Abstract
Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties of molecular and condensed matter systems. The quality of this procedure is based on accurate electronic structure calculations. The development of quantum processors has shown great potential for the efficient evaluation of accurate ground and excited state energies of molecular systems, opening up new avenues for molecular dynamics simulations. In this work we address the use of variational quantum algorithms for the calculation of accurate atomic forces to be used in AIMD. In particular, we provide solutions for the alleviation of the statistical noise associated to the measurements of the expectation values of energies and forces, as well as schemes for the mitigation of the hardware noise sources (in particular, gate infidelities, qubit decoherence and readout errors). Despite the relative large error in the calculation of the potential energy, our results show that the proposed algorithms can provide reliable MD trajectories in the microcanonical (constant energy) ensemble. Further, exploiting the intrinsic noise arising from the quantum measurement process, we also propose a Langevin dynamics algorithm for the simulation of canonical, i.e., constant temperature, dynamics. Both algorithms (microcanonical and canonical) are applied to the simulation of simple molecular systems such as H2 and H3+. Finally, we also provide results for the dynamics of H2 obtained with IBM quantum computer ibmq_athens.
Highlights
Quantum computing is emerging as a new computational paradigm for the solution, among others, of quantum mechanical many-body problems
While the quantum algorithms for electronic structure calculation show a favorable scaling comparing to the equivalent classical algorithms, their simulation with classical computers is far from efficient, especially when the classical calculation aims at reproducing the quantum variational approach, i.e., the variational quantum eigensolver (VQE) optimization as it would be implemented in a quantum computer
To validate our approach in the case of geometry optimization and microcanonical molecular dynamics (MD) simulations, we provide a solution obtained using the matrix representation (MR) of the Hamiltonian and its direct diagonalization (Exact) to obtain the ground state energy and the corresponding eigenvector
Summary
Quantum computing is emerging as a new computational paradigm for the solution, among others, of quantum mechanical many-body problems. In addition to the calculation of energies, quantum algorithms can provide an efficient solution to the calculation of the ab initio forces on the classical, pointlike, atomic particles These are of particular importance for the calculation of optimized molecular structures (through annealing) as well as to perform molecular dynamics (MD) in the different thermodynamic ensembles. We make use of the intrinsic statistical noise in evaluating quantum observables in a quantum computer to perform generalized Langevin dynamics [31,32] at constant (nonzero) temperature Both approaches are applied to the simulation of the dynamics of simple molecular systems such as H2 and H3+.
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