Quantum error correction using weak measurements

TL;DR

This paper explores quantum error correction using weak measurements, developing a probabilistic feedback protocol that corrects errors based on partial syndrome information, and demonstrating its effectiveness through numerical simulations.

Contribution

It introduces a novel quantum error correction method utilizing weak measurements and probabilistic feedback, expanding beyond traditional projective measurement approaches.

Findings

Error correction succeeds within specific measurement strength ranges.

The protocol maintains effectiveness when error rates are below certain thresholds.

Too weak measurements are ineffective for error correction.

Abstract

The standard quantum error correction protocols use projective measurements to extract the error syndromes from the encoded states. We consider the more general scenario of weak measurements, where only partial information about the error syndrome can be extracted from the encoded state. We construct a feedback protocol that probabilistically corrects the error based on the extracted information. Using numerical simulations of one-qubit error correction codes, we show that our error correction succeeds for a range of the weak measurement strength, where (a) the error rate is below the threshold beyond which multiple errors dominate, and (b) the error rate is less than the rate at which weak measurement extracts information. It is also obvious that error correction with too small a measurement strength should be avoided.