This work shows that SQD performance can be strongly influenced by uncontrolled growth of the classical diagonalization subspace, and establishes measurement-basis engineering as a promising route to improving quantum sampling methods for electronic structure.
Abstract
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.
The quantum-selected configuration interaction identifies important determinantal basis functions through real-time evolution of a reference wavefunction and diagonalizing the Hamiltonian matrix in the resulting selected subspace. However, implementing the full electronic Hamiltonian on noisy quantum devices leads to rapidly increasing circuit complexity, limiting its scalability. To address this issue, we identify the dominant fermionic excitation operators and perform reference-state fidelity loss analysis to construct a compact Hamiltonian, reducing computational overhead while retaining high precision. Applied to Group IIIA monofluorides (BF, AlF, GaF, InF, and TlF), the proposed framework achieves a near-quadratic improvement in Hamiltonian-term scaling, enabling resource-efficient simulations. We employ this framework to compute the relativistic ground-state energies and permanent electric dipole moments (PDMs) of the systems under consideration. After validating the framework via simulations, we demonstrate hardware execution for AlF and TlF on the IBM Marrakesh processor using active spaces of up to 20 qubits. For a 20-qubit TlF system, the reduced Hamiltonian yields a reduction of higher than $ 98\%$ in both circuit depth and two-qubit gate counts, with the resulting PDMs from quantum hardware matching complete active space configuration interaction values within $99.99\%$. These results demonstrate the scalability of this approach on noisy intermediate-scale quantum devices.
Suprava Sahoo, Abdul Kalam, Kenji Sugisaki et al.· 0 citations
This work introduces a methodology for performing anharmonic vibrational structure calculations that can be deployed in a hybrid, quantum-classical mode and demonstrates a hybrid, quantum-classical computational workflow, in which a quantum sampling algorithm provides the seed.
R. F. Ligório, Marco Antonio Barroca, Alan C. Duriez et al.· 0 citations
This work presents a hybrid DFT-Quantum Embedding (QDFT) framework integrating classical HPC-based DFT with a quantum electronic-structure solver, demonstrating quantum embedding's potential to improve selected electronic-structure properties while retaining classical HPC's scalability.
N. Manglani, S. Maity, Shashank Sharma et al.· 0 citations
Predicting spectra and photochemical pathways relies on the computation of molecular excited states. However, the practicality of near-term variational quantum algorithms is threatened by the prohibitive growth of measurement overheads. Integrating Quantum Subspace Expansion with the Contextual Subspace (CS) method, we propose a CS-QSE framework to resolve the scaling bottlenecks in excited-state energy estimation. By confining excitation operators to a compact CS, the framework removes redundant degrees of freedom and reduces Pauli string counts, thereby easing the measurement burden. The primary strength of CS-QSE lies in its substantial reduction of the operator-pool size. Benchmarking on LiH, HF, H2O, and HCl shows that CS-QSE achieves errors within the target tolerance of 1.6 × 10-3 Ha relative to full configuration interaction benchmarks in the same basis set while mitigating the prohibitive scaling inherent in the full-space method. Numerical simulations reveal that the operator pool size is consistently pruned by over 90% across all systems, with the reduction reaching as high as 99.7% for molecules such as HCl. This CS-QSE framework establishes a resource-efficient route for molecular simulations tailored to near-term noisy intermediate-scale quantum devices.
Chao Liu, Yuxin Deng· Journal of Chemical Theory a...· 0 citations
These benchmarks establish LUCJ+SQD as a practical route for integrating current quantum hardware into QM/MM molecular dynamics and provide an early demonstration of condensed-phase QM/MM dynamics driven by a quantum electronic-structure engine.
Susanta Das, Subhamoy Bhowmik, Zhen Li et al.· 0 citations
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.
Hayun Park, Younghun Kwon, Hunpyo Lee· 1 citation· ⚡1
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