Analytical Nuclear Gradients and Hessians on Quantum Hardware via Orbital-Optimized VQE with Error Mitigation

Optimizing Subspace Expansion in Quantum Chemistry through Operator Selection and Reference State Choice

The Virtual Quantum Subspace Expansion (VQSE) extends the Variational Quantum Eigensolver (VQE) by leveraging additional measurements on the reference state to capture the influence of excluded virtual orbitals. This makes VQSE attractive for chemical applications where accurate energy differences along potential energy surfaces are crucial for modeling reaction rates and kinetics. In this work, we analyze VQSE performance on H$_2$ dissociation including references that use Hartree--Fock molecular orbitals with broken spin symmetry. We identify two mechanisms which affect accuracy: overlap of the reference state with the exact full configuration interaction (FCI) wavefunction and operator pool expressivity. We show these mechanisms are strongly co-dependent. When operators are restricted to act only from the active to the virtual space, results become highly sensitive to the reference, and enlarging the active space does not guarantee improved accuracy. In this case, prioritizing reference overlap over energy minimization is therefore essential. Adding single excitations and number operators within the active space recovers the accuracy of MR-CISD (multi-reference configuration interaction singles and doubles) regardless of the reference. In our noisy hardware experiments, we achieve chemical accuracy by adding additional operators and using strict regularization. These findings motivate careful co-design of reference fidelity, pool expressivity, and hardware constraints for practical VQSE deployment.

HessFit: Deriving Molecule-Specific Force Fields from Quantum Mechanical Hessians.

Nonadiabatic Molecular Dynamics with Quantum Algorithms.

This work performs excited-state molecular dynamics simulations of the formaldimine molecule by combining the surface hopping nonadiabatic molecular dynamics technique with quantum algorithms, and evaluates the accuracy and feasibility of three different gradient calculation approaches integrated with the quantum computing components.

Resource-efficient quantum-selected configuration interaction for molecular properties

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.

ViBra: Configuration Interaction for Anharmonic Vibrational Spectroscopy and Quantum-Sampled Configuration Spaces

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.

Toward High-Throughput Virtual Screening via Quasi-Adiabatic Quantum Geometry Optimization Workflow

This work addresses the challenge of molecular geometry optimization at post-Hartree–Fock levels of theory using quantum computing methodologies. We present a novel potentially quasi-adiabatic approach based on the Variational Quantum Eigensolver (VQE) algorithm for efficient exploration of potential energy surfaces. The method combines quantum-circuit emulators with classical optimization routines and uses the Hellmann–Feynman theorem, including Pulay corrections, together with a finite-difference scheme to compute forces. Our implementation uses GPU-accelerated quantum-circuit operations within a parallelized framework, achieving computational efficiency by warm-starting the wavefunction and reoptimizing it at each subsequent geometry-optimization step. Benchmark results on small molecular systems demonstrate the feasibility of this hybrid quantum-classical approach, with detailed comparisons against established quantum chemistry methods, including CASCI and DFT optimizations. We discuss the current limitations, computational advantages, and potential future developments of this methodology in the context of quantum chemistry for drug discovery applications.