Realizing nonadiabatic holonomic quantum computation beyond the three-level setting

TL;DR

This paper extends nonadiabatic holonomic quantum computation beyond three-level systems by enlarging the Hilbert space, enabling more efficient and flexible quantum gates, including qudit-based implementations, thus advancing quantum information processing.

Contribution

It introduces a novel approach to NHQC by enlarging the system's Hilbert space and using bipartite graph structures, enabling qudit-based NHQC and reducing gate durations.

Findings

Enhanced NHQC efficiency and reduced gate duration.

Implementation of qudit-based holonomic gates.

Improved robustness of quantum gates.

Abstract

Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level {\Lambda} systems have become the typical building block for NHQC and a number of NHQC schemes have been developed based on such systems. In this paper, we investigate the realization of NHQC beyond the standard three-level setting. The central idea of our proposal is to improve NHQC by enlarging the Hilbert space of the building block system and letting it have a bipartite graph structure in order to ensure purely holonomic evolution. Our proposal not only improves conventional qubit-based NHQC by efficiently reducing its duration, but also provides implementations of qudit-based NHQC. Therefore, our proposal provides a further development of NHQC that can contribute significantly to the physical realization of efficient quantum information processors.