Unitary equivalence of quantum walks

Akihiro Narimatsu, Hiromichi Ohno, Kazuyuki Wada

Akihiro Narimatsu, Hiromichi Ohno, Kazuyuki Wada

This study investigates the unitary equivalence of split-step quantum walks (SSQW). We consider a new class of quantum walks which includes all SSQWs. We show the explicit form of quantum walks in this class, and clarify their unitary equivalence classes. Unitary equivalence classes of Suzuki's SSQW are also given.

Sanjeev Naguleswaran, Ian Fuss, Lang White

Hiromichi Ohno

This study investigated the unitary equivalence classes of one-dimensional quantum walks with and without initial states. We determined the unitary equivalence classes of one-dimensional quantum walks, two-phase quantum walks with one defect, complete two-phase quantum walks, one-dimensional quantum walks with one defect and translation-invariant one-dimensional quantum walks.

Jenia Rousseva, Yevgeniy Kovchegov

Shuji Kuriki, Md Sams Afif Nirjhor, Hiromichi Ohno

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 $N$.