Measurements of Quantum Hamiltonians with Locally-Biased Classical Shadows

• URL: http://arxiv.org/abs/2006.15788v1
• Date: Mon, 29 Jun 2020 03:08:03 GMT
• Title: Measurements of Quantum Hamiltonians with Locally-Biased Classical Shadows
• Authors: Charles Hadfield, Sergey Bravyi, Rudy Raymond, Antonio Mezzacapo
• Abstract summary: 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.
• Score: 6.434709790375755
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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