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arXiv · 2006.15788

Measurements of Quantum Hamiltonians with Locally-Biased Classical Shadows

Charles Hadfield·Sergey Bravyi·Rudy Raymond·Antonio Mezzacapo
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Abstract

Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer. We propose a novel estimator for this task, which is locally optimised with knowledge of the Hamiltonian and a classical approximation to the underlying quantum state. Our estimator is based on the concept of classical shadows of a quantum state, and has the important property of not adding to the circuit depth for the state preparation. We test its performance numerically for molecular Hamiltonians of increasing size, finding a sizable reduction in variance with respect to current measurement protocols that do not increase circuit depths.

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Charles Hadfield, Sergey Bravyi, Rudy Raymond, Antonio Mezzacapo. 2020-06-29. Measurements of Quantum Hamiltonians with Locally-Biased Classical Shadows. https://arxiv.org/abs/2006.15788

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