Order from chaos in quantum walks on cyclic graphs

Panda, Abhisek; Benjamin, Colin

doi:10.1103/physreva.104.012204

Cited by 9 publications

(2 citation statements)

References 25 publications

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“…Parrondo's paradox arises when losing strategies are combined to obtain a winning one and it cuts across various research areas. This counterintuitive phenomenon can be observed in DTQW on the line or cycle when two or more coin operators are applied in a deterministic sequence [79,80]. Therefore, we expect that our quantum circuit may also be of interest to quantum game theory [81].…”

Section: Discussionmentioning

confidence: 91%

Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers

Razzoli,

Cenedese,

Bondani

et al. 2024

Entropy

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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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Section: Discussionmentioning

confidence: 91%

Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers

Razzoli,

Cenedese,

Bondani

et al. 2024

Entropy

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“…Periodicity of discrete quantum walks is also studied using many different discrete quantum walk models [1,12]. Periodic quantum walks help to design new quantum algorithms in quantum cryptology [17]. It is also of interest in development of quantum chaos control theory [20].…”

Section: Introductionmentioning

confidence: 99%

Periodicity of bipartite walk on biregular graphs with conditional spectra

Chen¹

2022

Preprint

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In this paper we study a class of discrete quantum walks, known as bipartite walks. These include the well-known Grover's walks. Any discrete quantum walk is given by the powers of a unitary matrix U indexed by arcs or edges of the underlying graph. The walk is periodic if U k = I for some positive integer k. Kubota has given a characterization of periodicity of Grover's walk when the walk is defined on a regular bipartite graph with at most five eigenvalues. We extend Kubota's results-if a biregular graph G has eigenvalues whose squares are algebraic integers with degree at most two, we characterize periodicity of the bipartite walk over G in terms of its spectrum. We apply periodicity results of bipartite walks to get a characterization of periodicity of Grover's walk on regular graphs.

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Odd-periodic Grover Walks

Yoshie

2023

Quantum Inf Process

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Order from chaos in quantum walks on cyclic graphs

Cited by 9 publications

References 25 publications

Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers

Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers

Periodicity of bipartite walk on biregular graphs with conditional spectra

Odd-periodic Grover Walks

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