Bias-tailored quantum LDPC codes

Joschka Roffe1,2, Lawrence Z. Cohen3, Armanda O. Quintavalle2,4, Daryus Chandra5, and Earl T. Campbell2,4,6

1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
2Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom
3Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia
4Riverlane, Cambridge CB2 3BZ, United Kingdom
5School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom
6AWS Center for Quantum Computing, Cambridge CB1 2GA, United Kingdom

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Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise. In this work, we demonstrate that quantum low density parity check codes can be similarly bias-tailored. We introduce a bias-tailored lifted product code construction that provides the framework to expand bias-tailoring methods beyond the family of 2D topological codes. We present examples of bias-tailored lifted product codes based on classical quasi-cyclic codes and numerically assess their performance using a belief propagation plus ordered statistics decoder. Our Monte Carlo simulations, performed under asymmetric noise, show that bias-tailored codes achieve several orders of magnitude improvement in their error suppression relative to depolarising noise.

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[6] Jonathan F. San Miguel, Dominic J. Williamson, and Benjamin J. Brown, "A cellular automaton decoder for a noise-bias tailored color code", Quantum 7, 940 (2023).

[7] Christopher A. Pattison, Anirudh Krishna, and John Preskill, "Hierarchical memories: Simulating quantum LDPC codes with local gates", arXiv:2303.04798, (2023).

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