3-state Grover and Fourier quantum walks on C_N have finite period only for N=3 (T_3=6 and 12), via a cyclotomic field method that gives a necessary condition on coin operators.
Full state revivals in higher dimensional quantum walks
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abstract
Full state revivals in a quantum walk can be viewed as returning of the walker to the initial quantum state in a periodic fashion during the propagation of the walk. In this paper we show that for any given number of spatial dimensions, a coin operator can be constructed to generate a quantum walk having full revivals with any desired period. From the point of view of quantum computation and simulations, these coin operators can be useful in implementing quantum walks which oscillate between any two states with a finite periodicity.
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quant-ph 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Periodicity for the 3-state quantum walk on cycles
3-state Grover and Fourier quantum walks on C_N have finite period only for N=3 (T_3=6 and 12), via a cyclotomic field method that gives a necessary condition on coin operators.