The Selected Quantum Doubles (SQD) methods are among the most reliable approaches for quantum computation, capable of achieving high-accuracy simulations of electronic structure problems. Despite their strengths, SQD methods encounter challenges related to the selection of the initial state and the efficient management of extensive configuration spaces. This is particularly due to the presence of numerous configurations with low significance, which can limit scalability and accuracy. To address these issues, we have developed a perturbative quantum method capable of generating an initial state that is both accurate and flexible, alongside a procedure to manage the scalability of the method. Regarding the first objective, a parameterized Unitary Coupled Cluster Doubles (UCCD) approach has been developed, which generates a wavefunction comparable in quality to the Coupled Cluster Doubles (CCD) reference state. At this juncture, it is possible to augment this parameterized UCCD state to incorporate the principal single excited configurations. This augmentation step is essential to ensure that the initial state possesses sufficient flexibility to account for configurations that are combinations of single and double excited configurations. The second objective is the enhancement of the methodology's scalability. This objective is achieved by first identifying, through a perturbative approach, the most significant higher-order configurations. This allows for a smaller configurational CI Hamiltonian. Conversely, the second set of configurations will not be included in the Hamiltonian CI but will be evaluated solely within a perturbative framework using second-order perturbation theory (PT2). This combined approach leverages the strengths of both variational and perturbative methods, enabling the simulation to closely approximate Full Configuration Interaction (FCI) results while operating within a significantly reduced configurational space. This methodology resembles the most common Selected Configurations Interaction plus Perturbation methodology, while distinguishing itself through an improved selection process, which will be further refined in the future. The method will be tested on a highly correlated molecular system (linear chain of 8 Hydrogen) in minimal basis set. The molecule has been optimized in pyscf with MP2 method and def2-svp basis set.
The Selected Quantum Doubles (SQD) methods are among the most reliable approaches for quantum computation, capable of achieving high-accuracy simulations of electronic structure problems. Despite their strengths, SQD methods encounter challenges related to the selection of the initial state and the efficient management of extensive configuration spaces. This is particularly due to the presence of numerous configurations with low significance, which can limit scalability and accuracy. To address these issues, we have developed a perturbative quantum method capable of generating an initial state that is both accurate and flexible, alongside a procedure to manage the scalability of the method. Regarding the first objective, a parameterized Unitary Coupled Cluster Doubles (UCCD) approach has been developed, which generates a wavefunction comparable in quality to the Coupled Cluster Doubles (CCD) reference state. At this juncture, it is possible to augment this parameterized UCCD state to incorporate the principal single excited configurations. This augmentation step is essential to ensure that the initial state possesses sufficient flexibility to account for configurations that are combinations of single and double excited configurations. The second objective is the enhancement of the methodology's scalability. This objective is achieved by first identifying, through a perturbative approach, the most significant higher-order configurations. This allows for a smaller configurational CI Hamiltonian. Conversely, the second set of configurations will not be included in the Hamiltonian CI but will be evaluated solely within a perturbative framework using second-order perturbation theory (PT2). This combined approach leverages the strengths of both variational and perturbative methods, enabling the simulation to closely approximate Full Configuration Interaction (FCI) results while operating within a significantly reduced configurational space. This methodology resembles the most common Selected Configurations Interaction plus Perturbation methodology, while distinguishing itself through an improved selection process, which will be further refined in the future. The method will be tested on a highly correlated molecular system (linear chain of 8 Hydrogen) in minimal basis set. The molecule has been optimized in pyscf with MP2 method and def2-svp basis set.
Sample-based quantum diagonalization (SQD) has emerged as a promising route for quantum-centric supercomputing, relying on classical diagonalization of the molecular Hamiltonian within a hardware-sampled determinant subspace. However, its accuracy degrades in strongly correlated regimes where the relevant determinant space exceeds what finite-shot sampling can capture. In this work, we introduce Quantum Wavefunction Augmentation via Variational Autoencoders (Q-WAVE), a hybrid method that combines determinants sampled via SqDRIFT Krylov circuits and configuration interaction singles and doubles (CISD) determinants with generative machine learning. Using a custom β-annealed variational autoencoder (VAE) model, Q-WAVE iteratively expands this basis toward the variational ground state. The VAE learns the wavefunction's primary support structure from the combined hardware and CISD seed in a continuous latent space, generating new dominant determinants beyond any fixed excitation hierarchy. The resulting compact wavefunction exceeds what can be extracted from raw hardware samples alone. We demonstrate sub-millihartree accuracy compared to full configuration interaction for H2O and N2 dissociation. Finally, we establish Q-WAVE's scalability on a 52-qubit ethylene system (achieving sub-millihartree accuracy versus CCSD(T)) and a highly correlated 60-qubit Cr2 stress test that attains chemical accuracy upon a final perturbative correction.
In this study, we analyze the choice of local unitary cluster Jastrow (LUCJ) ansatz initialization and sensitivity of the sample-based quantum diagonalization (SQD) algorithm within the quantum-centric supercomputing (QCSC) framework. We examine six initialization strategies, including those based on coupled-cluster singles and doubles (CCSD), Møller-Plesset second-order perturbation theory (MP2), data-driven coupled-cluster (DDCC), and trivial (zeroes and random) initializations, across twelve molecular systems and three basis sets (STO-3G, cc-pVDZ, and aug-cc-pVDZ). We find that while the mean absolute percentage errors (MAPEs) between the alternative and CCSD-initialized t2-amplitudes span many orders of magnitude, the resulting SQD energies are largely insensitive to this variation. In particular, most initializations recover energies within chemical accuracy (+/-1.6 mEh) of the CCSD reference, with convergence improving as the basis set size increases. Notably, random initialization achieves performance competitive with CCSD across all basis sets, while zeroes initialization, despite having smaller deviations from CCSD, yields the worst energy agreement. Our results highlight that the proximity to the CCSD initialization is not a reliable predictor of the quality of electronic energies. These findings establish that configuration recovery within SQD, rather than circuit initialization, is the dominant factor governing energy accuracy, and suggest that computationally cheaper initialization strategies are viable alternatives to CCSD for QCSC workflows
The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi–Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.
The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we investigate ground-state energy calculations of ligand-like molecules using Sample-based Quantum Diagonalization (SQD) within the Density Matrix Embedding Theory (DMET) framework, focusing on low-symmetry systems with diverse bonding motifs that exhibit subsystem-dependent variations in fragment-environment entanglement. These entanglement-based variations directly influence bath orbital construction, impurity sizes, and the structure of the embedded Hamiltonians, posing nontrivial challenges for both embedding and quantum sampling. By combining DMET fragmentation with SQD-based construction of reduced configuration spaces through quantum sampling and iterative configuration recovery, we perform quantum simulations on IBM's Eagle R3 (IBM Sherbrooke) and IBM's Heron R3 (IBM Boston) superconducting quantum hardware thereby, showing that the entanglement structure across embedding subsystems plays a central role in determining the efficiency and accuracy of the simulations. Despite these complexities, we show that the DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1 kcal/mol) across all systems studied. These results demonstrate that SQD-based quantum simulations can be robustly extended to low-symmetry, chemically realistic, industry relevant molecules, and highlight the importance of entanglement-aware embedding strategies for scalable quantum electronic structure calculations.
Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of the molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding preprocessing technique with the variational quantum eigensolver, we solve for the ground-state energy of H 2, Li 2, and BeH 2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.
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.