A Sequence of Quantum Gates

TL;DR

This paper investigates a sequence of quantum gates derived from eigenvectors of unitary operators and explores their associated Hamiltonians, introducing a hierarchy of gates via the Cayley transform.

Contribution

It presents a novel method of constructing quantum gate hierarchies from eigenvector sequences and Hamiltonians using the Cayley transform.

Findings

Established a new hierarchy of quantum gates

Connected eigenvector sequences to Hamiltonian operators

Applied Cayley transform to generate quantum gate sequences

Abstract

We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton operators is also given. From the Hamilton operators we construct another hierarchy of quantum gates via the Cayley transform.