Related papers: Improved single-shot decoding of higher dimensiona…
Quantum error correction requires accurate and efficient decoding to optimally suppress errors in the encoded information. For concatenated codes, where one code is embedded within another, optimal decoding can be achieved using a…
Generalized-bicycle (GB) and more general two-block group-algebra (2BGA) quantum error-correcting codes have naturally redundant minimum-weight stabilizer generators. To use this redundancy, we constructed a large number of ``planar'' 2BGA…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
Quantum error correction requires decoders that are both accurate and efficient. To this end, union-find decoding has emerged as a promising candidate for error correction on the surface code. In this work, we benchmark a weighted variant…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
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,…
Hypergraph product codes are a promising avenue to achieving fault-tolerant quantum computation with constant overhead. When embedding these and other constant-rate qLDPC codes into 2D, a significant number of nonlocal connections are…
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,…
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,…
We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…
Single-shot error correction is a technique for correcting physical errors using only a single round of noisy check measurements, such that any residual noise affects a small number of qubits. We propose a general theory of single-shot…
Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the…
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…
The surface code scheme for quantum computation features a 2d array of nearest-neighbor coupled qubits yet claims a threshold error rate approaching 1% (NJoP 9:199, 2007). This result was obtained for the toric code, from which the surface…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and…
In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. These systems can be realized in large-scale quantum networks or condensed onto a single chip with closely situated nodes.…