Dark path holonomic qudit computation

TL;DR

This paper extends dark path holonomic quantum computation from qubits to qudits, demonstrating universal gates and efficient implementation of diagonal qudit gates with linear scaling in the number of loops.

Contribution

It introduces a method for qudit holonomic quantum computation using dark paths, showing universality and efficient diagonal gate implementation across dimensions.

Findings

Demonstrated one- and two-qudit universal gates.

Established linear scaling of loop number with qudit dimension.

Showed efficient implementation of diagonal qudit gates.

Abstract

Non-adiabatic holonomic quantum computation is a method used to implement high-speed quantum gates with non-Abelian geometric phases associated with paths in state space. Due to their noise tolerance, these phases can be used to construct error resilient quantum gates. We extend the holonomic dark path qubit scheme in [M.-Z. Ai {\t et al.}, Fundam. Res. {\bf 2}, 661 (2022)] to qudits. Specifically, we demonstrate one- and two-qudit universality by using the dark path technique. Explicit qutrit ($d=3$) gates are demonstrated and the scaling of the number of loops with the dimension $d$ is addressed. This scaling is linear and we show how any diagonal qudit gate can be implemented efficiently in any dimension.