On maximum-likelihood decoding with circuit-level errors

TL;DR

This paper presents an exact method for maximum-likelihood decoding of quantum circuits with errors, using the circuit error-equivalence group, and explores related LDPC codes and implications for highly-degenerate quantum codes.

Contribution

It introduces an exact description of error distributions for Clifford measurement circuits and connects them to LDPC codes, advancing quantum error correction decoding techniques.

Findings

Exact error probability distribution derived from circuit error-equivalence group

Family of asymmetric LDPC codes generated from marginal error distributions

Implications for decoding highly-degenerate quantum codes discussed

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.