Universal quantum computing with qubits embedded in trapped-ion qudits

TL;DR

This paper proposes a method for implementing quantum circuits with qubits embedded in qudits of dimensions 3 to 8 on trapped-ion platforms, enabling scalable quantum computing without increasing physical carriers.

Contribution

It introduces a compilation technique for quantum circuits using qudits in trapped-ion systems, utilizing single-qudit operations and the Molmer-Sorensen gate for multi-qubit gates.

Findings

Method for compiling quantum circuits with qudits of dimensions 3-8.

Demonstration of implementing single-qubit, two-qubit, and multiqubit gates.

Applicability to trapped-ion-based qudit quantum processors.

Abstract

Recent developments in qudit-based quantum computing, in particular with trapped ions, open interesting possibilities for scaling quantum processors without increasing the number of physical information carriers. In this work, we propose a method for compiling quantum circuits in the case, where qubits are embedded into qudits of experimentally relevant dimensionalities, $d=3,\ldots,8$, for the trapped-ion platform. In particular, we demonstrate how single-qubit, two-qubit, and multiqubit gates can be realized using single-qudit operations and the Molmer-Sorensen (MS) gate as a basic two-particle operation. We expect that our findings are directly applicable to trapped-ion-based qudit processors.