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arXiv:2602.07912

Doubling the size of quantum selected configuration interaction based on seniority-zero space and its application to QC-QSCI-AFQMC

Yuichiro Yoshida, Takuma Murokoshi, Naoya Kuroda, Wataru Mizukami

quant-phphysics.chem-phSubmitted Feb 8, 2026• Announced Feb 10, 2026• 0 citations
v1 · Feb 8, 2026v2 · Feb 27, 2026
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Abstract

We propose doubly occupied configuration interaction-quantum selected configuration interaction (DOCI-QSCI), which samples from the seniority-zero space. While the use of this space effectively doubles the qubit budget, equaling the number of spatial orbitals, this sector restriction can compromise quantitative accuracy. To compensate for this, we expand sampled bitstrings via their Cartesian product into a larger space that includes seniority-breaking determinants. The resulting wave function is also proposed using the trial state in phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) to recover dynamical correlations across the full orbital space (DOCI-QSCI-AFQMC). We evaluate the proposed methods on the H6 chain, N2 dissociation, and the addition of singlet O2 to a BODIPY dye. For the H6 chain, DOCI-QSCI-AFQMC reproduces the accuracy of the level of the complete-active-space counterpart with the quantum device ibm kobe. For N2 and BODIPY-O2, with (14e, 28o) and up to (20e, 20o) active spaces, it yields reasonable results, whereas single-reference CCSD(T) fails qualitatively. These results demonstrate that the DOCI-QSCI doubles the orbital space accessible to conventional QSCI and subsequent ph-AFQMC post-processing delivers reasonably high accuracy.

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8 pages, 5 figures

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We propose doubly occupied configuration interaction-quantum selected configuration interaction (DOCI-QSCI), which samples from the seniority-zero space. While the use of this space effectively doubles the qubit budget, equaling the number of spatial orbitals, this sector restriction can compromise quantitative accuracy. To compensate for this, we expand sampled bitstrings via their Cartesian product into a larger space that includes seniority-breaking determinants. The resulting wave function is also proposed using the trial state in phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) to recover dynamical correlations across the full orbital space (DOCI-QSCI-AFQMC). We evaluate the proposed methods on the H6 chain, N2 dissociation, and the addition of singlet O2 to a BODIPY dye. For the H6 chain, DOCI-QSCI-AFQMC reproduces the accuracy of the level of the complete-active-space counterpart with the quantum device ibm kobe. For N2 and BODIPY-O2, with (14e, 28o) and up to (20e, 20o) active spaces, it yields reasonable results, whereas single-reference CCSD(T) fails qualitatively. These results demonstrate that the DOCI-QSCI doubles the orbital space accessible to conventional QSCI and subsequent ph-AFQMC post-processing delivers reasonably high accuracy.
We present an approach that uses the doubly occupied configuration interaction (DOCI) wave function as the trial wave function in phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC). DOCI is a seniority-zero method focused on electron pairs. Although DOCI considers much fewer electron configurations than the complete active space (CAS) configuration interaction method, it efficiently captures the static correlation, while the consequent ph-AFQMC recovers the dynamical correlation across all orbitals. We also explore an orbital-optimized version (OO-DOCI) to further improve accuracy. We test this approach on several chemical systems, including single O-H bond breaking in water and polymer additives. In these cases, OO-DOCI-AFQMC closely matches CAS-based ph-AFQMC and even outperforms coupled-cluster singles, doubles, and perturbative triples. However, for strongly correlated systems, such as the carbon dimer and multi-bond dissociation in hydrogen systems and water, the method's accuracy drops. This suggests that seniority-zero space models may be insufficient as trial wave functions in ph-AFQMC for strongly correlated systems, suggesting the need for trial wave functions in an extended space. Despite such a limitation, our study demonstrates that DOCI- and OO-DOCI-based ph-AFQMC can reduce the steep cost of CAS approaches, offering a path to accurate multi-reference calculations for larger, more complex systems.
We present an approach that uses the doubly occupied configuration interaction (DOCI) wave function as the trial wave function in phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC). DOCI is a seniority-zero method focused on electron pairs. Although DOCI considers much fewer electron configurations than the complete active space (CAS) configuration interaction method, it efficiently captures the static correlation, while the consequent ph-AFQMC recovers the dynamical correlation across all orbitals. We also explore an orbital-optimized version (OO-DOCI) to further improve accuracy. We test this approach on several chemical systems, including single O-H bond breaking in water and polymer additives. In these cases, OO-DOCI-AFQMC closely matches CAS-based ph-AFQMC and even outperforms coupled-cluster singles, doubles, and perturbative triples. However, for strongly correlated systems, such as the carbon dimer and multibond dissociation in hydrogen systems and water, the method's accuracy drops. This suggests that seniority-zero space models may be insufficient as trial wave functions in ph-AFQMC for strongly correlated systems, suggesting the need for trial wave functions in an extended space. Despite such a limitation, our study demonstrates that DOCI- and OO-DOCI-based ph-AFQMC can reduce the steep cost of CAS approaches, offering a path to accurate multireference calculations for larger, more complex systems.
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.
Over the past few years, pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.
We present efficient algorithms for using selected configuration interaction (sCI) trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC). These advances, geared toward optimizing computational performance for longer configuration interaction expansions, allow us to use up to a million configurations in the trial state for ph-AFQMC. In one example, we found the cost of ph-AFQMC per sample to increase only by a factor of about 3 for a calculation with 104 configurations compared to that with a single one, demonstrating the tiny computational overhead due to a longer expansion. This favorable scaling allows us to study the systematic convergence of the phaseless bias in auxiliary field quantum Monte Carlo calculations with an increasing number of configurations and provides a means to gauge the accuracy of ph-AFQMC with other trial states. We also show how the scalability issues of sCI trial states for large system sizes could be mitigated by restricting them to a moderately sized orbital active space and leveraging the near-cancellation of out of active space phaseless errors.
Doubly occupied configuration interaction (DOCI), the exact diagonalisation of the Hamiltonian in the paired (seniority zero) sector of the Hilbert space, is a combinatorial cost wave function that can be very efficiently approximated by pair coupled cluster doubles (pCCD) at mean-field computational cost. As such, it is a very interesting candidate as a starting point for building the full configuration interaction (FCI) ground state eigenfunction belonging to all (not just paired) seniority sectors. The true seniority zero sector of FCI (referred to here as FCI0) includes the effect of coupling between all seniority sectors rather than just seniority zero, and is, in principle, different from DOCI. We here study the accuracy with which DOCI approximates FCI0. Using a set of small Hubbard lattices, where FCI is possible, we show that DOCI ∼ FCI0 under weak correlation. However, in the strong correlation regime, the nature of the FCI0 wavefunction can change significantly, rendering DOCI and pCCD a less than ideal starting point for approximating FCI.