The Quantum Amplitude Estimation Algorithms on Near-Term Devices: A Practical Guide

Author:

Maronese Marco12ORCID,Incudini Massimiliano34ORCID,Asproni Luca3,Prati Enrico156ORCID

Affiliation:

1. Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

2. Department of Pharmacy and Biotechnology, University of Bologna, Via Belmeloro 6, 40126 Bologna, Italy

3. Data Reply s.r.l., Corso Francia, 110, 10143 Torino, Italy

4. Dipartimento di Informatica, Universita di Verona, Strada Le Grazie, 15, 37134 Verona, Italy

5. Dipartimento di Fisica, Universita di Milano, Via Celoria 16, 20133 Milano, Italy

6. National Inter-University Consortium for Telecommunications (CNIT), Viale G.P. Usberti, 181/A Pal.3, 43124 Parma, Italy

Abstract

The Quantum Amplitude Estimation (QAE) algorithm is a major quantum algorithm designed to achieve a quadratic speed-up. Until fault-tolerant quantum computing is achieved, being competitive over classical Monte Carlo (MC) remains elusive. Alternative methods have been developed so as to require fewer resources while maintaining an advantageous theoretical scaling. We compared the standard QAE algorithm with two Noisy Intermediate-Scale Quantum (NISQ)-friendly versions of QAE on a numerical integration task, with the Monte Carlo technique of Metropolis–Hastings as a classical benchmark. The algorithms were evaluated in terms of the estimation error as a function of the number of samples, computational time, and length of the quantum circuits required by the solutions, respectively. The effectiveness of the two QAE alternatives was tested on an 11-qubit trapped-ion quantum computer in order to verify which solution can first provide a speed-up in the integral estimation problems. We concluded that an alternative approach is preferable with respect to employing the phase estimation routine. Indeed, the Maximum Likelihood estimation guaranteed the best trade-off between the length of the quantum circuits and the precision in the integral estimation, as well as greater resistance to noise.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),Astronomy and Astrophysics,Atomic and Molecular Physics, and Optics,Statistical and Nonlinear Physics

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