Bacon-Shor code with continuous measurement of non-commuting operators

TL;DR

This paper investigates a four-qubit Bacon-Shor quantum error-correcting code using continuous measurement of non-commuting operators, analyzing its error detection capabilities and comparing it to traditional projective measurement methods.

Contribution

It introduces a continuous measurement approach for the Bacon-Shor code and evaluates its performance and advantages over projective measurement schemes.

Findings

Logical error rate depends on decoherence models

Continuous measurement performance is comparable to projective methods

Passive continuous monitoring simplifies error syndrome detection

Abstract

We analyze the operation of a four-qubit Bacon-Shor code with simultaneous continuous measurement of non-commuting gauge operators. The error syndrome in this case is monitored via time-averaged cross-correlators of the output signals. We find the logical error rate for several models of decoherence, and also find the termination rate for this quantum error detecting code. The code operation is comparable to that based on projective measurements when the collapse timescale due to continuous measurements is an order of magnitude less than the time period between the projective measurements. An advantage of the continuous-measurement implementation is the absence of time-dependence in the code operation, with passive continuous monitoring of the error syndrome.