Quantum metrology via partial quantum error correction

TL;DR

This paper presents a novel quantum metrology method using partial quantum error correction to suppress local noise, enabling super-standard-quantum-limit sensing with fewer error correction checks.

Contribution

It introduces a new approach encoding probe states into superpositions of energetic states, requiring only partial error correction, unlike previous full-code schemes.

Findings

Partial error correction suppresses noise to the power of p^δ

Super-SQL performance maintained with adaptive strategy

Local operators used for checks and phase imprinting

Abstract

We introduce a new method for error-corrected quantum metrology where only partial quantum error correction (QEC) is needed to suppress local noise and maintain the probe states' super-standard-quantum-limit (super-SQL) sensing performance. This stands in contrast to the existing QEC-assisted sensing schemes in Phys. Rev. Lett. 112, 080801 (2014) and Phys. Rev. Lett. 112, 150802 (2014), where a probe state is encoded into the logical subspace of a quantum code and error correction involves measurements on all checks of the code. Here, we encode the probe states into superpositions of energetically different states of the underlying quantum code. For our probe states, error correction using a subset of checks is enough to suppress noise both before and after phase imprinting. We analyze the tradeoff in noise suppression. For noise parallel to our phase imprinter of operator weight $l$, we achieve a suppression of $p^\delta$, where $p$ is the noise strength and $\delta = \lfloor (l+1)/2 \rfloor$. We propose an adaptive imprinter-weight-increasing strategy to maintain super-SQL performance as we scale up the system. In all our examples, checks and phase imprinters are chosen to be local operators, avoiding non-local connectivity.