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arXiv:2605.23697

Noise and Configuration Recovery Impact on Quantum Selected Configuration Interaction

Nonia Vaquero-Sabater, Abel Carreras, Lukas Broers, Tomonori Shirakawa, Seiji Yunoki, David Casanova

quant-phSubmitted May 22, 2026• Announced May 25, 2026• 1 citation
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Abstract

Quantum-selected configuration interaction (QSCI) is a promising hybrid quantum-classical approach in which a quantum device generates configurations for subsequent classical diagonalization. Here, we analyze the performance of QSCI combined with the local unitary cluster Jastrow (LUCJ) ansatz, focusing on the interplay between ansatz expressivity, sampling, noise, and configuration recovery. Using the dissociation of N2 in a large active space as a benchmark, we show that noiseless LUCJ sampling produces compact and biased configurational spaces, limiting the accuracy of the resulting CI energies, particularly in strongly correlated regimes. By introducing a simple noise model, we demonstrate that sampling noise can enhance Hilbert-space exploration by generating additional configurations beyond those supported by the ideal ansatz. When combined with configuration recovery, this leads to systematically improved energies. Moreover, recovery alone (starting from randomly generated configurations) can efficiently construct accurate CI spaces, highlighting its central role in QSCI.

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28 pages, 4 figures

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Quantum-selected configuration interaction (QSCI) is a promising hybrid quantum-classical approach in which a quantum device generates configurations for subsequent classical diagonalization. Here, we analyze the performance of QSCI combined with the local unitary cluster Jastrow (LUCJ) ansatz, focusing on the interplay between ansatz expressivity, sampling, noise, and configuration recovery. Using the dissociation of N2 in a large active space as a benchmark, we show that noiseless LUCJ sampling produces compact and biased configurational spaces, limiting the accuracy of the resulting CI energies, particularly in strongly correlated regimes. By introducing a simple noise model, we demonstrate that sampling noise can enhance Hilbert-space exploration by generating additional configurations beyond those supported by the ideal ansatz. When combined with configuration recovery, this leads to systematically improved energies. Moreover, recovery alone (starting from randomly generated configurations) can efficiently construct accurate CI spaces, highlighting its central role in QSCI.
Quantum Selected Configuration Interaction (QSCI) methods (also known as Sample-based Quantum Diagonalization, SQD) have emerged as promising near-term approaches to solving the electronic Schrödinger equation with quantum computers. In this work, we perform numerical analysis to show that QSCI methods face critical limitations that severely hinder their practical applicability in chemistry. Using the nitrogen molecule and the iron-sulfur cluster [2Fe-2S] as examples, we demonstrate that while QSCI can, in principle, yield high-quality configuration interaction (CI) expansions similar to classical SCI heuristics in some cases, the method struggles with inefficiencies in finding new determinants as sampling repeatedly selects already seen configurations. This inefficiency becomes especially pronounced when targeting high-accuracy results or sampling from an approximate ansatz. In cases where the sampling problem is not present, the resulting CI expansions are less compact than those generated from classical heuristics, rendering QSCI an overall more expensive method. Our findings suggest a significant drawback in QSCI methods when sampling from the ground-state distribution as the inescapable trade-off between finding sufficiently many determinants and generating compact, accurate CI expansions. This ultimately hinders utility in quantum chemistry applications, as QSCI falls behind more efficient classical counterparts.
We present the quantum-selected configuration interaction-tailored coupled-cluster (QSCI-TCC) method, a hybrid quantum-classical scheme that tailors coupled-cluster (CC) theory with a quantum-selected configuration interaction (QSCI) wave function. QSCI provides a scalable, shot-efficient approach to reconstructing the many-electron state prepared on quantum hardware on a classical computer. The resulting active-space CI coefficients, which are free from additive shot noise, are mapped to fixed cluster amplitudes within the tailored coupled-cluster framework, after which a conventional CC calculation optimizes the remaining amplitudes. This workflow embeds static (strong) correlation from the quantum device and subsequently recovers dynamical (weak) correlation, yielding a balanced description of both. The method is classically simulated and applied to the simultaneous O-H bond dissociation in H2_22​O and the triple-bond dissociation in N2_22​. QSCI-TCC and its perturbative-triples variant, QSCI-TCC(T), provide accurate results even where CCSD or CCSD(T) begin to break down. Shot-count tests for the N2_22​ (6e, 6o) active space demonstrate that, with the (c) correction, chemically sufficient precision (≤1\leq 1≤1 kcal/mol) is achieved with only 1.0×1051.0 \times 10^51.0×105 shots in the strongly correlated regime (r=2.2r=2.2r=2.2 Å) -- an order of magnitude fewer than required by an earlier matchgate-shadows implementation [J. Chem. Theory Comput., 20, 5068 (2024)]. By pairing resource-efficient quantum sampling with the CC theory, QSCI-TCC provides a promising pathway to quantum-chemical calculations of classically intractable systems.
Quantum-selected configuration interaction (QSCI) methods use a quantum computer to identify dominant electronic configurations in the molecular ground state, while a classical computer diagonalizes the Hamiltonian within the reduced subspace spanned by those configurations. Sample-based quantum diagonalization (SQD), a leading QSCI approach, uses iterative classical post-processing to correct noisy quantum measurement to ensure that the corresponding configurations remain physically sensible. In this work, we show that SQD performance can be strongly influenced by uncontrolled growth of the classical diagonalization subspace. When classical resources are not explicitly constrained, classical uniform random sampling can reproduce SQD benchmarks as noise increases the diversity of sampled configurations. We show any fair benchmarking protocol of SQD must explicitly control diagonalization size over unique samples. We then address the problem of efficiently discovering physically relevant, energy-lowering configurations by introducing a measurement protocol based on non-orthogonal configuration interaction (NOCI). By distributing measurements across orbital bases optimized with respect to the molecular Hamiltonian, we obtain improved sample efficiency relative to measurements performed solely in the Hartree--Fock basis. Importantly, these improvements persist even under fixed classical resource budgets, demonstrating that the resulting configurations are of higher quality rather than being more numerous. Under our proposed benchmarking procedure, we establish measurement-basis engineering as a promising route to improving quantum sampling methods for electronic structure.
Quantum Selected Configuration Interaction (QSCI) and an extended protocol known as Sample-based Quantum Diagonalization (SQD) have emerged as promising algorithms to solve the electronic Schrödinger equation with noisy quantum computers. In QSCI/SQD a quantum circuit is repeatedly prepared on the quantum device, and measured configurations form a subspace of the many-body Hilbert space in which the Hamiltonian is diagonalized classically. For the dissociation of N 2 and a model [2Fe – 2S] cluster (correlating 10 electrons in 26 orbitals and 30 electrons in 20 orbitals, respectively) we show that a nonperturbative stochastic approach, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), using truncated SQD trial wave functions obtained from quantum hardware can recover a substantial amount (e.g., O (100) mHa) of correlation energy. This hybrid quantum-classical combination has the potential to greatly reduce the sampling burden placed on the QSCI/SQD procedure, and is a compelling alternative to recently proposed hybrid ph-AFQMC algorithms that rely on quantum state tomography.
Sample-based quantum diagonalization (SQD), equivalently quantum-selected configuration interaction (QSCI), has become a centre of gravity of pre-fault-tolerant quantum chemistry: a processor samples electronic configurations and the Hamiltonian is diagonalized classically in the resulting subspace. Accuracy is governed entirely by which configurations enter it -- a machine-learning selection problem, made acute by a coupon-collector bottleneck. We review the generative and learned selectors by what each generates and the signal it exploits, and identify one gap: no reward-proportional generative-flow-network proposer has been built for tail discovery. On the field's central question -- whether the quantum sampler beats classical selected CI -- the negative verdict is not ours to claim: priority belongs to Reinholdt et al. [JCTC 21, 6811 (2025)], and polynomial-time classical estimation of the flagship circuits has reinforced it. We state that verdict at the precision a falsifiable claim requires -- it concerns reproducible, same-active-space comparisons on molecular electronic structure -- and weigh the claims outside those qualifiers. We show that alpha-string weights are not invariant under rotations inside degenerate orbital shells, so determinant counts are undefined until the orbital gauge is declared. We distil a ten-element benchmarking standard and apply it to our own deposit, which returned defects that changed numbers printed here and retracted one from v1. FCI-exact experiments confirm one prediction and refute another: the single generative advantage we find keeps no consistent sign along the dissociation coordinate at device-calibrated noise and reverses under a symmetric readout model. It does beat a noise-matched classical recovery loop on N2 by a margin five seeds cannot resolve, and loses by over a factor of two to a classical selector that needs no sampler.
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.