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

• URL: http://arxiv.org/abs/2202.09080v1
• Date: Fri, 18 Feb 2022 08:55:59 GMT
• Title: Design for implementation of discrete-time quantum walk with circulant matrix on graph by optical polarizing elements
• Authors: Yusuke Mizutani, Etsuo Segawa, Yusuke Higuchi, Leo Matsuoka, Tomoyuki Horikiri
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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