Measurement based estimator scheme for continuous quantum error correction

TL;DR

This paper introduces a measurement-based estimator scheme for continuous quantum error correction that enables real-time error tracking and surpasses traditional discrete methods in efficiency and accuracy.

Contribution

The paper proposes a novel measurement-based estimator for continuous quantum error correction, improving real-time error detection and correction performance.

Findings

The estimator accurately tracks errors in real time.

The scheme outperforms discrete quantum error correction.

It allows immediate or delayed correction with high fidelity.

Abstract

Canonical discrete quantum error correction (DQEC) schemes use projective von Neumann measurements on stabilizers to discretize the error syndromes into a finite set, and fast unitary gates are applied to recover the corrupted information. Quantum error correction (QEC) based on continuous measurement, known as continuous quantum error correction (CQEC), in principle, can be executed faster than DQEC and can also be resource efficient. However, CQEC requires meticulous filtering of noisy continuous measurement data to reliably extract error syndromes on the basis of which errors could be detected. In this paper, we show that by constructing a measurement-based estimator (MBE) of the logical qubit to be protected, which is driven by the noisy continuous measurement currents of the stabilizers, it is possible to accurately track the errors occurring on the physical qubits in real time. We use this MBE to develop a continuous quantum error correction (MBE-CQEC) scheme that can protect the logical qubit to a high degree, surpassing the performance of DQEC, and also allows QEC to be conducted either immediately or in delayed time with instantaneous feedbacks.