Characterization of syndrome-dependent logical noise in detector regions

TL;DR

This paper presents a robust protocol for characterizing syndrome-dependent logical noise in quantum error correction, validated on a trapped-ion device, aiding in noise mitigation and fault tolerance.

Contribution

A new SPAM-robust protocol for estimating logical Pauli channels conditioned on syndrome outcomes in quantum error correction.

Findings

Improved noise diagnostic tests with noise tailoring strategies

Validated protocol on a trapped-ion quantum device

Enhanced fault tolerance through noise mitigation techniques

Abstract

Characterizing how quantum error correction circuits behave under realistic hardware noise is essential for testing the premises that enable scalable fault tolerance. Logical error rates conditioned on syndrome outcomes are needed to enable noise-aware decoding and validate threshold-relevant assumptions. We introduce a protocol to directly estimate the logical Pauli channels (and pure errors) associated with detector regions formed of two or more syndrome extraction gadgets, conditioned on observing a particular parity in the syndrome outcomes. The method is SPAM-robust and most suitable for flag-based syndrome measurement schemes. For classical processing of the experimental data we implement a Bayesian modelling approach. We validate this new protocol on a small error-detecting code using Quantinuum H1-1, a trapped-ion device, and demonstrate that several noise diagnostic tests for fault tolerance improve significantly when using noise tailoring and mitigation strategies, such as swapped measurements for leakage protection, and Pauli frame randomization.