On the role of entanglement in qudit-based circuit compression

TL;DR

This paper explores how using qudits instead of qubits can significantly reduce the complexity of quantum circuits, emphasizing the importance of entanglement and gate sets, with practical schemes for photonic and trapped-ion systems.

Contribution

It introduces principles and bounds for circuit compression using qudits and demonstrates potential advantages with experimental schemes for different quantum platforms.

Findings

Qudit encoding reduces multi-qubit circuit complexity.

Entanglement and gate set choices are crucial for optimization.

Experimental schemes show significant performance gains.

Abstract

Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the major experimental challenges since it requires controlled interactions between individual systems. To make the most of quantum hardware it is crucial to process information in the most efficient way. One promising avenue is to use higher-dimensional systems, qudits, as the fundamental units of quantum information, in order to replace a fraction of the qubit-entangling gates with qudit-local gates. Here, we show how the complexity of multi-qubit circuits can be lowered significantly by employing qudit encodings, which we quantify by considering exemplary circuits with exactly known (multi-qubit) gate complexity. We discuss general principles for circuit compression, derive upper and lower bounds on the achievable advantage, and highlight the key role played by entanglement and the available gate set. Explicit experimental schemes for photonic as well as for trapped-ion implementations are provided and demonstrate a significant expected gain in circuit performance for both platforms.