Magnetic field sensing with quantum error detection under the effect of energy relaxation

TL;DR

This paper investigates quantum error correction in solid-state spin sensors for magnetic fields, revealing that standard QEC does not improve sensitivity under energy relaxation, but postselection can enhance performance.

Contribution

It demonstrates that standard quantum error correction does not improve sensing sensitivity under energy relaxation, but a postselection strategy can provide an advantage in two-qubit sensors.

Findings

Standard QEC does not enhance sensitivity under energy relaxation.

Postselection improves sensing performance despite noise.

Two-qubit sensors with postselection outperform single-qubit sensors.

Abstract

A solid state spin is an attractive system with which to realize an ultra-sensitive magnetic field sensor. A spin superposition state will acquire a phase induced by the target field, and we can estimate the field strength from this phase. Recent studies have aimed at improving sensitivity through the use of quantum error correction (QEC) to detect and correct any bit-flip errors that may occur during the sensing period. Here, we investigate the performance of a two-qubit sensor employing QEC and under the effect of energy relaxation. Surprisingly, we find that the standard QEC technique to detect and recover from an error does not improve the sensitivity compared with the single-qubit sensors. This is a consequence of the fact that the energy relaxation induces both a phase-flip and a bit-flip noise where the former noise cannot be distinguished from the relative phase induced from the target fields. However, we have found that we can improve the sensitivity if we adopt postselection to discard the state when error is detected. Even when quantum error detection is moderately noisy, and allowing for the cost of the postselection technique, we find that this two-qubit system shows an advantage in sensing over a single qubit in the same conditions.