Mapping quantum random walks onto a Markov chain by mapping a unitary transformation to a higher dimension of an irreducible matrix

• URL: http://arxiv.org/abs/2006.11090v5
• Date: Mon, 24 Aug 2020 18:30:42 GMT
• Title: Mapping quantum random walks onto a Markov chain by mapping a unitary transformation to a higher dimension of an irreducible matrix
• Authors: Arie Bar-Haim
• Abstract summary: A new process, discrete in time and space, yields the results of both a random walk and a quantum random walk. Results for a quantum random walk on infinite and finite lines are introduced.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0> in space without interference, instead of two coin states |1>, |0> .For the case of no boundary conditions, the model is similar to a Markov chain with a stochastic matrix, i.e., it conserves the population distribution of the four coin states, and by using a proper transformation, yield probability distributions of the two quantum states |1>, |0> in space, similar to a unitary operator. Numerical results for a quantum random walk on infinite and finite lines are introduced.

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