Two dimensional quantum central limit theorem by quantum walks

• URL: http://arxiv.org/abs/2408.09578v1
• Date: Sun, 18 Aug 2024 19:35:51 GMT
• Title: Two dimensional quantum central limit theorem by quantum walks
• Authors: Keisuke Asahara, Daiju Funakawa, Motoki Seki, Akito Suzuki,
• Abstract summary: We investigate the weak limit theorem for a two-state discrete-time quantum walk on a two-dimensional square lattice. We derive a two-dimensional probability distribution whose support is the intersection of two ellipses. The distribution resembles the distribution of one-dimensional quantum walks while possessing a unique form specific to two dimensions.
• Score: 0.9499648210774584
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Quantum walks, mathematical models referred to as the quantum counterparts of random walks, have garnered significant attention in recent years with the advancement of quantum computing. The weak limit theorem for quantum walks, analogous to the central limit theorem for random walks, is one of the most important theorems in this field. In this study, we investigated the weak limit theorem for a two-state discrete-time quantum walk on a two-dimensional square lattice. As a result, we derived a two-dimensional probability distribution whose support is the intersection of two ellipses. The probability distribution we obtained resembles the distribution of one-dimensional quantum walks while possessing a unique form specific to two dimensions.

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