Towards the Simulation of Large Scale Protein-Ligand Interactions on NISQ-era Quantum Computers

Abstract

We explore the use of symmetry-adapted perturbation theory (SAPT) as a simple and efficient means to compute interaction energies between large molecular systems with a hybrid method combing NISQ-era quantum and classical computers. From the one-and two-particle reduced density matrices of the monomer wavefunctions obtained by the variational quantum eigensolver (VQE), we compute SAPT contributions to the interaction energy [SAPT(VQE)]. At first order, this energy yields the electrostatic and exchange contributions for non-covalently bound systems. We empirically find from ideal statevector simulations that the SAPT(VQE) interaction energy components display orders of magnitude lower absolute errors than the corresponding VQE total energies. Therefore, even with coarsely optimized low-depth VQE wavefunctions, we still obtain sub kcal/mol accuracy in the SAPT interaction energies. In SAPT(VQE), the quantum requirements, such as qubit count and circuit depth, are lowered by performing computations on the separate molecular systems. Furthermore, active spaces allow for large systems containing thousands of orbitals to be reduced to a small enough orbital set to perform the quantum portions of the computations. We benchmark SAPT(VQE) (with the VQE component simulated by ideal state-vector simulators) against a handful of small multi-reference dimer systems and the iron center containing human cancer-relevant protein lysine-specific demethylase 5 (KDM5A).

Quantum Computational Quantification of Protein-Ligand Interactions

“…Our approach differs significantly from that of Malone et al [24], who also used quantum computation to estimate protein-ligand binding energies. Their simulations were, however, performed on a classical quantum emulator.…”

“…Variational Quantum Eigensolver (VQE) quantum simulations of 6 small molecules and a subsection of the KDM5A protein were performed on a state-vector emulator to estimate their 1and 2-electron reduced density matrices, which were then employed in a classical SAPT (1) calculation. However computed interaction energies did not reproduce ligand rankings yielded by more accurate 2 nd order SAPT calculations, due to the missing induction and dispersion components in the 1 st order approximation [24].…”

“…Recently, Malone et al presented an attempt to utilise quantum computing to compute protein-ligand binding energies, via a 1st order Symmetry Adapted Perturbation Theory (SAPT) procedure [24]. Variational Quantum Eigensolver (VQE) quantum simulations of 6 small molecules and a subsection of the KDM5A protein were performed on a state-vector emulator to estimate their 1and 2-electron reduced density matrices, which were then employed in a classical SAPT (1) calculation.…”

The Variational Quantum Eigensolver: a review of methods and best practices

“…This could be as simple as ensuring that basis sets are sufficiently saturated [86], or that the complexity of the interactions with a wider system were sufficiently resolved. For instance, consider computing the energy of a series of protein-ligand complexes (for which methods extending VQE have already been proposed [121,122]): even if the VQE achieves better accuracy in lower computation time, it is not guaranteed that these accuracy gains lead to a practical advantage. For example, the accuracy gains may still be insufficient to predict the most appropriate ligand in a physical experiment due to the approximations in the treatment of the environment in the Hamiltonian.…”

Efficient quantum computation of molecular forces and other energy gradients

“…This covers highly diverse applications such as the description of heterogeneous processes on surfaces including catalysis [29], observation of phase transitions, such as nucleation processes for water [30], and maybe of highest importance for pharmaceutical research, the interaction of drugs with their targets in the human body [31]. By free energy calculations based on MD simulations, these interactions can be quantified, allowing the prediction of compound affinities [32,33], which are eventually linked to therapeutic doses. Beyond that, MD simulations of drug-target systems enable the observation of conformational changes of the target.…”