Revisiting one-dimensional discrete-time quantum walks with general coin

Mahesh N. Jayakody; Chandrakala Meena; Priodyuti Pradhan

doi:10.1016/j.physo.2023.100189

Revisiting one-dimensional discrete-time quantum walks with general coin

Mahesh N. Jayakody
, Chandrakala Meena
, Priodyuti Pradhan

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Indian Institute of Science Education and Research Thiruvananthapuram
Bar-Ilan University
Indian Institute of Information Technology Raichur

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Quantum walk (QW) is the quantum analog of the random walk. QW is an integral part of the development of numerous quantum algorithms. Hence, an in-depth understanding of QW helps us to grasp the quantum algorithms. We revisit the one-dimensional discrete-time QW and discuss basic steps in detail by incorporating the most general coin operator, constant in both space and time, and a localized initial state using numerical modeling. We investigate the impact of each parameter of the general coin operator on the probability distribution of the quantum walker. We show that by tuning the parameters of the general coin, one can regulate the probability distribution of the walker. We provide an algorithm for the one-dimensional quantum walk driven by the general coin operator. The study on general coin operators also includes the popular coins — Hadamard, Grover, and Fourier.

Original language	English
Article number	100189
Journal	Physics Open
Volume	17
DOIs	https://doi.org/10.1016/j.physo.2023.100189
State	Published - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s)

Funding

Mahesh N. Jayakody acknowledges the presidential scholarship of Bar-Ilan University, Israel for Ph.D. scholars and the research funding received from Dr. Eliahu Cohen (Faculty of Engineering, Bar-Ilan University). Moreover, he is thankful to Dr. Eliahu Cohen for useful discussions and Prof. Asiri Nanayakkara (National Institute of Fundamental Studies, Sri Lanka) for sharing QW code. C. Meena thanks the Planning and Budgeting Committee (PBC) of the Council for Higher Education, Israel, for support. She is also supported by the INSPIRE-Faculty grant (code IFA19-PH248) of the Department of Science and Technology (DST), India. P. Pradhan is indebted to Dr. Baruch Barzel for providing the postdoctoral research grant and acknowledges Bar-Ilan University, Israel for the Kollman-Soref postdoctoral fellowship. He also acknowledges the Science and Engineering Research Board (SERB), India grant TAR/2022/000657, Govt. of India. Mahesh N. Jayakody acknowledges the presidential scholarship of Bar-Ilan University, Israel for Ph.D. scholars and the research funding received from Dr. Eliahu Cohen (Faculty of Engineering, Bar-Ilan University) . Moreover, he is thankful to Dr. Eliahu Cohen for useful discussions and Prof. Asiri Nanayakkara (National Institute of Fundamental Studies, Sri Lanka) for sharing QW code. C. Meena thanks the Planning and Budgeting Committee (PBC) of the Council for Higher Education, Israel, for support. She is also supported by the INSPIRE-Faculty grant (code IFA19-PH248 ) of the Department of Science and Technology (DST), India. P. Pradhan is indebted to Dr. Baruch Barzel for providing the postdoctoral research grant and acknowledges Bar-Ilan University, Israel for the Kollman-Soref postdoctoral fellowship. He also acknowledges the Science and Engineering Research Board (SERB), India grant TAR/2022/000657 , Govt. of India.

Funders	Funder number
Bar-Ilan University, Israel for the Kollman-Soref
Faculty of Engineering, Bar-Ilan University
Department of Science and Technology, Ministry of Science and Technology, India
Science and Engineering Research Board	TAR/2022/000657
Council for Higher Education	IFA19-PH248
National Institute of Fundamental Studies

Keywords

Fourier coin
Grover coin
Hadamard coin
Quantum entanglement
Quantum walk

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10.1016/j.physo.2023.100189

Cite this

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Revisiting one-dimensional discrete-time quantum walks with general coin

Abstract

Bibliographical note

Funding

Keywords

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