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Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers

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arxiv 1907.13117 v4 pith:TLNRAE7T submitted 2019-07-30 quant-ph physics.chem-ph

William J. Huggins , Jarrod McClean , Nicholas Rubin , Zhang Jiang , Nathan Wiebe , K. Birgitta Whaley , Ryan Babbush This is my paper · ORCID
classification quant-phphysics.chem-ph
keywords measurementquantumsystemsboundscircuitefficientelectronicerror
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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 non-local 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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Predicting Features of Quantum Systems from Very Few Measurements

    quant-ph 2019-08 accept novelty 8.0 of 10

    Random Clifford measurements produce a classical shadow of a quantum state that predicts M linear features using only O(log M) measurements, independent of system size, with a matching lower bound.

  2. Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States

    quant-ph 2019-08 conditional novelty 7.0 of 10

    All elements of a qubit k-RDM can be measured with O(3^k log^{k-1} N) circuits, and all elements of a fermionic 2-RDM with O(N^2) circuits, matching a new Ω(N^2) lower bound for Clifford measurements.

  3. Measurement reduction in variational quantum algorithms

    quant-ph 2019-08 conditional novelty 6.0 of 10

    Unitary partitioning can always group molecular electronic-structure Hamiltonian terms into O(N^3) anticommuting sets, reducing the VQE term count by a factor linear in the number of orbitals.

  4. $O(N^3)$ Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians

    quant-ph 2019-08 conditional novelty 5.0 of 10

    For Jordan-Wigner encoded molecular Hamiltonians, the O(N^4) Pauli terms partition into O(N^3) commuting families of size O(N), cutting VQE measurement cost to O(N^3).

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