Genuinely noncyclic geometric gates in two-pulse schemes

TL;DR

This paper introduces a scheme for genuinely noncyclic geometric quantum gates that evolve along open geodesic paths, ensuring no dynamical phase is acquired, thus clarifying their geometric nature.

Contribution

It proposes a new method for constructing noncyclic geometric gates with open paths that eliminate dynamical phases from eigenstates, enhancing quantum gate design.

Findings

Scheme for noncyclic geometric gates using geodesic segments

Ensures no dynamical phase in eigenstates of the evolution

Extensible to multi-qubit and qudit systems

Abstract

While most approaches to geometric quantum computation is based on geometric phase in cyclic evolution, noncyclic geometric gates have been proposed to increase further the flexibility. While these gates remove the dynamical phase of the computational basis, they do not in general remove it from the eigenstates of the time evolution operator, which makes the geometric nature of the gates ambiguous. Here, we resolve this ambiguity by proposing a scheme for genuinely noncyclic geometric gates. These gates are obtained by evolving the computational basis along open paths consisting geodesic segments, and simultaneously assuring that no dynamical phase is acquired by the eigenstates of the time evolution operator. While we illustrate the scheme for the simplest nontrivial case of two geodesic segments starting at each computational basis state of a single qubit, the scheme can be straightforwardly extended to more elaborate paths, more qubits, or even qudits.