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Article overview
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Efficient quantum circuits for Szegedy quantum walks | T. Loke
; J.B. Wang
; | Date: |
1 Sep 2016 | Abstract: | A major advantage in using Szegedy’s formalism over discrete-time and
continuous-time quantum walks lies in its ability to define a unitary quantum
walk on directed and weighted graphs. In this paper, we present a general
scheme to construct efficient quantum circuits for Szegedy quantum walks that
correspond to classical Markov chains possessing transformational symmetry in
the columns of the transition matrix. In particular, the transformational
symmetry criteria do not necessarily depend on the sparsity of the transition
matrix, so this scheme can be applied to non-sparse Markov chains. Two classes
of Markov chains that are amenable to this construction are cyclic permutations
and complete bipartite graphs, for which we provide explicit efficient quantum
circuit implementations. We also prove that our scheme can be applied to Markov
chains formed by a tensor product. We also briefly discuss the implementation
of Markov chains based on weighted interdependent networks. In addition, we
apply this scheme to construct efficient quantum circuits simulating the
Szegedy walks used in the quantum Pagerank algorithm for some classes of
non-trivial graphs, providing a necessary tool for experimental demonstration
of the quantum Pagerank algorithm. | Source: | arXiv, 1609.0173 | Services: | Forum | Review | PDF | Favorites |
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