Mapping a finite and an infinite Hadamard quantum walk onto a unique case of a random walk process

• URL: http://arxiv.org/abs/2011.08767v1
• Date: Tue, 17 Nov 2020 16:49:00 GMT
• Title: Mapping a finite and an infinite Hadamard quantum walk onto a unique case of a random walk process
• Authors: Arie Bar-Haim
• Abstract summary: A new model that maps a quantum random walk described by a Hadamard operator is presented. The model is represented by a Markov chain with a matrix. The probability distributions in space of the two quantum states |1>, |0> are revealed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are positive, although the Hadamard operator contains negative entries. Using a proper transformation that is applied to the random walk distribution after n steps, the probability distributions in space of the two quantum states |1>, |0> are revealed. These show that a quantum walk can be entirely mapped to a particular case of a higher dimension of a random walk model. The random walk model and its equivalence to a Hadamard walk can be extended for other cases, such as a finite chain with two reflecting points

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