An effective Hamiltonian approach to quantum random walk

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• 作者：DEBAJYOTI SARKAR ; NILADRI PAUL ; KAUSHIK BHATTACHARYA ; TARUN KANTI GHOSH
• 关键词：Quantum information ; quantum random walk ; quantum computation
• 刊名：Pramana
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：88
• 期：3
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics, general; Astronomy, Observations and Techniques; Astrophysics and Astroparticles;
• 出版者：Springer India
• ISSN：0973-7111
• 卷排序：88

文摘

In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep.3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.