Parameterization of quantum walks on cycles

Abstract

This study investigate the unitary equivalence classes of quantum walks on cycles. We show that unitary equivalence classes of quantum walks on a cycle with $N$ vertices are parameterized by $2N$ real parameters. Moreover, the ranges of two of the parameters are restricted, and the ranges depend on the parity of $N$.

12 pages

References in corpus (1)

• Unitary Equivalence of Quantum Walks

Cited by in corpus (1)

• The Witten Index for One-dimensional Non-unitary Quantum Walks with Gapless Time-evolution