In situ calibration of unitary operations during quantum error correction

TL;DR

This paper introduces a Bayesian in situ calibration method for quantum error correction that dynamically updates error models, improving logical error rates and enabling real-time calibration of quantum gates in noisy qubits.

Contribution

It presents a novel approach combining Bayesian updates and Kalman filtering to enhance quantum error correction and perform in situ calibration of unitary operations.

Findings

Bayesian updates improve error rate estimation.

In situ calibration reduces gate errors.

Enhanced decoding performance with real-time error modeling.

Abstract

Quantum error correction uses the measurement of syndromes and classical decoding algorithms to estimate the location and type of errors while protecting the encoded quantum bits. Here we consider how prior information and Bayesian updates can play a critical role in improving the performance of QEC in the scenario of a particularly noisy qubit. This allows for leveraging even distance codes, which typically are less valued in QEC, to handle the noisy qubit, changing the power-law scaling of the logical error rate with the baseline physical error rate. A crucial component of this is updating the prior by real time feeding of decoder outputs into a approximate Kalman filter. Thus our approach provides a bootstrap to the actual error rates. We show this via simulation of the full closed-loop system: starting from uniform priors, the update procedure gradually learns site-specific error rates, enabling the decoder to outperform a fixed-prior baseline. In turn, we show that this enables in situ calibration of unitary operations via injection of gate set tomography operations with only moderate overhead in the more typical scenario of low noise qubits.