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arXiv:2606.24332

Enhancing quantum-classical configuration interaction methods using a neural-network classifier

Severino Zeni, Giovanni Varutti, Jacopo Nespolo, Dimitrios Trypogeorgos

physics.chem-phquant-phSubmitted Jun 23, 2026• Announced Jun 24, 2026• 0 citations
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Abstract

Selected configuration interaction methods achieve near-exact electronic structure calculations by iteratively constructing compact variational spaces, but their efficiency depends critically on the heuristics used to identify important determinants. Here, we introduce a data-driven selection framework that recasts determinant importance as a binary classification task and integrates a neural-network classifier into the iterative CI workflow through an active-learning loop. At each iteration, a random subset of candidate determinants is labelled via temporary diagonalisation, and the trained classifier guides selection of the remaining configurations. We demonstrate the utility of this framework for both classical and quantum CI methods by calculating the ground-state energy of a diatomic molecule. Our method achieves result parity with traditional configuration interaction methods at substantially lower computational cost: roughly a $\times 5$ reduction in memory and per-iteration cost for the classical cHCI variant, and convergence in markedly fewer iterations for the quantum-classical cSQD variant. These results establish classifier-assisted determinant selection as a lightweight, method-agnostic tool for compressing variational spaces and accelerating both classical and hybrid quantum-classical configuration interaction algorithms.

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Selected configuration interaction methods achieve near-exact electronic structure calculations by iteratively constructing compact variational spaces, but their efficiency depends critically on the heuristics used to identify important determinants. Here, we introduce a data-driven selection framework that recasts determinant importance as a binary classification task and integrates a neural-network classifier into the iterative CI workflow through an active-learning loop. At each iteration, a random subset of candidate determinants is labelled via temporary diagonalisation, and the trained classifier guides selection of the remaining configurations. We demonstrate the utility of this framework for both classical and quantum CI methods by calculating the ground-state energy of a diatomic molecule. Our method achieves result parity with traditional configuration interaction methods at substantially lower computational cost: roughly a ×5\times 5×5 reduction in memory and per-iteration cost for the classical cHCI variant, and convergence in markedly fewer iterations for the quantum-classical cSQD variant. These results establish classifier-assisted determinant selection as a lightweight, method-agnostic tool for compressing variational spaces and accelerating both classical and hybrid quantum-classical configuration interaction algorithms.
In this work, we introduce a perturbative Selective Configuration Interaction (SCI) approach guided by a binary machine-learning classifier. The method leverages a lightweight feedforward neural network (FNN), purposefully designed for fast and efficient training. Within this framework, we show that our model attains the accuracy of the state-of-the-art SCI method CIPSI (Configuration Interaction using a Perturbative Selection done Iteratively). Across all tested configuration-space sizes, our approach reliably identifies the most important Slater determinants using a binary cross-entropy metric, achieving FCI/CASCI-level accuracy within 10 –4 Hartree for both ground and excited states. Finally, the method remains robust for strained geometries and conformational changes, successfully classifying Slater determinants across multiple points of potential energy curves and surfaces. This capability opens the door to new regression-based strategies for molecular electronic structure and the construction of machine-learning-driven potential energy surfaces.
A neural-network approach to optimize the selection of Slater determinants in configuration interaction calculations for condensed-matter quantum many-body systems is developed. We exemplify our algorithm on the discrete version of the single-impurity Anderson model with up to 299 bath sites. Employing a neural network classifier and active learning, our algorithm enhances computational efficiency by iteratively identifying the most relevant Slater determinants for the ground state wave function. We benchmark our results against established methods and investigate the efficiency of our approach compared to another basis truncation scheme without a neural network. Our algorithm demonstrates a substantial improvement in the efficiency of determinant selection, yielding a more compact and computationally manageable basis without compromising accuracy. Given the straightforward application of our neural-network-supported selection scheme to other model Hamiltonians of quantum many-body clusters, our algorithm can significantly advance selective configuration interaction calculations in the context of correlated condensed matter.
Accurate ground-state energy calculations remain a central challenge in quantum chemistry due to the exponential scaling of the many-body Hilbert space. Variational Monte Carlo and variational quantum eigensolvers offer promising ansatz optimization approaches but face limitations in convergence as well as hardware constraints. We introduce a particular Selected Configuration Interaction (SCI) algorithm that uses auto-regressive neural networks (ARNNs) to guide subspace expansion for ground-state search. Leveraging the unique properties of ARNNs, our algorithm efficiently constructs compact variational subspaces from learned ground-state statistics, which in turn accelerates convergence to the ground-state energy. Benchmarks on molecular systems demonstrate that ARNN-guided subspace expansion combines the strengths of neural-network representations and classical subspace methods, providing a scalable framework for classical and hybrid quantum-classical algorithms.
Accurately solving the electronic Schrödinger equation for strongly correlated systems remains a central challenge in quantum chemistry, where the exponential growth of configuration space limits the applicability of exact methods. Selected Configuration Interaction (SCI) algorithms address this challenge by adaptively constructing compact determinantal expansions, yet their efficiency depends critically on the quality of the sampling strategy used to identify chemically important configurations. Here we introduce the Handover Iterative Neural Quantum State (HI-NQS) algorithm, which embeds a classically trained autoregressive Transformer neural quantum state within the iterative sample--diagonalize--update framework of Sample-Based Quantum Diagonalization. A dual-channel Transformer architecture with explicit spin-up/spin-down cross-attention encodes fermionic spin structure as an architectural inductive bias, enabling expressive and physically informed wavefunction representations. After each subspace diagonalization, the resulting eigenvector is distilled back into the network through a factorized spin-marginal teacher signal, establishing a closed feedback loop between generative sampling and exact diagonalization. Benchmarks across a range of small molecules and a systematic nitrogen active-space series demonstrate that HI-NQS achieves chemical accuracy on all systems tested, with determinant-count scaling substantially more favorable than conventional CIPSI-based SCI for all but the smallest active spaces. All calculations are performed on GPU hardware without quantum computing resources, establishing HI-NQS as an efficient and scalable purely classical approach to the selected configuration interaction problem.
Quantum many-body calculations are fundamentally limited by the exponential growth of the configuration space, making accurate treatment of strongly correlated systems computationally prohibitive. Here we present the Generative Transformer Neural Network Selected Configuration Interaction (GTNN-SCI), a Transformer-based machine learning approach that generatively samples important configurations to accelerate many-body quantum chemistry calculations. By leveraging the Transformer architecture’s self-attention mechanism to capture long-range electron correlations, GTNN-SCI achieves up to 10× speedup compared to state-of-the-art neural network methods while maintaining high accuracy. We demonstrate the efficacy of GTNN-SCI by calculating correlation and binding energies for representative molecules including N 2, H 2 O, and C 2 using both Gaussian (cc-pVDZ) and plane-wave basis sets, achieving faster convergence and lower energies than previously reported neural network-based selected CI techniques. Most significantly, our generative approach identifies higher-order excitations missed by conventional coupling schemes, yielding lower variational energies than established methods including heat-bath CI. This capability enables GTNN-SCI to accurately treat the strongly correlated [Fe 2 S 2 (SCH 3 ) 4 ] 2– ([2Fe–2S]) cluster system, achieving ground-state energies within chemical accuracy of DMRG benchmarks, whereas conventional selected CI methods have failed on this system. The GTNN-SCI method thus combines modern deep learning with high-performance electronic structure computation, providing an efficient and precise avenue for solving the electronic Schrödinger equation in challenging molecular systems.
Full configuration interaction (FCI) provides exact electronic structure within a given atomic basis, but its computational cost grows exponentially with the number of spin orbitals. Selected configuration interaction (SCI) methods alleviate this limitation by retaining only the most important Slater determinants. However, the repeated identification of important determinants remains a major computational bottleneck. We present a quantum assisted selected configuration interaction (QASCI) method that combines SCI with graph based block diagonalization (GBBD) of FCI Hamiltonian. The GBBD method partitions FCI Hamiltonian into independent blocks, within which determinant selection problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO problems for selecting determinants to construct SCI space are iteratively solved using a fast annealing approach. We benchmark method on H8-H18 hydrogen chains and Li2S in STO3G basis. For Hn chains, chemical accuracy is achieved while retaining only a small fraction of Slater determinants, and this fraction decreases with increasing n, despite the exponential growth of the FCI Hilbert space. For Li2S, QASCI results remain within chemical accuracy while retaining substantially fewer determinants than the full FCI space. We apply QASCI to N2 using the 631G basis, considering both active orbital and full orbital treatments. The full orbital QASCI calculation, using 50000 determinants, yields a lower ground state energy than an FCI calculation within an active space comprising 12 spin orbitals and 12 electrons. These results demonstrate that the combination of QASCI and the GBBD approach can substantially reduce computational cost of determinant selection while maintaining the accuracy of FCI based electronic structure calculations, thereby enabling accurate calculations in larger orbital spaces.