The EWF-(FCI,SQD) method, a wave-function-based embedding approach combining full configuration interaction (FCI) and sample-based quantum diagonalization (SQD), is a promising new tool for the simulation of molecular systems. However, applications of EWF-(FCI,SQD) have so far been limited to single-point calculations, whereas the study of complex chemical processes requires the ability to explore potential energy surfaces. In this work, we demonstrate geometry optimization with EWF-(FCI,SQD), scaling our simulations to molecules as large as menthone and benzidine within the STO-3G basis set. Without fragmentation, these systems comprise 73 and 82 molecular orbitals respectively, presenting an intractable Hilbert space for conventional exact or high-level subspace solvers and establishing a clear necessity for fragmentation-based methodologies. The underlying fragment SQD simulations in the EWF-(FCI,SQD) geometry optimizations use up to 70 qubits. The resulting geometries show exceptional accuracy relative to the classical reference, with deviations below 4 picometers.
Quantum-centric workflows are a promising route to improving the accuracy of property predictions in computational chemistry and materials science. By integrating quantum sampling algorithms with classical solvers, electronic structure calculations have recently demonstrated their potential even on noisy intermediate-scale quantum devices. In principle, the method of Vibrational Configuration Interaction (VCI) is suitable for integration with quantum sampling algorithms as well. However, demonstrations of computational workflows for quantum-centric, vibrational property predictions are still lacking. Here, we introduce a methodology for performing anharmonic vibrational structure calculations that can be deployed in a hybrid, quantum-classical mode. Starting from a quartic force field, the approach combines a Vibrational Self-Consistent Field (VSCF) with VCI in either Full, Selected (S-VCI), or Symmetry-Adapted (SA-VCI) mode. In S-VCI, an Epstein-Nesbet perturbative screening significantly reduces the configuration space while retaining high predictive accuracy. A state-list input enables the integration of externally generated vibrational configurations as a seed space. As a proof-of-concept, we demonstrate a hybrid, quantum-classical computational workflow, in which a quantum sampling algorithm provides the seed. Our vibrational wave function analysis package ViBra, equipped with a graphical interface, is available at https://github.com/raphafe96/ViBra.
R. F. Ligório, M. A. Barroca, Alan Duriez et al.· 0 citations
The seamless integration of Density Functional Theory (DFT) with quantum variational algorithms is essential for the predictive simulation of strongly correlated materials. In this work, we present an end-to-end computational pipeline - comprising DFT geometry relaxation, non-self-consistent field (NSCF) calculations, and Wannier-based orbital localization - to prepare active-space Hamiltonians for quantum embedding. We utilize the Adaptive Variational Quantum Eigensolver (ADAPT-VQE) framework, significantly enhanced by a Greedy-Operator Commutativity Partitioning (GOCP) approach and a Taylor-expanded O(5) operator evolution strategy to efficiently manage the exponential scaling of the Hilbert space. We demonstrate this framework through a systematic benchmark study of Li-hBN, mapping the system onto qubit registers and investigating the convergence behavior as the active space is expanded from 8 to 14 spatial orbitals. Our results quantify the relationship between active-space size and computational demand, identifying a critical"scaling wall"where classical simulation costs transition from manageable to intractable. This study provides a rigorous performance baseline for the DFT-to-ADAPT-VQE workflow and offers empirical insights into the memory and processing limits currently facing hybrid quantum-classical architectures using advanced co-processing strategies.
Quantum embedding methods offer a promising route to extend quantum chemical calculations to large multiscale systems by treating a chemically important subsystem at a high level of theory while describing its surrounding environment at an affordable level. The methods are also quite relevant for quantum computing approaches based on hardware with limited resources. Here, we present an iterative projection-based embedding framework combined with VQE, in which the environment density is allowed to respond self-consistently to the refined electronic structure of the embedded subsystem described by VQE. Unlike conventional one-shot approaches where the environment remains frozen after the initial orbital optimization, the proposed iterative scheme alternates between the VQE-level treatment of the subsystem and a mean-field-level refinement of the environment until mutual self-consistency is achieved. The convergence behavior of the scheme is first examined using several small test systems. Its practical applicability is then demonstrated with a composite system with a CH2NH molecule sandwiched by two benzene rings, with the C=N dihedral angle rotating from 0 to 90 deg. The iterative procedure consistently converges within ~10 iteration steps across all tested geometries, yielding energies below the conventional one-shot embedding results. The converged results well reproduce the fully correlated reference energy employing the same active space, and the resulting potential energy surface with respect to the dihedral rotation is also in good agreement with the reference one. These results demonstrate that our iterative embedding framework is numerically robust and physically sound, yielding a self-consistent and reliable treatment of inter-subsystem correlation. We expect that its formulation will be particularly compatible with the emerging paradigm of quantum-classical hybrid computing.
Hongseok Choi, Kyungmin Kim, Young Min Rhee· 0 citations
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.
S. Sahoo, Abdul Kalam, Kenji Sugisaki et al.· 0 citations
In variational Monte Carlo (VMC) calculations of $N$-site quantum systems with arbitrary all-to-all two-body interactions, evaluating the local energy generally costs $O(N^3)$. We introduce a new framework that reduces this cost to $O(N)$ for tensor network states, capable of scalable and accurate computation of real-time dynamics and ground states. As a result, we obtain accurate simulations of the adiabatic real-time protocol of a $10\times10$ dipolar XY model realized in a Rydberg simulator [C. Chen et al., Nature 616, 691 (2023)], which was previously beyond the reach of classical simulation. Going beyond quantum experiments, we also directly perform ground state VMC to compare with the adiabatic state preparation. Our work demonstrates tensor network VMC as a powerful classical simulator for long-range quantum platforms such as Rydberg and ion-trap simulators, which are currently in urgent need of scalable classical benchmarking tools. As a separate technical contribution, we resolve the pathology of evolving from product states within of tensor network VMC.
Nuclear gradients and Hessians are fundamental quantities in computational chemistry, essential for a wide range of applications including geometry optimization, vibrational spectroscopy, and molecular property calculations. In this work, we present their analytical implementation on quantum hardware. The methodology is formulated within an active-space framework combining orbital optimization and linear-response theory. On the quantum-computing side, the approach employs the tiled unitary product state (tUPS) ansatz to directly evaluate the tensor elements required for solving the response equations. Moreover, the expectation values are corrected using an adapted confusion-matrix error-mitigation scheme in combination with post-selection criteria. The resulting workflow is assessed on molecular hydrogen and on water through the calculation of potential energy surfaces, nuclear gradients, Hessians, and vibrational frequencies, enabling the evaluation of both its capabilities and current limitations. The results demonstrate good performance for the hydrogen molecule, whereas the water molecule provides a more demanding test of quantum-hardware resources and highlights the trade-offs associated with error-mitigation strategies. The quantified analysis of the results identify the main sources of errors, suggesting improvement directions for more accurate quantum computer applications.
Renato Olarte Hernandez, K. M. Ziems, Erik Kjellgren et al.· 0 citations