Localized Virtual Purification

TL;DR

This paper introduces a localized purification method for quantum simulators that reduces measurement complexity by leveraging system locality, enabling more practical error mitigation and cooling in quantum many-body experiments.

Contribution

It proposes a novel localized purification approach that replaces global entangled measurements with local operations, supported by theoretical guarantees and numerical validation.

Findings

Localized purification reduces measurement complexity.

Method is effective even when ideal conditions are not met.

Bridges locality principles with quantum simulation techniques.

Abstract

Analog and digital quantum simulators can efficiently simulate quantum many-body systems that appear in natural phenomena. However, experimental limitations of near-term devices still make it challenging to perform the entire process of quantum simulation. The purification-based quantum simulation methods can alleviate the limitations in experiments such as the cooling temperature and noise from the environment, while this method has the drawback that it requires global entangled measurement with a prohibitively large number of measurements that scales exponentially with the system size. In this Letter, we propose that we can overcome these problems by restricting the entangled measurements to the vicinity of the local observables to be measured, when the locality of the system can be exploited. We provide theoretical guarantees that the global purification operation can be replaced with local operations under some conditions, in particular for the task of cooling and error mitigation. We furthermore give a numerical verification that the localized purification is valid even when conditions are not satisfied. Our method bridges the fundamental concept of locality with quantum simulators, and therefore expected to open a path to unexplored quantum many-body phenomena.