Entanglement-efficient bipartite-distributed quantum computing

TL;DR

This paper introduces an entanglement-efficient protocol for distributed quantum computing that optimizes the use of entanglement resources by packing multiple nonlocal gates and employing heuristic algorithms based on graph representations.

Contribution

It extends existing protocols to pack multiple nonlocal gates with minimal entanglement, providing algorithms to optimize entanglement use in bipartite DQC.

Findings

Significant reduction in entanglement cost for bipartite DQC of unitary circuits.

Development of heuristic algorithms based on packing and conflict graphs.

Provision of a constructive upper bound on entanglement cost for quantum circuit DQC.

Abstract

In noisy intermediate-scale quantum computing, the limited scalability of a single quantum processing unit (QPU) can be extended through distributed quantum computing (DQC), in which one can implement global operations over two QPUs by entanglement-assisted local operations and classical communication. To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the protocol in [Eisert et. al., PRA, 62:052317(2000)] implementing each nonlocal controlled-unitary gate locally with one maximally entangled pair to a packing protocol, which can pack multiple nonlocal controlled-unitary gates locally using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks, namely the distributing processes and embedding processes. Each distributing process distributes corresponding gates locally with one entangled pair. The efficiency of entanglement is then enhanced by embedding processes, which merge two non-sequential distributing processes and hence save the entanglement cost. We show that the structure of distributability and embeddability of a quantum circuit can be fully represented by the corresponding packing graphs and conflict graphs. Based on these graphs, we derive heuristic algorithms for finding an entanglement-efficient packing of distributing processes for a given quantum circuit to be implemented by two parties. These algorithms can determine the required number of local auxiliary qubits in the DQC. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant reduction of entanglement cost through embeddings. This method can determine a constructive upper bound on the entanglement cost for the DQC of quantum circuits.