Error correcting Bacon-Shor code with continuous measurement of noncommuting operators

TL;DR

This paper investigates the continuous measurement-based operation of the nine-qubit Bacon-Shor quantum error-correcting code, comparing its performance to discrete methods and highlighting its passive error monitoring advantages.

Contribution

It introduces a continuous measurement scheme for the Bacon-Shor code with noncommuting gauge operators and analyzes its error correction performance.

Findings

Continuous and discrete modes have similar performance at strong measurement strength.

A crossover error rate is identified below which continuous correction outperforms discrete.

Passive error monitoring reduces circuit complexity and resource requirements.

Abstract

We analyze the continuous operation of the nine-qubit error correcting Bacon-Shor code with all noncommuting gauge operators measured at the same time. The error syndromes are continuously monitored using cross-correlations of sets of three measurement signals. We calculate the logical error rates due to $X$, $Y$ and $Z$ errors in the physical qubits and compare the continuous implementation with the discrete operation of the code. We find that both modes of operation exhibit similar performances when the measurement strength from continuous measurements is sufficiently strong. We also estimate the value of the crossover error rate of the physical qubits, below which continuous error correction gives smaller logical error rates. Continuous operation has the advantage of passive monitoring of errors and avoids the need for additional circuits involving ancilla qubits.