Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction

TL;DR

This work addresses the challenge of weak/strong correlation in electronic structure by introducing Quantum-Selected Configuration Interaction (QSCI), a hybrid quantum-classical workflow that samples configurations on a quantum device and diagonalises the projected Hamiltonian classically. The method combines SCI with multireference perturbation theory and augments the determinant subspace via time-evolved quantum sampling using $U=e^{-iHt}$, implemented with stochastic circuit compilation ($qDRIFT$) and a configuration-sampling scheme guided by measured occupancies. Key results show that QSCI can produce ground-state wavefunctions that are over 200x more compact than conventional SCI at stretched bond lengths, with PT2-corrected and extrapolated energies closely matching the best-in-class HCI and maintaining smooth potential energy curves; this demonstrates meaningful quantum utility in chemistry. The work highlights a viable quantum-centric approach to HPC workflows, offering substantial potential to reduce classical subspace sizes while preserving accuracy, and points toward future improvements that could surpass current state-of-the-art multiconfigurational methods.

Abstract

A recent direction in quantum computing for molecular electronic structure sees the use of quantum devices as configuration sampling machines integrated within high-performance computing (HPC) platforms. This appeals to the strengths of both the quantum and classical hardware; where state-sampling is classically hard, the quantum computer can provide computational advantage in the selection of high quality configuration subspaces, while the final molecular energies are evaluated by solving an interaction matrix on HPC and is therefore not corrupted by hardware noise. In this work, we present an algorithm that leverages stochastic Hamiltonian time evolution in Quantum-Selected Configuration Interaction (QSCI), with multireference perturbation theory capturing missed correlations outside the configuration subspace. The approach is validated through a hardware demonstration utilising 42 qubits of an IQM superconducting device to calculate the potential energy curve of the inorganic silane molecule, SiH4 using a 6-31G atomic orbital basis set, under a stretching of the Si-H bond length. We assess the resulting wavefunctions for compactness, a point on which QSCI has previously been criticised. At large separations, where static correlation dominates, we find a configuration space more than 200 times smaller than that obtained from a conventional SCI selection criterion yields comparable energies. We also compare against the best-in-class Heatbath Configuration Interaction algorithm and observe similar wavefunction compactness at convergence. This result is achieved with a configuration sampling scheme that uses the experimental orbital occupancies of a time-evolved quantum state to predict likely single and double excitations away from existing configurations to bias the subspace expansion procedure.

Figures (6)

• Figure 1: Qubit utilisation in chemistry since the beginning of 2013, highlighting the transition from Variational Quantum Algorithms to Quantum-Selected Configuration Interaction techniques after 2024. Dates are taken from the first appearance of the preprint, not the final publication date. Stars indicate work produced by our research group.
• Figure 2: Coupling graph for the IQM Emerald 54-qubit superconducting device. Dotted couplings were not operational at the time of circuit execution.
• Figure 3: Spin-orbital occupancy distributions for Hamiltonian time evolution applied to the Hartree-Fock reference state on a noisy quantum processor. The time propagation unitary $e^{-iH\tau}$ was applied up to a maximum of five times for increments of $\tau=\frac{2\pi}{5}$ over different Si-H bond lengths in the SiH4 6-31G system, consisting of 42 qubits. The top left subplot shows the final orbital occupancies obtained by solving the sampled configuration spaces.
• Figure 4: Energy convergence against the size of configuration subspace for our sampling scheme in time-evolved QSCI, compared with the SCI selection criterion in PySCF, the variational stage of HCI as implemented in PyCI, and CASCI calculations over subspaces $(8o,8e), (10o,10e), (12o,12e), (14o,14e)$; the active spaces were selected from the CCSD natural orbitals. The first five colours in the QSCI curve relate to different iterations of the sampling scheme and therefore correspond with the five experimental occupancy distributions in Figure \ref{['fig:occ_dists']}, excluding the dark blue points which correspond with collating configurations from neighbouring points in the PEC to further expand the subspace.
• Figure 5: (a) QSCI correlation energy against second-order perturbation correction. The observed linearity motivates an extrapolation scheme to approximate the FCI energy, where the perturbation correction must decay to zero as the configuration space approaches completeness. (b) Comparing time-evolved QSCI, QSCI(PT2) and the extrapolated QSCI(PT$2\rightarrow0$) curves against SCI/HCI.