Complex Hadamard Matrices, Instantaneous Uniform Mixing and Cubes

2013/05/24 by Ada Chan, Chan, Ada · 2 citations
Computer Science · #Combinatorics (math.CO) #FOS: Mathematics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.1305.5811

openalex publication_date 2013/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the continuous-time quantum walks on graphs in the adjacency algebra of the n-cube and its related distance regular graphs. For k≥ 2, we find graphs in the adjacency algebra of (2^k+2-8)-cube that admit instantaneous uniform mixing at time π/2^k and graphs that have perfect state transfer at time π/2^k. We characterize the folded n-cubes, the halved n-cubes and the folded halved n-cubes whose adjacency algebra contains a complex Hadamard matrix. We obtain the same conditions for the characterization of these graphs admitting instantaneous uniform mixing.

Citations

• Quantum computation and decision trees

Cited by

• Uniform mixing in continuous-time quantum walks on oriented, nonabelian Cayley graphs
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