Neural Error Mitigation of Near-Term Quantum Simulations. (arXiv:2105.08086v1 [quant-ph])

One of the promising applications of early quantum computers is the
simulation of quantum systems. Variational methods for near-term quantum
computers, such as the variational quantum eigensolver (VQE), are a promising
approach to finding ground states of quantum systems relevant in physics,
chemistry, and materials science. These approaches, however, are constrained by
the effects of noise as well as the limited quantum resources of near-term
quantum hardware, motivating the need for quantum error mitigation techniques
to reduce the effects of noise. Here we introduce $textit{neural error
mitigation}$, a novel method that uses neural networks to improve estimates of
ground states and ground-state observables obtained using VQE on near-term
quantum computers. To demonstrate our method’s versatility, we apply neural
error mitigation to finding the ground states of H$_2$ and LiH molecular
Hamiltonians, as well as the lattice Schwinger model. Our results show that
neural error mitigation improves the numerical and experimental VQE computation
to yield low-energy errors, low infidelities, and accurate estimations of
more-complex observables like order parameters and entanglement entropy,
without requiring additional quantum resources. Additionally, neural error
mitigation is agnostic to both the quantum hardware and the particular noise
channel, making it a versatile tool for quantum simulation. Applying quantum
many-body machine learning techniques to error mitigation, our method is a
promising strategy for extending the reach of near-term quantum computers to
solve complex quantum simulation problems.



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