Quantum circuits for discrete-time quantum walks with position-dependent coin operator

Nzongani, Ugo; Zylberman, Julien; Carlo-Elia, Doncecchi,; Perez, A.; Arnault, Pablo

doi:10.1007/s11128-023-03957-8

Cited by 4 publications

(1 citation statement)

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“…However, devising efficient implementations on digitized quantum computers is desirable and necessary in order to make DTQWs available to develop quantum algorithms for general purpose quantum computers and, in general, quantum protocols to be implemented in circuit models. A first circuit implementation of a DTQW on the cycle was realized on a multiqubit nuclear magnetic resonance system [47], and thereafter, proposals for efficient implementation on certain graphs [48][49][50][51], for position-dependent coin operators [52], and for staggered quantum walks (a coinless discrete-time model of quantum walk) [53] have been devised.…”

Section: Introductionmentioning

confidence: 99%

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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