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Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers.
Razzoli, Luca; Cenedese, Gabriele; Bondani, Maria; Benenti, Giuliano.
Afiliação
  • Razzoli L; Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy.
  • Cenedese G; Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy.
  • Bondani M; Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy.
  • Benenti G; Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy.
Entropy (Basel) ; 26(4)2024 Apr 02.
Article em En | MEDLINE | ID: mdl-38667867
ABSTRACT
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the 2n-cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only O(n2+nt) two-qubit gates compared to the O(n2t) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers.
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Texto completo: 1 Base de dados: MEDLINE Idioma: En Ano de publicação: 2024 Tipo de documento: Article

Texto completo: 1 Base de dados: MEDLINE Idioma: En Ano de publicação: 2024 Tipo de documento: Article