Bias-tailored Quantum LDPC Codes

Joschka Roffe^1,2, Lawrence Z. Cohen³, Armanda O. Quintavalle^2,4, Daryus Chandra⁵, and Earl T. Campbell^2,4,6

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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Abstract

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.

Featured image: Left: The word error rate of a $[[416,18,dleq 20]]$ bias-tailored qLDPC code for increasing values of $X$-bias. Right: The factor graph of the $[[12,2,3]]$ twisted XZZX toric code. This toric code is constructed from the bias-tailored lifted product of two repetition codes.

► BibTeX data

@article{Roffe2023biastailoredquantum, doi = {10.22331/q-2023-05-15-1005}, url = {https://doi.org/10.22331/q-2023-05-15-1005}, title = {Bias-tailored quantum {LDPC} codes}, author = {Roffe, Joschka and Cohen, Lawrence Z. and Quintavalle, Armanda O. and Chandra, Daryus and Campbell, Earl T.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1005}, month = may, year = {2023}<br /> }

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Cited by

[1] Jonathan F. San Miguel, Dominic J. Williamson, and Benjamin J. Brown, “A cellular automaton decoder for a noise-bias tailored color code”, arXiv:2203.16534, (2022).

[2] Qian Xu, Nam Mannucci, Alireza Seif, Aleksander Kubica, Steven T. Flammia, and Liang Jiang, “Tailored XZZX codes for biased noise”, Physical Review Research 5 1, 013035 (2023).

[3] Oscar Higgott, Thomas C. Bohdanowicz, Aleksander Kubica, Steven T. Flammia, and Earl T. Campbell, “Fragile boundaries of tailored surface codes and improved decoding of circuit-level noise”, arXiv:2203.04948, (2022).

[4] 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).

[5] Matt McEwen, Dave Bacon, and Craig Gidney, “Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics”, arXiv:2302.02192, (2023).

[6] Antonio deMarti iOlius, Josu Etxezarreta Martinez, Patricio Fuentes, and Pedro M. Crespo, “Performance enhancement of surface codes via recursive MWPM decoding”, arXiv:2212.11632, (2022).

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

[8] Qian Xu, Guo Zheng, Yu-Xin Wang, Peter Zoller, Aashish A. Clerk, and Liang Jiang, “Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits”, arXiv:2210.13406, (2022).

[9] Nithin Raveendran, Narayanan Rengaswamy, Filip Rozpędek, Ankur Raina, Liang Jiang, and Bane Vasić, “Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound”, Quantum 6, 767 (2022).

[10] Élie Gouzien, Diego Ruiz, Francois-Marie Le Régent, Jérémie Guillaud, and Nicolas Sangouard, “Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126133 Cat Qubits”, arXiv:2302.06639, (2023).

[11] T. R. Scruby and K. Nemoto, “Local Probabilistic Decoding of a Quantum Code”, arXiv:2212.06985, (2022).

[12] Vincent Paul Su, ChunJun Cao, Hong-Ye Hu, Yariv Yanay, Charles Tahan, and Brian Swingle, “Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning”, arXiv:2305.06378, (2023).

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