Network-assisted collective operations for efficient distributed quantum computing

TL;DR

This paper introduces a scalable method for distributing collective quantum operations across remote quantum processors using pre-shared entanglement and local operations, improving efficiency over traditional entanglement swapping methods.

Contribution

It proposes a novel scheme leveraging distributed fan-out operations for efficient collective quantum gates in network architectures, reducing entanglement overhead.

Findings

General diagonal gates can be distributed with bounded ebit cost.

Single multicontrolled gate distribution requires only one Bell pair more than the optimal.

Distributed Grover's search shows linear Bell pair growth with iterations.

Abstract

Distributed quantum computing relies on coordinated operations between remote quantum processing units (QPUs), yet most existing work either assumes full connectivity, unrealistic for large networks, or relies on entanglement swapping. To mitigate the overhead of communication, we propose a scheme for the distribution of collective quantum operations among remote quantum processing units by exploiting distributed fan-out operations to a central node in network architectures similar to those used for high-performance computing, which requires only pre-shared entanglement, local operations and classical communication. We show that a general diagonal gate can be distributed among any number of nodes and provide the ebit cost bounds. For a single distributed multicontrolled gate, this amounts to a single additional Bell pair over the theoretically optimal calculation with all-to-all pre-shared entanglement, demonstrating better scalability when compared to current proposals based on entanglement swapping through a network. We provide a recipe for the lumped distribution of gates such as arbitrarily-sized Toffoli and multicontrolled Z, and $R_{zz}(\theta)$ gates. Finally, we provide an exact implementation of a distributed Grover's search algorithm using this protocol to partition the circuit, with Bell pair cost growing linearly with the number of Grover iterations and the number of partitions, and show how these techniques can be applied to other algorithms such as QAOA. Our results show that alternative approaches to entanglement swapping can provide major benefits in distributed quantum computing, pointing to promising avenues for future research.