Maturity of QC/QM/MM embedding methodology

Resolve the active-space, embedding-boundary, polarisation, coupling, convergence, measurement-overhead, and resource-estimation issues required for quantum-computing/quantum-mechanics/molecular-mechanics (QC/QM/MM) calculations to become a mature methodology.

Background

QC/QM/MM methods embed a small, strongly correlated quantum-computed region within quantum-mechanical and molecular-mechanical regions evaluated on classical high-performance computers. This architecture is intended to make realistic chemical systems accessible while concentrating quantum resources on the most demanding local region.

The paper explicitly lists unresolved requirements for methodological maturity: selecting the active space and its boundary, controlling boundary artefacts, treating polarisation and electrostatic response, coupling and converging the quantum and classical layers, handling measurement costs, and estimating the total hybrid resource requirements.

References

These studies collectively suggest that combining quantum-derived active-space wave functions with classical correlation treatments provides a promising route toward chemically accurate simulations. However, previous demonstrations have been restricted primarily to relatively small molecular systems, leaving its applicability to realistic catalytic problems unresolved.

— Tailored coupled cluster method with sample-based quantum diagonalization: Application to titanium-based metallocene catalytic reactions for 1-hexene production  (2609.16558 - Lin et al., 15 Sep 2026) in Introduction

Several issues nonetheless remain unresolved before QC/QM/MM can be considered a mature methodology: the principles for selection of the active space and of its boundary with the surrounding QM/MM region; errors introduced at that embedding boundary, including truncation and basis-set artefacts; treatment of polarisation and electrostatic response between the quantum algorithm, HPC QM, and HPC MM layers; the scheme used to couple the quantum and classical layers, and its convergence; the measurement overhead required to extract energies, gradients, or properties from the quantum layer at each optimisation or dynamics step; and resource estimation for hybrid HPC-QC calculations, including scaling of the individual component calculations.

— Scientific applications of quantum computing: challenges and opportunities  (2608.16568 - Camino et al., 17 Aug 2026) in Section 3, HPC and QC to tackle calculations on realistic chemical systems

The dependence of $E\text{A-B}_\text{nad}$ on the relaxed density $\gamma\text{A}_\text{emb}$ is generally unknown.

— Iterative Projection-Based Embedding Scheme Combined with Variational Quantum Eigensolver  (2608.19715 - Choi et al., 20 Aug 2026) in Section 2.1, following Eq. (4)