Error-mitigated quantum metrology via enhanced virtual purification

TL;DR

This paper introduces enhanced virtual channel purification techniques to improve noise resilience and precision in quantum metrology, demonstrating significant advantages in bias reduction and sampling cost under practical noise conditions.

Contribution

It proposes a novel error mitigation method called enhanced virtual channel purification, improving upon existing protocols for near-term quantum metrology.

Findings

Substantial bias reduction in quantum parameter estimation.

Quantum advantages in sampling cost for error rates p^{-1}.

Numerical simulations show improved robustness against practical noise.

Abstract

Quantum metrology stands as a leading application of quantum science and technology, yet noise often constrains its precision and sensitivity. In near-term quantum metrology, existing protocols largely depend on virtual state purification, but significant noise accumulation and additional noise from the implementations of these protocols can impede their effectiveness. We propose enhanced virtual channel purification to address these problems, yielding enhanced virtual state purification as a by-product. Within sequential quantum metrology schemes, our error analysis reveals substantial bias reduction and quantum advantages in sampling cost when the number of encoding channels is ${\mathcal{O}}(p^{-1})$, where $p$ represents the error rate of encoding channels. In this range, our methods demonstrate significant improvements in parameter estimation precision and robustness against practical noise, as evidenced by numerical simulations for both single- and multi-parameter tasks. Particularly, these methods can naturally extend beyond quantum metrology, indicating their broad applicability in quantum information and quantum computation.