Quantum walks on Cayley graphs

Abstract

We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterise quantum walks on free groups and present partial results on more general cases. Some examples are given, including a family of quantum walks on the hypercube involving a Clifford Algebra.

J. Phys. A (accepted for publication)

References in corpus (6)

• A Quantum Random Walk Search Algorithm
• Quantum Walks driven by many coins
• Limit Theorem for Continuous-Time Quantum Walk on the Line
• Spacetime structures of continuous time quantum walks
• Slow transport by continuous time quantum walks
• Diffusive-ballistic crossover in 1D quantum walks

Cited by in corpus (9)

• Quantum walks: a comprehensive review
• Quantum walks with a one-dimensional coin
• Quantum walks defined by digraphs and generalized Hermitian adjacency matrices
• Conditional Probability Distributions of Finite Absorbing Quantum Walks
• Virtually Abelian Quantum Walks
• Simple derivation of the Weyl and Dirac quantum cellular automata
• Chirality from quantum walks without quantum coin
• Simulating Non Commutative Geometry with Quantum Walks
• Response to glassy disorder in coin on spread of quantum walker