Efficient feedback controllers for continuous-time quantum error correction

TL;DR

This paper introduces an efficient approximate quantum filtering method for continuous-time quantum error correction with real-time feedback, suitable for systems where instantaneous error recovery isn't feasible.

Contribution

It extends low-dimensional quantum filtering to include error recovery via feedback, providing an approximate model that performs comparably to exact models.

Findings

Approximate filter performs similarly to exact models in simulations.

The method is suitable for systems with non-instantaneous error recovery.

Develops a reduced-dimensional model for continuous quantum error correction.

Abstract

We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model.