Curve-Fitted QPE: Extending Quantum Phase Estimation Results for a Higher Precision using Classical Post-Processing

TL;DR

This paper introduces a hybrid quantum-classical method called Curve-Fitted QPE that enhances quantum phase estimation precision through classical post-processing, achieving near-optimal accuracy and comparable error resolution to existing algorithms.

Contribution

It presents a novel hybrid approach combining standard QPE with curve-fitting post-processing, improving precision and efficiency in quantum phase estimation.

Findings

Achieves high precision close to Cramér-Rao bound

Comparable error resolution with VQE and Maximum Likelihood methods

Potential extension to multiple phase estimation

Abstract

Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical approach that consists of the standard QPE circuit and classical post-processing using curve-fitting, where special attention is given to the latter. We show that our approach achieves high precision with optimal Cram\'er-Rao lower bound performance and is comparable in error resolution with the Variational Quantum Eigensolver and Maximum Likelihood Amplitude Estimation algorithms. Our method could potentially be further extended to the case of estimating multiple phases.