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Distributed quantum computation is often proposed to increase the scalabilityof quantum hardware, as it reduces cooperative noise and requisite connectivityby sharing quantum information between distant quantum devices. However, suchexchange of quantum information itself poses unique engineering challenges,requiring high gate fidelity and costly non-local operations. To mitigate this,we propose near-term distributed quantum computing, focusing on approximateapproaches that involve limited information transfer and conservativeentanglement production. We first devise an approximate distributed computingscheme for the time evolution of quantum systems split across any combinationof classical and quantum devices. Our procedure harnesses mean-fieldcorrections and auxiliary qubits to link two or more devices classically,optimally encoding the auxiliary qubits to both minimize short-time evolutionerror and extend the approximate scheme's performance to longer evolutiontimes. We then expand the scheme to include limited quantum informationtransfer through selective qubit shuffling or teleportation, broadening ourmethod's applicability and boosting its performance. Finally, we build uponthese concepts to produce an approximate circuit-cutting technique for thefragmented pre-training of variational quantum algorithms. To characterize ourtechnique, we introduce a non-linear perturbation theory that discerns thecritical role of our mean-field corrections in optimization and may be suitablefor analyzing other non-linear quantum techniques. This fragmented pre-trainingis remarkably successful, reducing algorithmic error by orders of magnitudewhile requiring fewer iterations.

Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits