Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques

TL;DR

The paper addresses bringing quantum computing utility to realistic chemical problems by integrating quantum algorithms into multiscale, hybrid QM/MM workflows. It surveys environmental modeling via QM/MM and continuum solvation, two quantum embedding methods (PBE and DMET), and qubit-subspace techniques (Frozen Core, Qubit Tapering, Contextual Subspace) to reduce resource demands. A proof-of-concept demonstrates QSCI energy evaluations embedded in a QM/MM workflow for proton transfer in solvated water, reducing qubit counts to 16 on near-term hardware. The work argues that such hybrid, subspace-enabled quantum-classical approaches can deliver meaningful quantum advantages in chemistry before fault-tolerant devices arrive and outlines practical considerations for scaling and error mitigation.

Abstract

The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the workload to classical hardware where tractable, we may broaden the applicability of quantum computation in the near term. In this perspective, we review techniques that facilitate the study of subdomains of chemical systems with quantum computers and present a proof-of-concept demonstration of quantum-selected configuration interaction deployed within a multiscale/multiphysics simulation workflow leveraging classical molecular dynamics, projection-based embedding and qubit subspace tools. This allows the technology to be utilised for simulating systems of real scientific and industrial interest, which not only brings true quantum utility closer to realisation but is also relevant as we look forward to the fault-tolerant regime.

Figures (9)

• Figure 1: Multiscale simulation workflow for embedding quantum computational capabilities within a surrounding classical molecular dynamics environment. The workflow consists of several nested layers of abstraction. At the highest level, we identify some molecular target entity within a larger system; while the former is resolved via quantum mechanics (QM) methods, the latter is treated at the classical molecular mechanics (MM) level for computational tractability. Within the QM region, the molecule is further partitioned into an active subsystem and surrounding environment via projection-based embedding (PBE), allowing a subdomain to be treated at a higher level of QM theory, while the environment is rendered at the density functional theory (DFT) level. Finally, within the embedded QM subsystem we may deploy qubit subspace techniques to further reduce the qubit overhead to utilise near-term quantum hardware in large-scale molecular simulation workflows. This allows us to leverage quantum processing units (QPUs) integrated with high-performance computing (HPC) platforms. Sotorasib molecule in water solvent drawn with VMD VMD.
• Figure 2: Bond dissociation of perfluoromethane in STO-3G basis. In blue and pink are the whole-system Hartree-Fock and density functional theory (B3LYP). Orange gives the whole system CCSD energy. $\mu$-shift embedded CCSD-in-DFT energy is given by yellow squares, while purple crosses show the embedded FCI-in-DFT energy.
• Figure 3: Benzene (C6H6) STO-3G molecular orbital energies computed with the restricted Hartree-Fock method. The lowest twelve spin-orbitals may be frozen without dramatically affecting ground-state energy estimates.
• Figure 4: Discrete geometrical symmetries are described by abelian subgroups of the molecular point-group, consisting of rotations, reflections and inversions. For example, benzene (C6H6) belongs to $D_{6h}$, which consists of group elements $C_6$ ($60^{\circ}$ rotations around the central axis perpendicular to the plane of the molecule), $C_2/C_2^\prime$ ($180^{\circ}$ rotations through axes parallel to the molecular plane), a reflection $\sigma_{h}$ across the horizontal plane, two vertical reflections $\sigma_v/\sigma_d$, and finally the inversion symmetry $i$.
• Figure 5: Molecular hydrogen, H2 STO-3G, under the Jordan-Wigner transformation describes a noncontextual system with (a)$2$-clique compatibility graph and (b) noncontextual energy spectrum, whose minimum coincides with the FCI energy.