One qubit as a universal approximant

Adrián Pérez-Salinas, David López-Núñez, Artur García-Sáez, P. Forn-Díaz, and José I. Latorre
Phys. Rev. A 104, 012405 – Published 2 July 2021

Abstract

A single-qubit circuit can approximate any bounded complex function stored in the degrees of freedom defining its quantum gates. The single-qubit approximant presented in this work is operated through a series of gates that take as their parametrization the independent variable of the target function and an additional set of adjustable parameters. The independent variable is re-uploaded in every gate while the parameters are optimized for each target function. The output state of this quantum circuit becomes more accurate as the number of re-uploadings of the independent variable increases, i.e., as more layers of gates parameterized with the independent variable are applied. In this work, we provide two proofs of this claim related to both the Fourier series and the universal approximation theorem for neural networks, and we benchmark both methods against their classical counterparts. We further implement a single-qubit approximant in a real superconducting qubit device, demonstrating how the ability to describe a set of functions improves with the depth of the quantum circuit. This work shows the robustness of the re-uploading technique on quantum machine learning.

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  • Received 5 March 2021
  • Revised 28 May 2021
  • Accepted 15 June 2021

DOI:https://doi.org/10.1103/PhysRevA.104.012405

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Adrián Pérez-Salinas1,2,*, David López-Núñez1,2,3, Artur García-Sáez1,4, P. Forn-Díaz3,4, and José I. Latorre4,5,6

  • 1Barcelona Supercomputing Center, Barcelona 08034, Spain
  • 2Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos, Universitat de Barcelona, Barcelona 08028, Spain
  • 3Institut de Física d'Altes Energies, The Barcelona Institute of Science and Technology, Bellaterra 08193, Spain
  • 4Qilimanjaro Quantum Tech, Barcelona 08007, Spain
  • 5Center for Quantum Technologies, Singapore 117543, Singapore
  • 6Quantum Research Centre, Technology Innovation Institute, P.O. Box 9639, Abu Dhabi, United Arab Emirates

  • *adrian.perezsalinas95@gmail.com

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Issue

Vol. 104, Iss. 1 — July 2021

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