High-threshold error-correcting codes for biased noise with advanced decoding strategies
Abstract
Quantum computers are highly sensitive to noise due to interactions with the environment, which severely limits the utility of near-term devices. Quantum error correction addresses this challenge by encoding logical information over multiple qubits in order to preserve information in the presence of noise. This facilitates the realization of the theoretical advantages of quantum computing such as exponential speed-up compared to classical computers for certain algorithms.
Physical realizations of qubits may have different noise profiles, including biased noise, where phase-flip errors may be more likely than bit-flip errors. We propose a quantum error-correcting code, the XYZ² code, which is tailored to biased noise. The code has high error thresholds against biased noise, below which logical errors are exponentially suppressed with the linear dimension of the code.
The important classical task of deriving corrections given partial information about errors is called decoding. We investigate several decoding strategies tailored to specific challenges, ranging from a novel maximum-likelihood sampling decoder, to a model-free, data-driven, neural-network-based decoder, to an efficient multi-step decoder for concatenated codes. We also study the link between quantum error-correcting codes and their statistical-mechanical counterparts by mapping to generalized random-bond Ising models and subsequently deriving the exact results for finite-size corrections under biased noise for moderate code sizes.
Quantum error correction is still in its developing stages, and this work provides a useful contribution to the field by bridging a gap between theory and practice. By adapting well-studied topological codes to error models that are closer to reality, this work paves the way for the realization of a fault-tolerant quantum architecture.
Parts of work
Basudha Srivastava, Anton Frisk Kockum, and Mats Granath. “The XYZ² hexagonal stabilizer code”. Quantum 6, 698 (2022). https://dx.doi.org/10.22331/q-2022-04-27-698 Karl Hammar, Alexei Orekhov, Patrik Wallin Hybelius, Anna Katariina Wisakanto, Basudha Srivastava, Anton Frisk Kockum, and Mats Granath. “Error-rate-agnostic decoding of topological stabilizer codes”.
Physical Review A 105, 042616 (2022). https://dx.doi.org/10.1103/PhysRevA.105.042616 Moritz Lange, Pontus Havström, Basudha Srivastava, Valdemar Bergentall, Karl Hammar, Olivia Heuts, Evert van Nieuwenburg, and Mats Granath. “Data-driven decoding of quantum error correcting codes using graph neural networks” (2023). https://doi.org/10.48550/arXiv.2307.01241 Yinzi Xiao, Basudha Srivastava, and Mats Granath. “Exact results on finite size corrections for surface codes tailored to biased noise”. Quantum 8, 1468 (2024). https://doi.org/10.22331/q-2024-09-11-1468 Basudha Srivastava, Yinzi Xiao, Anton Frisk Kockum, Ben Criger, and Mats Granath. “Two-level decoding scheme for the XYZ² hexagonal stabilizer code”. unpublished (2024).
Degree
Doctor of Philosophy
University
University of Gothenburg. Faculty of Science.
Institution
Department of Physics ; Institutionen för fysik
Disputation
Fredagen den 13 december, 2024 kl. 9:00, PJ-salen, Institutionen för fysik, Fysik Origo, Fysikgården 4, Göteborg
Date of defence
2024-12-13
basudha.srivastava@physics.gu.se
Date
2024-11-18Author
Srivastava, Basudha
Publication type
Doctoral thesis
ISBN
978-91-8115-028-5 (PRINT) and 978-91-8115-029-2 (PDF)
Language
eng