TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.4.180
TI  - NISQ algorithm for the matrix elements of a generic observable
PY  - 2023/10/30
UR  - https://scipost.org/SciPostPhys.15.4.180
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 4
SP  - 180
A1  - Erbanni, Rebecca
AU  - Bharti, Kishor
AU  - Kwek, Leong-Chuan
AU  - Poletti, Dario
AB  - The calculation of off-diagonal 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 off-diagonal 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.
ER  -

@Article{10.21468/SciPostPhys.15.4.180,
	title={{NISQ algorithm for the matrix elements of a generic observable}},
	author={Rebecca Erbanni and Kishor Bharti and Leong-Chuan Kwek and Dario Poletti},
	journal={SciPost Phys.},
	volume={15},
	pages={180},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.4.180},
	url={https://scipost.org/10.21468/SciPostPhys.15.4.180},
}