Efficient calculation of nuclear forces on noisy intermediate-scale quantum computers

Accurate nuclear forces are required to simulate the movement of atoms and molecules over time, an essential computational tool for drug discovery. 

However, most current quantum computing algorithms only focus on determining an accurate estimate of the ground state energy. In contrast to the ground state problem, calculating the nuclear forces of N_a atoms requires to estimate 3N_a expectation values of operators which do not commute with the Hamiltonian. 

In this talk, we show how to use noisy intermediate-scale quantum (NISQ) computers to extract nuclear forces and optimize the number of required samples from the quantum computer by using basis rotation groupings, importance sampling and fermionic shadows. We perform numerical simulations on hydrogen chains and water clusters, compare our findings to the cost of measuring the ground state energy and discuss the consequences of our results for quantum-enhanced molecular dynamics simulations.