Holonomic quantum manipulation in the Weyl Disk

TL;DR

This paper explores the potential of holonomic quantum manipulation within Weyl disks in superconducting nanostructures, demonstrating phase gate implementation and analyzing fidelity through numerical simulations.

Contribution

It provides a detailed analysis of holonomic manipulation in Weyl disks, including connection computation, gate design, and fidelity assessment with numerical methods.

Findings

The connection in the Weyl disk is Abelian and suitable for phase gates.

A complete quantum manipulation protocol including state preparation and read-out is proposed.

Numerical simulations show high fidelity for certain gate execution times.

Abstract

It has been shown that a Weyl point in a superconducting nanostructure may give rise to a Weyl disk where two quantum states are almost degenerate in a 2D manifold in the parametric space. This opens up the possibility of a holonomic quantum manipulation: a transformation of the wave function upon adiabatic change of the parameters within the degenerate manifold. In this paper, we investigate in detail the opportunities for holonomic manipulation in Weyl disks. We compute the connection at the manifold in quasiclassical approximation to show it is Abelian and can be used for a phase gate. To provide a closed example of quantum manipulation that includes a state preparation and read-out, we augment the holonomic gate with a change of parameters that brings the system out of the degenerate subspace. For numerical illustrations, we use a finite value of quasiclassical parameter and exact quantum dynamics. We investigate the fidelity of an example gate for different execution times.