Faster Quantum Algorithm for Multiple Observables Estimation in Fermionic Problems

TL;DR

This paper introduces a generalized adaptive quantum gradient estimation framework with two variants that significantly reduce the cost of estimating properties of fermionic systems, demonstrating quadratic speedup and substantial query improvements.

Contribution

It proposes two novel variants of adaptive quantum gradient estimation tailored for fermionic systems, achieving minimal resource usage and quadratic speedup over existing algorithms.

Findings

Quadratic speedup in fermionic partial tomography.

Query improvements by factors of 100 and 500 for specific fermionic problems.

Numerical validation on nitrogenase FeMo cofactor and Fermi-Hubbard model.

Abstract

Achieving quantum advantage in efficiently estimating collective properties of quantum many-body systems remains a fundamental goal in quantum computing. While the quantum gradient estimation (QGE) algorithm has been shown to achieve doubly quantum enhancement in the precision and the number of observables, it remains unclear whether one benefits in practical applications. In this work, we present a generalized framework of adaptive QGE algorithm, and further propose two variants which enable us to estimate the collective properties of fermionic systems using the smallest cost among existing quantum algorithms. The first method utilizes the symmetry inherent in the target state, and the second method enables estimation in a single-shot manner using the parallel scheme. We show that our proposal offers a quadratic speedup compared with prior QGE algorithms in the task of fermionic partial tomography for systems with limited particle numbers. Furthermore, we provide the numerical demonstration that, for a problem of estimating fermionic 2-RDMs, our proposals improve the number of queries to the target state preparation oracle by a factor of 100 for the nitrogenase FeMo cofactor and by a factor of 500 for Fermi-Hubbard model of 100 sites.