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Perfect State Transfer in Quantum Walks on Graphs

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We provide a brief survey of perfect state transfer in quantum walks on finite graphs. The ability to transfer a quantum state from one part of a quantum computer to another is a key ingredient of scalable architectures. Transfer through structures that do not require locally varying dynamic control simplifies the design and hence reduces the opportunities for errors to arise. Continuous time walks quantum walks on highly structured graphs exhibit perfect state transfer for the complete graph of size 2, the path of length 3, and the cycle of size 4. From these, larger graphs can be constructed, and the use of edge weights widens this set considerably. Discrete-time quantum walks have more flexibility through exploiting the coin degrees of freedom, but with the disadvantage that local control of the coin is required if the degree of the vertices varies. The closely related property of periodicity (exact return to the starting state) is also mentioned.
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Keywords: QUANTUM COMPUTATION; QUANTUM TRANSPORT; QUANTUM WALKS

Document Type: Review Article

Publication date: 2011-03-01

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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