Single-shot decoding of good quantum LDPC codes

TL;DR

This paper demonstrates that quantum Tanner codes enable single-shot quantum error correction with constant measurement rounds, robustness to adversarial noise, and efficient decoding, advancing quantum fault-tolerance.

Contribution

It proves that quantum Tanner codes support single-shot QEC with constant measurement rounds and efficient decoding algorithms, a novel result for quantum LDPC codes.

Findings

Single-shot QEC is possible with quantum Tanner codes.

Constant-time decoding suffices for error suppression.

Codes are robust against adversarial and correlated noise.

Abstract

Quantum Tanner codes constitute a family of quantum low-density parity-check (LDPC) codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Z\'emor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.