An Error-aware and Adaptive Method for the Estimation of Quantum Observables on Qudit-Based Quantum Computers

TL;DR

AQUIRE is a novel, error-aware Bayesian protocol for accurately estimating quantum observables on qudit-based quantum computers, adapting measurements in real-time to hardware noise and imperfections.

Contribution

It introduces the first adaptive, error-aware estimation protocol for qudit quantum computers, extending qubit-based techniques to higher-dimensional systems.

Findings

AQUIRE accurately estimates observables and their errors on simulated qudit systems.

It quantifies hardware noise effects during estimation.

Demonstrated on a trapped-ion qudit quantum processor.

Abstract

The accurate estimation of observables is a crucial task in quantum computing. Recent advances have highlighted the need for (a) specialized protocols for qudit-based devices, that include (b) error-aware strategies. Here, we present AQUIRE, the first protocol that can (a) accurately estimate both the mean and the error of an observable on qudit-based quantum computers. AQUIRE achieves this by constructing a Bayesian model to accommodate generalized Pauli operators. It is designed to continuously monitor the estimated average and the associated error of the observable, adjusting the subsequent measurements in real-time. Additionally, AQUIRE is (b) device- and experiment-specific error-aware, and accounts for hardware imperfections and experimental noise during the estimation process. We demonstrate AQUIRE's advantage via numerical simulations and showcase its ability to quantify the noise affecting the estimation by implementing it on a trapped-ion qudit quantum processor. By exploiting general commutation relations and overlap grouping measurements, our protocol is state-of-the-art when restricted to qubit-based quantum computers and extends this advantage to the qudit case.