Quantum computational quantification of protein–ligand interactions

Abstract

We have demonstrated a prototypical hybrid classical and quantum computational workflow for the quantification of protein-ligand interactions. The workflow combines the density matrix embedding theory (DMET) embedding procedure with the variational quantum eigensolver (VQE) approach for finding molecular electronic ground states. A series of β -secretase (BACE1) inhibitors is rank-ordered using binding energy differences calculated on the latest superconducting transmon (IBM) and trapped-ion (Quantinuum) noisy intermediate scale quantum (NISQ) devices. This is the first application of real quantum computers to the calculation of protein-ligand binding energies. The results shed light on hardware and software requirements which would enable the application of NISQ algorithms in drug design. | INTRODUCTIONThe advent of quantum mechanics at the turn of the 20th century changed the way we look at the physical sciences. For chemistry, the implications were profound, as Dirac famously noted: "the fundamental laws … for the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved" [1]. Indeed, calculations of accurate solutions of the electronic Schrödinger equation, such as the full configuration interaction method (FCI), of molecules scale exponentially with the number of atoms [2], rendering them applicable only to the smallest systems. Practical approximations to FCI, such as, for example, CCSD(T) [3], touted as computational chemistry's gold standard, do exist, but their applicability is limited: single-reference methods like CCSD(T) fail for strongly correlated ("multireference") systems and the formal scaling of CCSD(T) with system size is O(N 7 ), rendering it useful only for relatively small molecules. While the scaling limitation of CCSD(T) can be dramatically reduced via localized methods such as DLPNO [4] at the expense of accuracy, FCI-based methods for strongly correlated systems scale exponentially with the number of correlated electrons and, even for systems small enough to be tractable, require expert knowledge to be applied. Emerging approaches for strongly correlated systems, such as DMRG [5] and selected CI [6] can achieve results close to FCI at lower cost, thereby extending the limit to about 100 orbitals. In most cases, the correlated method is applied to an active space of selected orbitals, the choice of which has traditionally been arbitrary but can also be performed by automated procedures [7,8]. On the other hand, mean-field methods, such as Hartree-Fock (HF) and density functional theory (DFT), which either dispense with electron correlation completely or treat it in an approximate, implicit manner, are routinely applied to organic and inorganic systems of sizes up to few hundred atoms. This is possible due to their relatively low, O N 3 -O N 4 À Á , formal scaling, which could be reduced even to O N ð Þ in approximate implementations for systems comprised of thousands of atoms...

Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications

“…131 Energy-weighted DMET 132 and Gutzwiller variational embedding 133 approaches have been tested on current quantum processors. Pharmaceutical model systems have also been studied, including a study of protein− ligand interactions using DMET 134 and our own work on a multilayer embedding approach. 135 6.2.…”

Quantum computing in pharma: A multilayer embedding approach for near future applications

“…As classical force fields have difficulty in treating the latter accurately, QM/MM methods are typically used to characterize such reactions and as some of these involve strong correlation, quantum computing may be especially useful in this context. A quantum computational study of protein–ligand interactions using DMET has already been carried out recently 110 . In the following, we will illustrate how an active space can be selected for a specific enzyme reaction and use the embedding treatment developed above for the environment.…”

“…A quantum computational study of protein-ligand interactions using DMET has already been carried out recently. 110 In the following, we will illustrate how an active space can be selected for a specific enzyme reaction and use the embedding treatment developed above for the environment. The smallest meaningful active space will be selected, so that the calculation will actually reflect what is possible or nearly possible on today's quantum computers.…”

Large-Scale Simulation of Quantum Computational Chemistry on a New Sunway Supercomputer

“…14. Here by using the "frozen protein" approximation [55] to remove the protein-protein interactions, we use E b = E ligand in protein − E ligand to get the binding energy E b , which is then used as the metric for ranking. We use the geometries of the 13 neutral ligands from Ref.…”