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arXiv · 2202.09080

Design for implementation of discrete-time quantum walk with circulant matrix on graph by optical polarizing elements

Yusuke Mizutani·Etsuo Segawa·Yusuke Higuchi·Leo Matsuoka·Tomoyuki Horikiri
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Abstract

In this paper, we introduce a quantum walk whose local scattering at each vertex is denoted by a unitary circulant matrix; namely the circulant quantum walk. We also introduce another quantum walk induced by the circulant quantum walk; namely the optical quantum walk, whose underlying graph is a $2$-regular directed graph and obtained by blowing up the original graph in some way. We propose a design of an optical circuit which implements the stationary state of the optical quantum walk. We show that if the induced optical quantum walk does not have $+1$ eigenvalue, then the stationary state of the optical quantum walk gives that of the original circulant quantum walk. From this result, we give a useful condition for the setting of the circulant quantum walks which can be implemented by this optical circuit.

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Yusuke Mizutani, Etsuo Segawa, Yusuke Higuchi, Leo Matsuoka, Tomoyuki Horikiri. 2022-02-18. Design for implementation of discrete-time quantum walk with circulant matrix on graph by optical polarizing elements. https://doi.org/10.1103/physreva.106.022402

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