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Absorption problems for quantum walks in one dimension

Norio Konno·Takao Namiki·Takahiro Soshi·Aidan Sudbury
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Abstract

This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N is finite or infinite by using a new path integral approach based on an orthonormal basis P, Q, R and S of the vector space of complex 2 times 2 matrices. Our method studied here is a natural extension of the approach in the classical random walk.

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Norio Konno, Takao Namiki, Takahiro Soshi, Aidan Sudbury. 2003-02-07. Absorption problems for quantum walks in one dimension. https://doi.org/10.1088/0305-4470%2F36%2F1%2F316

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