# Structured Error Recovery for Codeword-Stabilized Quantum Codes

@article{Li2009StructuredER, title={Structured Error Recovery for Codeword-Stabilized Quantum Codes}, author={Yunfan Li and Ilya Dumer and Markus Grassl and Leonid P. Pryadko}, journal={ArXiv}, year={2009}, volume={abs/0912.3245} }

Code-word-stabilized (CWS) codes are, in general, nonadditive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical nonlinear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less and employs a separate n-qubit measurement in each test. In this article, we suggest an error grouping technique that allows one to…

## 5 Citations

High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping

- Computer ScienceIEEE Transactions on Information Theory
- 2011

These codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension and are of the codeword stabilized (CWS) type, conceptually simple encoding and decoding circuits are available.

Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes

- Computer Science
- 2016

It is shown how the limits of non-transversality can be overcome by performing rounds of intermediate error-correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement.

Non-Pauli observables for CWS codes

- Computer ScienceQuantum Inf. Process.
- 2013

Some results are established on the kind of non-Pauli operators that can be used as observables in the decoding scheme of CWS codes and a procedure to obtain those observables is proposed.

Heuristic construction of codeword stabilized codes

- Computer SciencePhysical Review A
- 2019

It is shown that graphs that give large codes typically yield clique graphs with a large number of nodes, and it is demonstrated that n -node graphs yielding largeClique graphs can be found using a genetic algorithm that uses a crossover operation based on spectral bisection to be superior to more standard crossover operations.

Decoder for Nonbinary CWS Quantum Codes

- Computer ScienceArXiv
- 2012

A decoder for nonbinary CWS quantum codes using the structure of union codes using a union of stabilizer codes to detect a sequence of errors and builds a new code, called union code, that allows to correct the errors.

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