
The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general…
We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing…
Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional…
In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural…
We discuss error-correction properties for families of quantum low-density parity check (LDPC) codes with relative distance that tends to zero in the limit of large blocklength. In particular, we show that any family of LDPC codes, quantum…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
For any positive integer $g \ge 2$, we derive general condition for the existence of a $2g$-cycle in the Tanner graph of two-dimensional ($2$-D) classical quasi-cyclic (QC) low-density parity-check (LDPC) codes. Depending on whether $p$ is…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
We study the implementation of quantum key distribution (QKD) systems over quantum repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we…
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…
Long, powerful soft detection forward error correction codes are typically constructed by concatenation of shorter component codes that are decoded through iterative Soft-Input Soft-Output (SISO) procedures. The current gold-standard is Low…
Quantum computing requires effective error correction strategies to mitigate noise and decoherence. Quantum Low-Density Parity-Check (QLDPC) codes have emerged as a promising solution for scalable Quantum Error Correction (QEC) applications…
We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
Since the discovery of turbo codes 20 years ago and the subsequent re-discovery of low-density parity-check codes a few years later, the field of channel coding has experienced a number of major advances. Up until that time, code designers…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…