Genuinely noncyclic geometric gates in two-pulse schemes

• While most approaches to geometric quantum computation are based on geometric phases 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 of 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.

Subject headings

NATURVETENSKAP  -- Fysik -- Atom- och molekylfysik och optik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Atom and Molecular Physics and Optics (hsv//eng)

Keyword

Quantum gates

geometric phase

Physics with spec. in Atomic, Molecular and Condensed Matter Physics

Fysik med inriktning mot atom- molekyl- och kondenserande materiens fysik

Publication and Content Type

ref (subject category)

art (subject category)