Method for quantum-jump continuous-time quantum error correction

TL;DR

This paper introduces a formalism for continuous-time quantum error correction using weak measurements and unitaries, optimizing ancillary system size and demonstrating improved performance over existing methods.

Contribution

It formulates a new class of protocols for CTQEC applicable to any stabilizer code, minimizing ancillary qubits and providing performance comparisons.

Findings

Minimal ancillary system size is n-k+1 qubits.

Proposed scheme meets the minimal ancillary requirement.

Our method outperforms existing CTQEC schemes in key performance metrics.

Abstract

Continuous-time quantum error correction (CTQEC) is a technique for protecting quantum information against decoherence, where both the decoherence and error correction processes are considered continuous in time. Given any [[n,k,d]] quantum stabilizer code, we formulate a class of protocols to implement CTQEC, involving weak coherent measurements and weak unitary corrections. Under this formalism, we show that the minimal required size of the ancillary system is n-k+1 qubits, and we propose one scheme that meets this minimal requirement. Furthermore, we compare our method with other known schemes, and show that a particular measure of performance described in this paper is better when using our method.