Qudits and high-dimensional quantum computing

TL;DR

This paper reviews the development and implementation of qudit-based quantum computing, highlighting its advantages over qubits, including larger state space and simplified circuits, with discussions on gates, algorithms, and physical realizations.

Contribution

It provides a comprehensive overview of qudit quantum computing, covering theoretical gates, algorithms, and experimental platforms, which is a significant expansion beyond qubit-focused research.

Findings

Qudit gates include pi/8, SWAP, and multi-level-controlled gates.

Qudit algorithms like Deutsch-Jozsa, Fourier transform, and phase estimation are adapted.

Physical implementations include photonic, ion traps, and NMR platforms.

Abstract

Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity, simplification of the experimental setup and enhancement of the algorithm efficiency. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. We first discuss the qudit gate universality and a variety of qudit gates including the pi/8 gate, the SWAP gate, and the multi-level-controlled gate. We then present the qudit version of several representative quantum algorithms including the Deutsch-Jozsa algorithm, the quantum Fourier transform, and the phase estimation algorithm. Finally we discuss various physical realizations for qudit computation such as the photonic platform, iron trap, and nuclear magnetic resonance.