Hybrid quantum gap estimation algorithm using a filtered time series

TL;DR

This paper introduces a hybrid quantum-classical algorithm that uses long-time filtering of time series data to exponentially reduce the circuit depth needed for quantum time evolution, enabling more feasible quantum simulations of complex many-body problems.

Contribution

It presents a novel filtering-based classical post-processing technique that enhances quantum simulation efficiency, specifically for estimating energy gaps in quantum systems.

Findings

Filtering exponentially reduces circuit depth requirements.

Successful proof-of-concept simulation for a spin model.

Sets groundwork for near-term unbiased quantum simulation.

Abstract

Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time evolution and noise seem to rule out unbiased quantum simulation in the near term. We prove that classical post-processing, i.e., long-time filtering of an offline time series, exponentially improves the circuit depth needed for quantum time evolution. We apply the filtering method to the construction of a hybrid quantum-classical algorithm to estimate energy gap, an important observable not governed by the variational theorem. We demonstrate, within an operating range of filtering, the success of the algorithm in proof-of-concept simulation for finite-size scaling of a minimal spin model. Our findings set the stage for unbiased quantum simulation to offer memory advantage in the near term.