Distributed Quantum-Centric Supercomputing with Multi-Layered Generative Learning for Intermolecular Interactions

Abstract

Quantum-centric supercomputing (QCSC) approaches, such as sample-based quantum diagonalization (SQD), combine quantum processors with high-performance computers (HPC), offering a promising route toward solving challenging electronic structure problems. However, implementation of QCSC approaches to large active space calculations is constrained by the associated number of qubits, deep quantum circuits, sampling cost, and large-scale Hamiltonian diagonalization. To overcome these limitations, we introduce a distributed QCSC framework that decomposes complex molecular problems into parallel sub-problems requiring fewer qubits, shallower circuits, and reduced shot budgets. A physically motivated, two-step aggregation scheme then reconstructs the global solution: first, a computational bit assignment strategy optimizes a cost function to appropriately map local bit indices to global ones, yielding a mapped tensor product state (MTPS); second, an inter-fragment correlation recovery module restores missing cross-fragment interactions. Herein, we employ a multi-layered generative machine learning architecture, starting with utilizing the recently proposed physics-informed generative SQD (PIGen-SQD) as a distributed QCSC solver, followed by a secondary generative module to model configuration distributions and identify dominant sectors of the global Hilbert space. For water and formamide dimers, our method achieves up to $95\%$ reduction in the diagonalization dimension while enhancing energy accuracy by an order of magnitude over conventional SQD. Furthermore, application to the water hexamer ($\mathrm{(H_2O)_6}$) cage successfully decomposes a 120-qubit problem into six 20-qubit monomeric subsystems, and stitches the monomers under a dimeric approximation, demonstrating excellent agreement with the reference classical methods.

The paper asks whether sample-based quantum diagonalization (SQD) can treat molecular assemblies using quantum samples only from smaller fragments, while reconstructing inter-fragment correlations classically. It introduces PIGen-SQD(MAPS), combining fragment molecular orbital (FMO) partitioning with parallel fragment solvers that use hardware samples, perturbatively selected determinants, and restricted Boltzmann machines (RBMs). An orbital-overlap- and energy-based linear assignment maps fragment occupation bitstrings into the supersystem basis. Their mapped products are augmented with cross-fragment single excitations, CISD configurations, and perturbative triples, then refined through a second RBM-driven selection/diagonalization loop. An alternative uses SQD’s S-CORE recovery initialized with the same mapped space. Tests use IBM Heron R3 samples and classical electronic-structure references for water and formamide dimers in a 6-31G basis. Relative to conventional full-dimer SQD, the reported improvements reach a $95\%$ reduction in diagonalization dimension and roughly an order of magnitude lower energy error. PIGen-SQD(MAPS) gives approximately $0.4\,\mathrm{m}E_h$ errors against heat-bath CI across the studied separation curves. For a water hexamer, sampling is restricted to six 20-spin-orbital monomers; classical recovery treats 15 fragment pairs. The resulting FMO-2 energy differs from the FMO-2 heat-bath-CI reference by $0.915\,\mathrm{m}E_h$, rather than benchmarking an unfragmented 120-qubit solution. The framework assumes predominantly local correlation and weaker inter-fragment coupling. Fragmentation and many-body expansion order are user choices; including larger fragment combinations increases classical cost. Recovery also depends on initialization, configuration thresholds, and sampling quality.