Error mitigation for logical circuits using decoder confidence

TL;DR

This paper introduces a decoder confidence score (DCS) based on swim distance for fault-tolerant quantum error correction, demonstrating its effectiveness in estimating and mitigating logical error probabilities in quantum circuits.

Contribution

It proposes a novel DCS metric derived from tensor network contractions and shows how to use it for significant error mitigation in quantum circuits.

Findings

DCS reliably estimates logical error probability in noisy quantum circuits.

Rejecting low DCS instances greatly reduces logical error rates.

DCS-based maximum likelihood estimation improves noise reduction without extra quantum resources.

Abstract

Fault-tolerant quantum computers use decoders to monitor for errors and find a plausible correction. A decoder may provide a decoder confidence score (DCS) to gauge its success. We adopt a swim distance DCS, computed from the shortest path between syndrome clusters. By contracting tensor networks, we compare its performance under phenomenological noise to the well-known complementary gap and find that both reliably estimate the logical error probability (LEP) in a decoding window. We explore ways to use this to mitigate the LEP in entire logical circuits. For shallow circuits, we just abort if any decoding window produces an exceptionally low DCS: for a distance-13 surface code under circuit-level noise, rejecting a mere 0.1% of possible DCS values improves the entire circuit's LEP by more than 5 orders of magnitude. For larger algorithms comprising up to billions of windows, DCS-based rejection remains effective for enhancing observable estimation. Moreover, one can use the DCS to assign each circuit's output a unique LEP, and use it as a basis for maximum likelihood estimation. This can reduce the effects of noise by an order of magnitude at no quantum cost; methods can be combined for further improvements.