Symmetry of distribution for the one-dimensional Hadamard walk
Norio Konno, Takao Namiki, Takahiro Soshi
TL;DR
This paper investigates the symmetry properties of the probability distribution in a one-dimensional quantum walk using the Hadamard transformation, providing insights into its distributional behavior.
Contribution
It introduces a transition matrix approach to analyze the symmetry of the Hadamard walk's probability distribution, offering new theoretical insights.
Findings
Symmetry conditions for the Hadamard walk distribution
Construction of a transition matrix for the quantum walk
Results on distributional symmetry in quantum walks
Abstract
In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetry of probability distributions for the Hadamard walk.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications