STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Walks on the Hypercube
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On mixing in continuous-time quantum walks on some circulant graphs
Quantum Information & Computation
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Mixing and decoherence in continuous-time quantum walks on cycles
Quantum Information & Computation
Universal mixing of quantum walk on graphs
Quantum Information & Computation
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This paper give new observations on the mixing dynamics of a continuous-time quantumwalk on circulants and their bunkbed extensions. These bunkbeds are defined throughtwo standard graph operators: the join G + H and the Cartesian product G × H ofgraphs G and H. Our results include the following: (i) The quantum walk is average uniform mixing oncirculants with bounded eigenvalue multiplicity. This extends a known fact about thecycles Cn. (ii) Explicit analysis of the probability distribution of the quantum walk onthe join of circulants. This explains why complete partite graphs are not averageuniform mixing, using the fact Kn = K1 + Kn-1 and Kn....,n = Kn + ... + Kn.(iii)The quantum walk on the Cartesian product of a m-vertex path Pm and a circulantG, namely, Pm × G, is average uniform mixing if G is. This highlights a differencebetween circulants and the hypercubes Qn = P2 × Qn-1.Our proofs employ purely elementary arguments based on the spectra of the graphs.