Sergey Bravyi, Guillaume Duclos-Cianci, et al.
Quantum Information and Computation
Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of quantum 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.
Sergey Bravyi, Guillaume Duclos-Cianci, et al.
Quantum Information and Computation
Masayasu Muraoka, Tetsuya Nasukawa, et al.
WWW 2020
Sergey Bravyi, David Gosset, et al.
FOCS 2019
Sergey Bravyi, David Gosset, et al.
Physical Review Letters