46 citations · 73 across the 17 of their papers we have counts for
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math.SP2017★ 2 cited
Up and down grover walks on simplicial complexes
Xin Luo, Tatsuya Tate
A notion of up and down Grover walks on simplicial complexes are proposed and their properties are investigated. These are abstract Szegedy walks, which is a special kind of unitar…
math.FA2017
Eigenvalues of quantum walks of Grover and Fourier types
Takashi Komatsu, Tatsuya Tate
A necessary and sufficient conditions for certain class of periodic unitary transition operators to have eigenvalues are given. Applying this, it is shown that Grover walks in any…