Harnessing Bayesian Statistics to Accelerate Iterative Quantum Amplitude Estimation

TL;DR

This paper introduces Bayesian Iterative Quantum Amplitude Estimation (BIQAE), a novel method that leverages Bayesian statistics to improve measurement efficiency and accuracy in quantum amplitude estimation tasks across various fields.

Contribution

The paper develops a unified statistical framework and demonstrates that Bayesian inference significantly enhances the performance of quantum amplitude estimation methods.

Findings

BIQAE outperforms existing QAE methods in sample complexity.

Rigorous proofs and simulations confirm Bayesian statistics as the key to efficiency gains.

BIQAE accurately estimates quantum amplitudes and molecular energies.

Abstract

We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this framework to harness Bayesian statistics for improved measurement efficiency with rigorous interval estimates at all iterations of Iterative Quantum Amplitude Estimation. We demonstrate the resulting method, Bayesian Iterative Quantum Amplitude Estimation (BIQAE), accurately and efficiently estimates both quantum amplitudes and molecular ground-state energies to high accuracy, and show in analytic and numerical sample complexity analyses that BIQAE outperforms all other QAE approaches considered. Both rigorous mathematical proofs and numerical simulations conclusively indicate Bayesian statistics is the source of this advantage, a finding that invites further inquiry into the power of statistics to expedite the search for quantum utility.