Entanglement-efficient bipartite-distributed quantum computing with entanglement-assisted packing processes

In noisy intermediate-scale quantum computing, the scalability of a quantum processor unit (QPU) is limited. The scalability of a single 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 (LOCC). To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the standard protocol implementing each single controlled-unitary gate with one maximally entangled pair [Eisert et. al., PRA, 62:052317(2000)] to a new protocol based on entanglement-assisted packing processes, which can implement multiple controlled-unitary gates using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks of entanglement-efficient DQC, namely the distributing processes and embedding processes. The efficiency of entanglement is 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 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. One can also set an upper limit on the local auxiliary qubits. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant entanglement reduction through embeddings. This method can be employed to determine a constructive upper bound on entanglement cost for a quantum circuit approaching its lower bound.Comment: 25+8 pages, 16+2 figure