Open-shell $3d$ transition-metal complexes challenge electronic-structure methods because competing spin states, charge transfer, and solvation jointly determine their energetics. Here, we combine sample-based quantum diagonalization (SQD) with the integral-equation-formalism polarizable continuum model (IEF-PCM), extending SQD to correlated open-shell transition-metal systems in a dielectric environment.
We investigate the octahedrally coordinated $\mathrm{[Co(H_2O)_5CO_2]^{2+/3+}}$ complex across two oxidation states, four spin multiplicities, and a metal-ligand dissociation coordinate. We study the Co(III) singlet and quintet states and the Co(II) doublet and quartet states, incorporating open-shell references into SQD-IEF-PCM through an outer self-consistent reaction-field loop. Using samples collected on an IBM Heron quantum processor and active spaces of up to 50 qubits, SQD reproduces coupled-cluster and heat-bath configuration-interaction benchmarks within the same active space in the gas phase and implicit solvent, with a largest observed deviation below 9 $mE_h$. Along the dissociation coordinate of high-spin quintet $\mathrm{[Co(H_2O)_5CO_2]^{3+}}$, SQD resolves an avoided crossing caused by internal charge transfer; this feature is absent in the singlet and the lower oxidation state of the complex. Relative to the gas phase, implicit solvation stabilizes for the quintet state the neutral CO$_2$ dissociation and suppresses the avoided-crossing feature.
To our knowledge, this is the first hardware demonstration of SQD for an open-shell $3d$ transition-metal complex in gas phase and implict solvent. These results establish SQD as a robust quantum-centric approach for transition-metal chemistry where spin state ordering, charge transfer, and environmental effects are strongly intertwined.
Open-shell 3d transition-metal complexes challenge electronic-structure methods because competing spin states, charge transfer, and solvation jointly determine their energetics. Here, we combine sample-based quantum diagonalization (SQD) with the integral-equation-formalism polarizable continuum model (IEF-PCM), extending SQD to correlated open-shell transition-metal systems in a dielectric environment.
We investigate the octahedrally coordinated [Co(H2O)5CO2]2+/3+ complex across two oxidation states, four spin multiplicities, and a metal-ligand dissociation coordinate. We study the Co(III) singlet and quintet states and the Co(II) doublet and quartet states, incorporating open-shell references into SQD-IEF-PCM through an outer self-consistent reaction-field loop. Using samples collected on an IBM Heron quantum processor and active spaces of up to 50 qubits, SQD reproduces coupled-cluster and heat-bath configuration-interaction benchmarks within the same active space in the gas phase and implicit solvent, with a largest observed deviation below 9 mEh. Along the dissociation coordinate of high-spin quintet [Co(H2O)5CO2]3+, SQD resolves an avoided crossing caused by internal charge transfer; this feature is absent in the singlet and the lower oxidation state of the complex. Relative to the gas phase, implicit solvation stabilizes for the quintet state the neutral CO2 dissociation and suppresses the avoided-crossing feature.
To our knowledge, this is the first hardware demonstration of SQD for an open-shell 3d transition-metal complex in gas phase and implict solvent. These results establish SQD as a robust quantum-centric approach for transition-metal chemistry where spin state ordering, charge transfer, and environmental effects are strongly intertwined.
The sample-based quantum diagonalization (SQD) method shows great promise in quantum-centric simulations of ground state energies in molecular systems. Inclusion of solute-solvent interactions in simulations of electronic structure is critical for biochemical and medical applications. However, all of the previous applications of the SQD method were shown for gas-phase simulations of the electronic structure. The present work aims to bridge this gap by introducing the integral equation formalism polarizable continuum model (IEF-PCM) of solvent into the SQD calculations. We perform SQD/cc-pVDZ IEF-PCM simulations of methanol, methylamine, ethanol, and water in aqueous solution using quantum hardware and compare our results to CASCI/cc-pVDZ IEF-PCM simulations. Our simulations on ibm_cleveland, ibm_kyiv, and ibm_marrakesh quantum devices are performed with 27, 30, 41, and 52 qubits demonstrating the scalability of SQD IEF-PCM simulations.
Quantum-chemical simulations are essential for predicting energies of chemical reactions. Accurately solving the many-body Schrödinger equation for reagent and product states of most relevant chemical processes is, however, unfeasible. Quantum computing offers a pathway for predicting energies of correlated electronic systems with localized interactions. Here, we apply a quantum embedding approach for investigating oxygen reduction reactions at the electrode surface in Lithium batteries, a representative example of energetic analysis in localized chemical reactions. We employ an active space selection method based on density difference analysis for identifying the orbitals involved in the reaction. Leveraging the Local Unitary Cluster Jastrow ansatz for state preparation, the active-space orbitals are then processed on a quantum computer. As quantum algorithms, we use Sample-based Quantum Diagonalization, SQD, and its extended version, Ext-SQD, which integrates electronic excitations into the quantum-selected electronic configuration subspace. The largest configurations are represented by quantum circuits mapped onto 80 qubits of an IBM Heron R2 quantum processing unit. For up to 12 orbitals, we are able to benchmark the quantum-computed reaction energies against results obtained with Complete Active Space Configuration Interaction. For benchmarking results in active spaces as large as 32 orbitals, we resort to Heat-Bath Configuration Interaction and Coupled Cluster Singles and Doubles calculations, respectively. At 27 orbitals, the Ext-SQD results exhibit prediction accuracy improvements with regard to the standard, quantum-chemical reference methods that remain computationally feasible at that scale. The results indicate the potential of sample-based quantum diagonalization for performing high-accuracy reaction modeling in chemistry and materials science.
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.
High Resolution Image Download MS PowerPoint Slide This study involves quantum simulations of the dissociation of the ground-state triplet and first excited singlet states of the CH 2 molecule (methylene), which are relevant for interstellar and combustion chemistry. These were modeled as (6e, 23o) systems using 52 qubits on a quantum processor by applying the sample-based quantum diagonalization (SQD) method within a quantum-centric supercomputing framework. We evaluated the ability of SQD to provide accurate results of the singlet-triplet gap in comparison to selected configuration interaction (SCI) calculations and experimental values. To our knowledge, this is the first study of an open-shell system (the CH 2 triplet) using SQD. To obtain accurate energy values, we implemented post-SQD orbital optimization and employed a warm-start approach using previously converged states. The results for the singlet state dissociation were highly accurate, differing by only a few milli-Hartrees from the SCI reference values. Similarly, the SQD-calculated singlet-triplet energy gap aligned well with both experimental and SCI values, underscoring the method’s capability to capture key features of CH 2 chemistry. However, the triplet state exhibited greater variability, likely due to differences in bit-string handling within the SQD method for open- versus closed-shell systems and the inherently complex wavefunction character of the triplet state. These findings highlight the strengths and limitations of SQD for modeling open-shell systems while laying a foundation for its application in large-scale electronic structure studies using quantum algorithms.
Diazirines and diazo compounds are widely employed as photoreactive precursors for generating carbenes, key intermediates in chemical biology and materials science. However, computationally modeling their reaction pathways remains challenging due to the need for large active spaces and the requirement to accurately capture excited-state surfaces along with transition states and conical intersections. In this work, we utilize a hybrid quantum-classical workflow for investigating carbene formation in representative diazirine-diazomethane systems. Our approach leverages Sample-based Quantum Diagonalization (SQD) and its extended variant, Extended Sample-based Quantum Diagonalization (Ext-SQD), for ground- and excited-state analysis, combined with classical tools for geometry optimization, active-space selection, and diagnostic evaluation. Quantum computations were carried out on superconducting quantum processors, and results for both aliphatic and aryl-substituted diazirine-diazomethane pairs were benchmarked against established classical methods, including density functional theory (DFT), coupled cluster with singles and doubles (CCSD), complete active space configuration interaction (CASCI), and selected configuration interaction (SCI). SQD achieves accuracy surpassing the chemical accuracy threshold for nearly all stationary points on the potential energy surface of parent diazirine relative to the CASCI(12,10) reference, and remains close to chemical accuracy for phenyl-substituted diazirine in a (30,30) active space, with an average deviation of 1.1 kcal/mol relative to the SCI benchmark. SQD closely follows CASCI and SCI trends, showing consistent agreement. The findings demonstrate the promise of quantum computing frameworks in modeling photochemical transformations of electronically complex and pharmacologically relevant molecules.
We develop a hybrid quantum-classical workflow combining sample-based quantum diagonalization (SQD) and the localized active space self-consistent field method (LASSCF) to solve for the ground states of transition-metal complexes, a longstanding challenge for both classical and quantum algorithms. The resulting approach, named LASSQD, integrates quantum sampling with fragment-based multireference theory to reduce the computational cost of solving strongly correlated active spaces. We test LASSQD on multiple iron-based complexes and demonstrate that it agrees with LASSCF within 1 kcal/mol, albeit at a much reduced computational cost. The cost reduction originates from the use of a sparse approximation of the exact and combinatorially large ground-state wavefunction, which also enables LASSQD to treat fragment sizes that are computationally inaccessible to LASSCF, as demonstrated by our computation of the spin gap of iron-porphyrin. These results establish that LASSQD is a scalable strategy for generating reliable multireference wave functions, providing a robust starting point for post-SCF correlation methods that recover dynamic correlation beyond the active space, and a promising pathway toward quantum-enhanced electronic structure calculations.