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Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuring M copies of a noisy state ρ. This enables us to estimate expectation values with respect to a state with dramatically reduced error ρ M/Tr (ρ M) without explicitly preparing it, hence the name “virtual distillation.” As M increases, this state approaches the closest pure state to ρ exponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant …