High Resolution Image Download MS PowerPoint Slide Selected Configuration Interaction (SCI) is a method in molecular electronic structure theory that allows for the construction of configuration subspaces adapted to the particular system under study. This adaptability is achieved by guiding subspace construction with respect to a selection criterion designed to identify and retain the most important configurations for an accurate description of the system. Quantum-SCI (QSCI) introduces quantum resources to inform the construction of these subspaces, motivated by the classical hardness of state sampling and system dynamics. As with conventional SCI, the CI routine is still performed classically and is therefore not corrupted by hardware noise; only the subspace quality is affected by deficiencies in the quantum hardware. Previous QSCI approaches take the measurements produced by a physically motivated circuit construction, often with a recovery step to mitigate against errors, and form a subspace from the resulting configurations. We propose an alternative approach that is more aligned with conventional selection criteria but attempts to inject classically inaccessible information into the selection step with the aim of enabling new subspace expansion pathways. The approach presented in this work uses the population statistics of a time-evolved quantum state to predict likely single and double excitations away from existing configurations to bias the subspace expansion procedure. Importantly, this occupancy-guided expansion complements rather than replaces the direct inclusion of valid configurations sampled from the time-evolved quantum state, so determinants containing higher-order excitations can still enter the variational space in a single iteration. We also include multireference perturbation theory to capture missed correlations outside the configuration subspace. This is demonstrated on hardware by using 42 qubits of an IQM superconducting device to compute the potential energy curve of SiH 4 in a 6-31G basis set as the Si–H bonds are stretched. We benchmark against the best-in-class Heatbath CI algorithm to assess the compactness of the resulting wave function.
High Resolution Image Download MS PowerPoint Slide Selected Configuration Interaction (SCI) is a method in molecular electronic structure theory that allows for the construction of configuration subspaces adapted to the particular system under study. This adaptability is achieved by guiding subspace construction with respect to a selection criterion designed to identify and retain the most important configurations for an accurate description of the system. Quantum-SCI (QSCI) introduces quantum resources to inform the construction of these subspaces, motivated by the classical hardness of state sampling and system dynamics. As with conventional SCI, the CI routine is still performed classically and is therefore not corrupted by hardware noise; only the subspace quality is affected by deficiencies in the quantum hardware. Previous QSCI approaches take the measurements produced by a physically motivated circuit construction, often with a recovery step to mitigate against errors, and form a subspace from the resulting configurations. We propose an alternative approach that is more aligned with conventional selection criteria but attempts to inject classically inaccessible information into the selection step with the aim of enabling new subspace expansion pathways. The approach presented in this work uses the population statistics of a time-evolved quantum state to predict likely single and double excitations away from existing configurations to bias the subspace expansion procedure. Importantly, this occupancy-guided expansion complements rather than replaces the direct inclusion of valid configurations sampled from the time-evolved quantum state, so determinants containing higher-order excitations can still enter the variational space in a single iteration. We also include multireference perturbation theory to capture missed correlations outside the configuration subspace. This is demonstrated on hardware by using 42 qubits of an IQM superconducting device to compute the potential energy curve of SiH 4 in a 6-31G basis set as the Si–H bonds are stretched. We benchmark against the best-in-class Heatbath CI algorithm to assess the compactness of the resulting wave function.
Accurate solutions to the electronic Schrödinger equation remain a central challenge in quantum chemistry due to the exponential growth of the many-electron Hilbert space. Selected configuration interaction (SCI) methods mitigate this challenge by restricting the wavefunction expansion to a subset of important determinants, but their efficiency is limited by the quality/cost of determinant selection and Hamiltonian diagonalization. In this work, we propose QUBO-SCI, a novel approach that reformulates the selection step in SCI as a quadratic unconstrained binary optimization (QUBO) problem. This formulation enables the sampling of low-energy electronic configurations as bitstrings using both quantum-inspired approaches and quantum annealing hardware. The sampled configurations are then incorporated into an iterative SCI framework using a perturbative importance criterion. We demonstrate the method on small benchmark systems, including H 2 , C 2 , H 2 O, and N 2 , showing that QUBO-SCI achieves near-FCI accuracy with a significantly reduced number of determinants. The results highlight the potential of annealing-based sampling as an efficient alternative to both conventional determinant selection strategies and circuit-based quantum SCI approaches in electronic structure calculations.
We present a quantum-classical hybrid algorithm for calculating the ground state and its energy of the quantum many-body Hamiltonian by proposing an adaptive construction of a quantum state for the quantum-selected configuration interaction (QSCI) method. QSCI allows us to select important electronic configurations in the system to perform configuration interaction (CI) calculation (subspace diagonalization of the Hamiltonian) by sampling measurement for a proper input quantum state on a quantum computer, but how we prepare a desirable input state remains a challenge. We propose an adaptive construction of the input state for QSCI in which we run QSCI repeatedly to grow the input state iteratively. We numerically illustrate that our method, dubbed ADAPT-QSCI, can yield accurate ground-state energies for small molecules, including a noisy situation for eight qubits where error rates of two-qubit gates and the measurement are both as large as 1%. ADAPT-QSCI serves as a promising method to take advantage of current noisy quantum devices and pushes forward its application to quantum chemistry.
Predicting many molecular properties requires accurate ground-state energies of molecular Hamiltonians. Quantum-selected configuration interaction (QSCI) obtains such energies by measuring an input state to select important electronic configurations and classically diagonalizing the Hamiltonian in the subspace they span. ADAPT-QSCI, an adaptive extension of QSCI, improves the input state through iterative circuit growth. For single-reference molecules, the sampling distribution is dominated by the Hartree-Fock (HF) configuration, so most measurements reproduce a configuration already known. We reduce this redundancy by placing the HF configuration in the diagonalization subspace classically, before any measurement. This invalidates the operator-selection criterion of ADAPT-QSCI, and we derive a consistent replacement with energy and gradient in closed form, adding no query to the quantum device. At the per-iteration shot budgets previously used for ADAPT-QSCI, the proposed scheme reaches chemical accuracy with approximately 63% and 43% of the CNOT gates for H4 and H6, and 44% and 40% of the total shots. The advantage depends on the budget, however: in the infinite-shot limit the H4 CNOT count increases to 125% of that of ADAPT-QSCI. These results identify the per-iteration shot budget as a key design variable governing resource savings in QSCI-based algorithms.
Quantum-selected configuration interaction (QSCI) has emerged as a feasible approach for approximating electronic ground states on noisy quantum devices toward large-system demonstrations. In QSCI, Slater determinants are sampled from a quantum-prepared state, and the Hamiltonian is then diagonalized in the sampled subspace. To create a high-quality subspace under hardware constraints, the design of the state-preparation circuit is crucial. Here, we present a Generative Quantum Eigensolver (GQE)-based framework that optimizes ansatz structures using a Transformer policy trained on the QSCI subspace energy. We validate the framework on N2 in active spaces of up to 32 qubits. We found that the optimized circuits reach chemical precision with substantially lower gate counts than time-evolved circuits. Quantitatively, this corresponds to an average reduction of 98% in the required two-qubit gate count relative to the single-step first-order Trotterized approximation and 83% relative to the qDRIFT approximation. Furthermore, the resulting wavefunctions are competitive with heat-bath configuration interaction (HCI) in terms of compactness. In stretched-bond, strongly correlated regimes, they achieve chemical precision with subspaces that are 50% smaller than those required by HCI.
This review provides a detailed anatomical dissection of Quantum-Selected Configuration Interaction (QSCI), a hybrid quantum-classical algorithm introduced by Kanno et al. (2026) that leverages noisy quantum devices solely for sampling important electron configurations from an input state, followed by exact classical diagonalization of the Hamiltonian in the resulting reduced subspace. We systematically evaluate its methodological innovations, noise resilience, and strict adherence to the variational principle. A comprehensive comparison is drawn with at least twelve competing or complementary paradigms in NISQ-era quantum chemistry and classical selected configuration interaction (SCI), including VQE and its adaptive/excited-state variants, Quantum Subspace Expansion (QSE), ASCI, CIPSI, MCCI, FCIQMC, DMRG, Classically-Boosted VQE, and time-evolved input extensions (TE-QSCI). Pros and cons are articulated with reference to recent critical analyses highlighting sampling inefficiencies and subspace compactness. The review further explores the ontological status of configuration selection via quantum measurement and the epistemological guarantees afforded by classical post-processing. Possible extensions—hybrid adaptive pipelines, subspace recycling for molecular dynamics, and integration with machine-learned wavefunctions—are proposed. Also available on Academia.edu: https://www.academia.edu/attachments/133411942/download_file?s=portfolio
Quantum-selected configuration interaction (QSCI) utilizes an input quantum state on a quantum device to select important bases (electron configurations in quantum chemistry) that define a subspace in which to diagonalize a target Hamiltonian, i.e., perform selected configuration interaction, on classical computers. Previous proposals for preparing a good input state, which is crucial for the quality of QSCI, based on optimization of quantum circuits may suffer from optimization difficulty and require many runs of the quantum device. Here, we propose using a time-evolved state by the target Hamiltonian (for some initial state) as an input of QSCI. Our proposal is based on the intuition that the time evolution by the Hamiltonian creates electron excitations of various orders when applied to the initial state. We numerically investigate the accuracy of the energy obtained by the proposed method for quantum chemistry Hamiltonians describing electronic states of small molecules. Numerical results reveal that our method can yield sufficiently accurate ground-state energies for the investigated molecules. Systematic analysis when increasing the number of qubits in a hydrogen chain shows that the subspace size required for sufficiently accurate results is reasonable at system sizes that cannot be solved by naive classical diagonalization. Our proposal provides a systematic and optimization-free method to prepare the input state of QSCI and could contribute to practical applications of quantum computers in quantum chemistry calculations.