Work

Harnessing Bayesian Statistics to Accelerate Iterative Quantum Amplitude Estimation

Year: 2026

Type: article

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.

Source: Quantum

DOI: 10.22331/q-2026-01-14-1962

Authors: Qilin Li, Atharva Vidwans, Yazhen Wang, Micheline B. Soley

Institution: University of Wisconsin–Madison

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funder: National Science Foundation