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

Jun-Yi WuKosuke MatsuiTim Forrer ...+4 Mio Murao
Dec 2022
In noisy intermediate-scale quantum computing, the scalability of a quantumprocessor unit (QPU) is limited. The scalability of a single QPU can beextended through distributed quantum computing (DQC), in which one canimplement global operations over two QPUs by entanglement-assisted localoperations and classical communication (LOCC). To facilitate this type of DQCin experiments, we need an entanglement-efficient protocol. To this end, weextend the standard protocol implementing each single controlled-unitary gatewith one maximally entangled pair [Eisert et. al., PRA, 62:052317(2000)] to anew protocol based on entanglement-assisted packing processes, which canimplement multiple controlled-unitary gates using one maximally entangled pair.In particular, two types of packing processes are introduced as the buildingblocks of entanglement-efficient DQC, namely the distributing processes andembedding processes. The efficiency of entanglement is enhanced by embeddingprocesses, which merge two non-sequential distributing processes and hence savethe entanglement cost. We show that the structure of distributability andembeddability of a quantum circuit can be fully represented by packing graphsand conflict graphs. Based on these graphs, we derive heuristic algorithms forfinding an entanglement-efficient packing of distributing processes for a givenquantum circuit to be implemented by two parties. These algorithms candetermine the required number of local auxiliary qubits in the DQC. One canalso set an upper limit on the local auxiliary qubits. We apply thesealgorithms for bipartite DQC of unitary coupled-cluster circuits and find asignificant entanglement reduction through embeddings. This method can beemployed to determine a constructive upper bound on entanglement cost for aquantum circuit approaching its lower bound.