On the role of entanglement in qudit-based circuit compression

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 or-der to replace a fraction of the qubit-entangling gates with quditlocal 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 trappedion implementations are provided and demonstrate a significant expected gain in circuit performance for both platforms.

Automated summary

Gate-based universal quantum computation involves two types of operations: local single-qubit gates and two-qubit entangling gates. The complexity of multi-qubit circuits can be lowered by using higher-dimensional systems for encoding. We discuss the principles of circuit compression, derive bounds on the achievable advantage, and provide experimental schemes to demonstrate improved circuit performance.