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arXiv:2409.06813 · Journal of Chemical Theory and Computation

Multiscale Embedding for Quantum Computing

Leah P. Weisburn, Minsik Cho, Moritz Bensberg, Oinam Romesh Meitei, Markus Reiher, Troy Van Voorhis

Published Apr 15, 2025• 19 citations
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Abstract

We present a novel multiscale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that facilitates BE calculations on extended systems using classical computers with limited memory resources. Benchmark data suggest the combination of these two strategies as a robust path in attaining the correlation energies of large realistic systems, combining the proven accuracy of BE with chemical and biological systems of interest in a lower computational cost method. Due to the flexible tunability of the resource requirements and systematic fragment construction, future developments in the realization of quantum computers naturally offer improved accuracy for multiscale BE calculations.

DOI
10.1021/acs.jctc.5c00241

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We present a novel multiscale embedding scheme that links conventional QM/MM embedding and bootstrap embedding (BE) to allow simulations of large chemical systems on limited quantum devices. We also propose a mixed-basis BE scheme that facilitates BE calculations on extended systems using classical computers with limited memory resources. Benchmark data suggest the combination of these two strategies as a robust path in attaining the correlation energies of large realistic systems, combining the proven accuracy of BE with chemical and biological systems of interest in a lower computational cost method. Due to the flexible tunability of the resource requirements and systematic fragment construction, future developments in the realization of quantum computers naturally offer improved accuracy for multiscale BE calculations.
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We present a multiscale workflow for coupling quantum computing algorithms for quantum chemical calculations with conventional High-Performance Computing (HPC) software. The resulting embedding framework, implemented in the multiscale computational chemistry environment ChemShell, combines a generic N-layer subtractive Quantum Mechanics/Molecular Mechanics (QM/MM) scheme and selection of an active orbital space for the quantum algorithm region. We have benchmarked the embedding models for gas phase and solvated molecules to understand the performance, benefits and current limitations of embedding quantum computing algorithms within a QM/MM model. We compare the performance of simulated Quantum Phase Estimation (QPE) calculations on an HPC cluster using Graphical Processing Units (GPUs) and Central Processing Units (CPUs).
Simulating strongly correlated molecular systems on near-term quantum hardware remains challenging because current hardware offers limited quantum volume and moderate-fidelity qubits. One way to address this challenge is through bootstrap embedding (BE). Bootstrap embedding partitions molecules into smaller fragments that are then embedded in the ``bath'' of other fragments iteratively. Bootstrap embedding is appealing for quantum simulation because fragmentation reduces the qubit requirements of each fragment problem. In this work, we develop a quantum bootstrap embedding (QBE) workflow that uses variational quantum eigensolver (VQE) fragment solvers and examines the algorithmic choices that determine the success of the overall VQE-QBE procedure. To improve efficiency, we introduce FastAdaptVQE, a sparse-matrix-accelerated form of the adaptive variational quantum eigensolver (ADAPT-VQE) that replaces symbolic commutator evaluation with direct statevector calculations, and MatrixFreeAdaptVQE, a matrix-free extension that removes the sparse-matrix memory bottleneck that arises for larger fragments. We also explore modifying the ADAPT-VQE operator-selection step by replacing the purely greedy choice with a lookahead strategy. Benchmarks on H4_44​, F2_22​, and selected geometries of H6_66​ reach chemical accuracy, within 1 kcal/mol of BE results obtained with a full configuration interaction (FCI) solver. For nnn-butane, density-matching residuals converged, but energy errors remained outside chemical accuracy. These results show that combining QBE with VQE can accurately compute molecular energies, while density convergence alone does not ensure energy accuracy. This work lays the foundation for extending these energy calculations to larger molecular systems and quantum materials on near-term quantum hardware.
We present a multiscale workflow for coupling quantum computing algorithms for quantum chemical calculations with conventional high-performance computing (HPC) software. The resulting embedding framework, implemented in the multiscale computational chemistry environment ChemShell, combines a generic N-layer subtractive quantum mechanics/molecular mechanics (QM/MM) scheme and selection of an active orbital space for the quantum algorithm region. We have benchmarked the embedding models for gas phase and solvated molecules to understand the performance, benefits and current limitations of embedding quantum computing algorithms within a QM/MM model. We compare the performance of simulated quantum phase estimation (QPE) calculations on an HPC cluster using graphical processing units (GPUs) and central processing units (CPUs).
Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [ J. Chem. Theory Comput. 2019, 15, 4497–4506; J. Phys. Chem. Lett. 2019, 10, 6368–6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O ( N 3 ) for the integral transform and O ( N ) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.