The calculation of offdiagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and offdiagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian without explicitly preparing its eigenstates. By means of numerical simulations we show that this approach finds many of the matrix elements for the one and two qubits cases. Specifically, while in the first case, one can initialize the ansatz parameters over a broad interval, in the latter the optimization landscape can significantly slow down the speed of convergence and one should therefore be careful to restrict the initialization to a smaller range of parameters.
 Award ID(s):
 2013771
 NSFPAR ID:
 10284474
 Date Published:
 Journal Name:
 Frontiers in Physics
 Volume:
 9
 ISSN:
 2296424X
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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