Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers

By William J. Huggins, Jarrod R. McClean, N. Rubin, Zhang Jiang, Nathan Wiebe, Birgitta Whaley, Ryan Babbush. npj Quantum Information, 2019

300 citations recorded by the source corpus.

Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of these techniques to larger molecules might be infeasible. We present a measurement strategy based on a low-rank factorization of the two-electron integral tensor. Our approach provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems we consider. Although our technique requires execution of a linear-depth circuit prior to measurement, this is compensated for by eliminating challenges associated with sampling nonlocal Jordan–Wigner transformed operators in the presence of measurement error, while enabling a powerful form of error mitigation based on efficient postselection. We numerically characterize these benefits with noisy quantum circuit simulations for ground-state energies of strongly correlated electronic systems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/64ee64016dc5fbc67c171ad33df0526af872753b

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Citations in the corpus

Information-theoretic bounds on quantum advantage in machine learning (2021, background): “muting observables [30,31]; See the Supplemental Material, App.”
Quantum error mitigation (2022, methodology): “As discussed above, we can greatly simplify the measurement circuit through post-processing, but this will come at a higher sampling overhead, which scales as Cai, 2021c; Huggins et al. , 2021b).”
qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor (2019, methodology): “…to obtain the gradient at each iteration; the number of these measurements is roughly equal to the size of the pool times the number of terms in the Hamiltonian [31], although the number of measurements needed to compute the mean energy can be decreased using recently developed techniques [32, 33].”
Variational quantum algorithms (2020, methodology): “For using VQE on fermionic systems, this scaling can actually be brought down to either quadratic or, for simpler cases even linear in n [193].”