Quantum centric supercomputing (QCSC) framework, such as sample-based quantum diagonalization (SQD) holds immense promise toward achieving practical quantum utility to solve challenging problems. QCSC leverages quantum computers to perform the classically intractable task of sampling the dominant fermionic configurations from the Hilbert space that have substantial support to a target state, followed by Hamiltonian diagonalization on a classical processor. However, noisy quantum hardware produces erroneous samples upon measurements, making robust and efficient configuration-recovery strategies essential for a scalable QCSC pipeline. Toward this, in this work, we introduce PIGen-SQD, an efficiently designed QCSC workflow that utilizes the capability of generative machine learning (ML) along with physics-informed configuration screening via implicit low-rank tensor decompositions for accurate fermionic state reconstruction. The physics-informed pruning is based on a class of efficient perturbative measures that, in conjunction with hardware samples, provide a substantial overlap with the target state. This distribution induces an anchoring effect on the generative ML models to stochastically explore only the dominant sector of the Hilbert space for effective identification of additional important configurations in a self-consistent manner. Our numerical experiments performed on IBM Heron R2 quantum processors demonstrate this synergistic workflow produces compact, high-fidelity subspaces that substantially reduce diagonalization cost while maintaining chemical accuracy under strong electronic correlations. By embedding classical many body intuitions directly into the generative ML model, PIGen-SQD advances the robustness and scalability of QCSC algorithms, offering a promising pathway toward chemically reliable quantum simulations on utility-scale quantum hardware.
Quantum centric supercomputing (QCSC) framework, such as sample-based quantum diagonalization (SQD) holds immense promise toward achieving practical quantum utility to solve challenging problems. QCSC leverages quantum computers to perform the classically intractable task of sampling the dominant fermionic configurations from the Hilbert space that have substantial support to a target state, followed by Hamiltonian diagonalization on a classical processor. However, noisy quantum hardware produces erroneous samples upon measurements, making robust and efficient configuration-recovery strategies essential for a scalable QCSC pipeline. Toward this, in this work, we introduce PIGen-SQD, an efficiently designed QCSC workflow that utilizes the capability of generative machine learning (ML) along with physics-informed configuration screening via implicit low-rank tensor decompositions for accurate fermionic state reconstruction. The physics-informed pruning is based on a class of efficient perturbative measures that, in conjunction with hardware samples, provide a substantial overlap with the target state. This distribution induces an anchoring effect on the generative ML models to stochastically explore only the dominant sector of the Hilbert space for effective identification of additional important configurations in a self-consistent manner. Our numerical experiments performed on IBM Heron R2 quantum processors demonstrate this synergistic workflow produces compact, high-fidelity subspaces that substantially reduce diagonalization cost while maintaining chemical accuracy under strong electronic correlations. By embedding classical many body intuitions directly into the generative ML model, PIGen-SQD advances the robustness and scalability of QCSC algorithms, offering a promising pathway toward chemically reliable quantum simulations on utility-scale quantum hardware.
Abstract Quantum centric supercomputing (QCSC) framework, such as sample-based quantum diagonalization (SQD) holds immense promise toward achieving practical quantum utility to solve classically hard sampling problems in quantum chemistry. QCSC leverages quantum computers to perform the classically intractable task of sampling the dominant fermionic configurations from the Hilbert space that have substantial support to a target state, followed by Hamiltonian diagonalization on a classical processor. However, noisy quantum hardware produces erroneous samples upon measurements, making robust and efficient configuration-recovery strategies essential for scalable QCSC pipelines. Toward this, in this work, we introduce PIGen-SQD, an efficiently designed QCSC workflow that utilizes the capability of generative machine learning (ML) along with physics-informed configuration screening via implicit low-rank tensor decompositions for accurate fermionic state reconstruction. The physics-informed pruning is based on a class of efficient perturbative measures that, in conjunction with samples drawn from quantum hardware, provide a substantial overlap with the target state. This distribution induces an anchoring effect on the generative ML models to stochastically explore only the dominant sector of the Hilbert space for effective identification of additional important configurations in a self-consistent manner. Our numerical experiments performed on IBM Heron R2 and R3 quantum processors with up to 58 qubit experiments demonstrate this synergistic workflow produces compact, high-fidelity subspaces that substantially reduce diagonalization cost while maintaining chemical accuracy under strong electronic correlations. With such a concerted integration of classical many-body intuitions, generative ML and quantum computers as a sampling engine, PIGen-SQD offers a promising pathway toward accurate and systematically improvable quantum simulations on utility-scale quantum hardware.
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 ((H2O)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.
Sample-based Quantum Diagonalization (SQD), an extension of Quantum Selected Configuration Interaction (QSCI), has emerged as a promising hybrid quantum-classical paradigm for computing molecular ground state energies. By leveraging quantum sampling instead of variational optimization, QSCI avoids barren plateaus and enables direct reconstruction of correlated electronic wavefunctions. However, existing configuration recovery techniques primarily enforce symmetry constraints without guaranteeing optimal selection of the most physically relevant configurations, often leading to unnecessarily large subspaces and increased classical diagonalization costs. In this work, we introduce a machine-learned compact subspace generation protocol based on Restricted Boltzmann Machines (RBMs), termed QSCI-RBM, and integrate it within the Density Matrix Embedding Theory (DMET) framework. The RBM is trained on quantum-sampled configurations to learn the underlying probability distribution of dominant determinants, enabling the targeted generation of high-probability configurations. We apply this framework to the simulation of a protein-ligand complex involving the inhibitor Carmofur bound to the SARS-CoV-2 main protease (Mpro). Our results demonstrate that DMET-QSCI-RBM achieves energies within the chemical accuracy threshold by accessing only approximately 4% of the configuration subspace. In contrast, standard DMET-SQD simulations failed to reach chemical accuracy while accessing up to 20% of the subspace, even as the chemical potential itself nearly converged. These findings highlight that RBM-assisted configuration generation produces significantly more compact subspaces while preserving physical accuracy, thereby reducing classical computational overhead and enabling the scalable quantum embedding simulation of complex biological systems.
Sample-based quantum diagonalization (SQD) has emerged as a promising route for quantum-centric supercomputing, relying on classical diagonalization of the molecular Hamiltonian within a hardware-sampled determinant subspace. However, its accuracy degrades in strongly correlated regimes where the relevant determinant space exceeds what finite-shot sampling can capture. In this work, we introduce Quantum Wavefunction Augmentation via Variational Autoencoders (Q-WAVE), a hybrid method that combines determinants sampled via SqDRIFT Krylov circuits and configuration interaction singles and doubles (CISD) determinants with generative machine learning. Using a custom β-annealed variational autoencoder (VAE) model, Q-WAVE iteratively expands this basis toward the variational ground state. The VAE learns the wavefunction's primary support structure from the combined hardware and CISD seed in a continuous latent space, generating new dominant determinants beyond any fixed excitation hierarchy. The resulting compact wavefunction exceeds what can be extracted from raw hardware samples alone. We demonstrate sub-millihartree accuracy compared to full configuration interaction for H2O and N2 dissociation. Finally, we establish Q-WAVE's scalability on a 52-qubit ethylene system (achieving sub-millihartree accuracy versus CCSD(T)) and a highly correlated 60-qubit Cr2 stress test that attains chemical accuracy upon a final perturbative correction.
Sampling-based quantum diagonalization method exploits Quantum-centric supercomputing platforms to sample bitstrings for Hamiltonian projection on a quantum computer, and then classically diagonalize the Hamiltonian to estimate the eigenvalues and eigenvectors. In current quantum devices an algorithm is useful when shallow quantum circuits with error mitigation support can discover better results while having either a proof of convergence or some method to explain trust in experiment. In this paper, we introduce DF-SQD, a hybrid algorithm that derives deterministic auxiliary-field circuits from selected double-factorization leaves of the two-electron tensor. The circuits propose occupation-number configurations, while selected configuration interaction evaluates the original active-space Hamiltonian and can recentre subsequent proposal rounds. On N2 (32 qubits; 6-31G basis) and a 40-qubit [Fe2S2(SCH3)4]2- active-space Hamiltonian, we show that DF-SQD improves the energy obtained from sampled determinant spaces while using shallow number-preserving circuits in both simulator and hardware runs. For N2, DF-SQD is 45x more accurate with a 11.23\% smaller subspace, and due to its ability to sample better bitstrings at lesser shots it is 2.93x faster than SQD in quantum devices. For the iron-sulfur cluster, DF-SQD generated a subspace dimension of 221M with 400K shots, while SQD needed 1.5M shots to generate a 238M subspace, thus we have better subspace recovery evident from the hardware at 3.75x reduced shots. At a matched 50M subspace dimension, DF-SQD is 1.32x more accurate (achieves a 24.5\% relative error reduction over standard SQD). So overall, our method is able to discover better results with shallower circuits, is sample efficient, uses configuration recovery (so has targeted error mitigation) and we have empirical convergence observation.
Predicting ground state energies of quantum many-body systems is one of the central computational challenges in quantum chemistry, physics, and materials science. Krylov subspace methods, such as Krylov Quantum Diagonalization and Sample-based Krylov Quantum Diagonalization, are promising approaches for this task on near-term quantum computers. However, both require repeated quantum circuit executions for each Krylov subspace and for every new Hamiltonian, posing a major bottleneck under noisy hardware constraints. We introduce Generative Krylov Subspace Representations (GenKSR), a framework that learns a classical generative representation of the entire Krylov diagonalization process. To enable effective modeling of quantum systems, GenKSR leverages a conditional generative model framework. We investigate two representative backbone architectures, the standard Transformer and the Mamba state-space model. By learning the distribution of measurement outcomes conditioned on Hamiltonian parameters and evolution time, GenKSR generates Krylov subspace samples for unseen Hamiltonians and for larger subspace dimensions than those used in training. This enables full energy reconstruction purely from the classical model, without additional quantum experiments. We validate our approach through simulations of 15-qubit 1D and 16-qubit 2D Heisenberg models, as well as a hardware experiment on a 20-qubit XXZ chain executed on an IBM quantum processor. Our model successfully learns the distribution from experimental data and generates a high-fidelity representation of the quantum process. This representation enables classical reproduction of experimental outcomes, supports reliable energy estimates for unseen Hamiltonians, and significantly reduces the need for further quantum computation.