On maximum-likelihood decoding with circuit-level errors

Abstract

Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of circuit errors are also analyzed; these generate a family of related asymmetric LDPC codes of varying degeneracy. More generally, such a family is associated with any quantum code. Implications for decoding highly-degenerate quantum codes are discussed.

arXiv comment15 pages, 4 figures. In v2, added analysis of marginal distributions and discussion of decoding. In v3, some typos corrected and references added. In v4, only license has been updated

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• Fundamental thresholds of realistic quantum error correction circuits from classical spin models
• Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition
• Vulnerability of fault-tolerant topological quantum error correction to quantum deviations in code space
• Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory