A differentiable quantum phase estimation algorithm

TL;DR

This paper introduces a fully differentiable quantum phase estimation algorithm that accurately estimates electronic properties, enabling advanced quantum simulations for chemical systems with improved precision and flexibility.

Contribution

It develops a smooth estimator integrated with quantum phase estimation, allowing differentiation and optimization for electronic structure calculations.

Findings

Estimator retains accuracy for arbitrary initial states

Outperforms standard majority rule in estimation precision

Successfully applied to geometry optimization with up to 19 qubits

Abstract

The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem by developing a strategy to integrate the quantum phase estimation algorithm within a fully differentiable framework. This is accomplished by devising a smooth estimator able to tackle arbitrary initial states. We provide analytical expressions to characterize the statistics and algorithmic cost of this estimator. Furthermore, we provide numerical evidence that the estimation accuracy is retained when an arbitrary state is considered and that it exceeds the one of standard majority rule. We explicitly use this procedure to estimate chemically relevant quantities, demonstrating our approach through ground-state and triplet excited state geometry optimization with simulations involving up to 19 qubits. This work paves the way for new quantum algorithms that combine interference methods and quantum differentiable programming.