Title: A universal quantum circuit design for periodical functions

Abstract

We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains N-qubits to store the information on the different N-Fourier components and M + 2 auxiliary qubits with M = ⌈log₂ N⌉ for control operations. The desired output will be measured in the last qubit q_N with a time complexity of the computation of $$O({N}^{2}{\lceil {\mathrm{log}}_{2}\enspace N\rceil }^{2})$$, which leads to polynomial speedup under certain circumstances. We illustrate the approach by constructing the quantum circuit for the square wave function with accurate results obtained by direct simulations using the IBM-QASM simulator. The approach is general and can be applied to any arbitrary periodic function.

Authors:

Li, Junxu ;

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• Search DOE PAGES for ORCID "0000-0002-2189-0626"
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Kais, Sabre

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• Search DOE PAGES for ORCID "0000-0003-0574-5346"
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Publication Date:

2021-10-19

Research Org.:

Purdue Univ., West Lafayette, IN (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:

1826621

Alternate Identifier(s):

OSTI ID: 1823660; OSTI ID: 1835064

Grant/Contract Number:  

No.de-sc0019215; SC0019215

Resource Type:

Published Article

Journal Name:

New Journal of Physics

Additional Journal Information:

Journal Name: New Journal of Physics Journal Volume: 23 Journal Issue: 10; Journal ID: ISSN 1367-2630

Publisher:

IOP Publishing

Country of Publication:

United Kingdom

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum algorithm; quantum circuit; quantum simulation