Virtual entanglement purification via noisy entanglement

Distributed quantum computation (DQC) is a promising approach for scalable quantum computing, where high-fidelity non-local operations among remote devices are required for universal quantum computation. These operations are typically implemented through state and gate teleportation with the consumption of high-fidelity entanglement prepared via entanglement purification. However, noisy local operations and classical communication (LOCC) limit the fidelity of purified entanglement, thereby degrading the quality of non-local operations. Meanwhile, circuit knitting and cutting, which simulate non-local operations by preparing separable states along with LOCC, has been considered for DQC as an alternative. Although this approach needs no entanglement among remote devices, it requires excessive circuit runs. Here, we present a protocol utilizing virtual operations that purifies noisy entanglement at the level of expectation values. Our protocol offers the following advantages over conventional methods: surpasses the fidelity limit of entanglement purification in the presence of noise in LOCC, requires fewer sampling shots than circuit knitting, and exhibits robustness against infidelity fluctuations in shared noisy Bell states, unlike probabilistic error cancellation. Our protocol bridges the gap between the entanglement-based and circuit-knitting DQC methods, offering a flexible approach to achieve further scalability despite hardware limitations.