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We propose the X$^3$Z$^3$ Floquet code, a dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…
The discovery of the family of balanced product codes was pivotal in the subsequent development of 'good' low density quantum error correcting codes that have optimal scaling of the key parameters of distance and storage density. We review…
The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…
The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing…
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…
We consider a topological stabilizer code on a honeycomb grid, the "XYZ$^2$" code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor. 48, 215302…
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…
To make practical quantum algorithms work, large-scale quantum processors protected by error-correcting codes are required to resist noise and ensure reliable computational outcomes. However, a major challenge arises from defects in…
Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…
We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation and fault-tolerant quantum computation. We…
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 define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all unitary quantum gates, and it is found that the…
Tensor-network codes enable the construction of large stabilizer codes out of tensors describing smaller stabilizer codes. An application of tensor-network codes was an efficient and exact decoder for holographic codes. Here, we show how to…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
This paper characterizes Goppa codes of certain maximal curves over finite fields defined by equations of the form $y^n = x^m + x$. We investigate Algebraic Geometric and quantum stabilizer codes associated with these maximal curves and…
A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a…