Abstract
We introduce a framework for fault-tolerant postselection (FTPS) of fault-tolerant codes and channels—such as those based on surface codes—using soft-information metrics based on visible syndrome and erasure information. We introduce several metrics for ranking configurations of syndromes and erasures. In particular, we introduce the logical gap (and variants thereof) as a powerful soft-information metric for predicting logical error rates of fault-tolerant channels based on topological error-correcting codes. The logical gap is roughly the unsigned weight difference between inequivalent logical corrections and is adaptable to any tailored noise model or decoder. We deploy this framework to prepare high-quality surface-code magic states with low overhead under a model of independent and identically distributed (IID) Pauli and erasure errors. Postselection strategies based on the logical gap can suppress the encoding error rate (EER) of a magic state preparation channel to the level of the physical error rate with low overhead. For example, when operating at of the bulk threshold of the corresponding surface code, an overall reduction of the EER by a factor of is achievable with a relative overhead factor of (approximately times less than that of simple syndrome-counting rules). We analyze a schematic buffer architecture for implementing postselection rules on magic state factories in the context of magic state distillation. The FTPS framework can be utilized for mitigating errors in more general fault-tolerant logical channels.
- Received 8 December 2022
- Accepted 11 September 2023
DOI:https://doi.org/10.1103/PRXQuantum.5.010302
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
General-purpose fault-tolerant quantum computation is a paradigm-shifting technology poised to usher in a new era of computational capacity for humanity. Although promising, with many tantalizing applications ranging from simulations of chemical and materials systems to financial modeling, unstructured search, and cryptography, quantum computers require extremely precise, high-quality physical hardware to manipulate the delicate quantum information sensitive to the slightest environmental noise. It is for this reason that quantum error correction and fault tolerance has emerged as a vital requirement in building quantum computing platforms that perform useful large-scale quantum computations.
Our work significantly advances the state of the art in fault tolerance by showing how “logical blocks” that implement quantum gates can be screened and filtered for quality in a very efficient and practical manner under a new framework we call fault-tolerant postselection. We apply this framework and the protocols developed therein to the context of a magic state preparation for magic state distillation, a resource-intensive procedure that is integral to the universality (and hence power) of quantum computation, demonstrating significant resource reductions for strong suppression of logical error rates.
