Scalability of quantum error mitigation techniques: from utility to advantage
arxiv(2024)
摘要
Error mitigation has elevated quantum computing to the scale of hundreds of
qubits and tens of layers; however, yet larger scales (deeper circuits) are
needed to fully exploit the potential of quantum computing to solve practical
problems otherwise intractable. Here we demonstrate three key results that pave
the way for the leap from quantum utility to quantum advantage: (1) we present
a thorough derivation of random and systematic errors associated to the most
advanced error mitigation strategies, including probabilistic error
cancellation (PEC), zero noise extrapolation (ZNE) with probabilistic error
amplification, and tensor-network error mitigation (TEM); (2) we prove that TEM
(i) has the lowest sampling overhead among all three techniques under realistic
noise, (ii) is optimal, in the sense that it saturates the universal lower cost
bound for error mitigation, and (iii) is therefore the most promising approach
to quantum advantage; (3) we propose a concrete notion of practical quantum
advantage in terms of the universality of algorithms, stemming from the
commercial need for a problem-independent quantum simulation device. We also
establish a connection between error mitigation, relying on additional
measurements, and error correction, relying on additional qubits, by
demonstrating that TEM with a sufficient bond dimension works similarly to an
error correcting code of distance 3. We foresee that the interplay and
trade-off between the two resources will be the key to a smooth transition
between error mitigation and error correction, and hence between near-term and
fault-tolerant quantum computers. Meanwhile, we argue that quantum computing
with optimal error mitigation, relying on modest classical computer power for
tensor network contraction, has the potential to reach larger scales in
accurate simulation than classical methods alone.
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