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.
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.
This study explores the electronic structure of the CH2 molecule, modeled as a (6e, 23o) system using a 52-qubit quantum experiment, which is relevant for interstellar and combustion chemistry. We focused on calculating the dissociation energies for CH2 in the ground state triplet and the first excited state singlet, applying the Sample-based Quantum Diagonalization (SQD) method within a quantum-centric supercomputing framework. We evaluated the ability of SQD to provide accurate results compared to Selected Configuration Interaction (SCI) calculations and experimental values for the singlet-triplet gap. To our knowledge, this is the first study of an open-shell system, such as the CH2 triplet, using SQD. To obtain accurate energy values, we implemented post-SQD orbital optimization and employed a warm-start approach using previously converged states. While the results for the singlet state dissociation were only a few milli-Hartrees from the SCI reference values, the triplet state exhibited greater variability. This discrepancy likely arises from differences in bit-string handling within the SQD method for open- versus closed-shell systems, as well as the inherently complex wavefunction character of the triplet state. The SQD-calculated singlet-triplet energy gap matched well with experimental and SCI values. This study enhances our understanding of the SQD method for open-shell systems and lays the groundwork for future applications in large-scale electronic structure studies using quantum algorithms.
Abstract The simulation of molecular electronic structure is an important application of quantum devices. Recently, it has been shown that quantum devices can be effectively combined with classical supercomputing centers in the context of the sample-based quantum diagonalization (SQD) algorithm. This allowed the largest electronic structure quantum simulation to date (77 qubits) and opened near-term devices to practical use cases in chemistry toward the hundred-qubit mark. However, the description of many important physical and chemical properties of those systems, such as photo-absorption/-emission, requires a treatment that goes beyond the ground state alone. In this work, we extend the SQD algorithm to determine low-lying molecular excited states. The extended-SQD method improves over the original SQD method in accuracy, at the cost of an additional computational step. It also improves over quantum subspace expansion based on single and double electronic excitations, a widespread approach to excited states on pre-fault-tolerant quantum devices, in both accuracy and efficiency. We employ the extended SQD method to compute the first singlet (S 1) and triplet (T 1) excited states of the nitrogen molecule with a correlation-consistent basis set, and the ground- and excited-state properties of the [2Fe-2S] cluster.
Open-shell 3d transition-metal complexes pose a stringent challenge for correlated electronic-structure methods because near-degenerate metal d orbitals give rise to competing spin states and oxidation-state-dependent charge transfer, while solvation can reshape the relative stability of the resulting electronic configurations. Building on prior demonstrations of open-shell sample-based quantum diagonalization (SQD) for light-atom systems and, separately, closed-shell SQD coupled to the integral-equation-formalism polarizable continuum model (IEF-PCM), we combine these capabilities through an open-shell SQD--IEF-PCM framework and apply it to the octahedrally coordinated [Co(H2O)5CO2]2+/3+ complex, spanning the Co(III) singlet and quintet and Co(II) doublet and quartet states along a metal--ligand dissociation coordinate. Using quantum samples collected on an IBM Heron processor and active spaces of up to 50 qubits, SQD closely reproduces coupled-cluster and heat-bath configuration-interaction benchmarks within the same active spaces in both gas phase and implicit solvent; for high-spin quintet [Co(H2O)5CO2]3+, it additionally resolves an avoided crossing associated with internal charge transfer that is absent in the corresponding singlet and in the lower oxidation state, while IEF-PCM suppresses this crossover by preferentially stabilizing the dissociation channel leading to neutral CO2. To our knowledge, this work provides the first hardware demonstration of SQD for an open-shell 3d transition-metal complex with discrete metal-centered d-orbital chemistry, and the first application of open-shell SQD in a dielectric continuum, establishing a quantum-centric framework for transition-metal chemistry in regimes where spin-state energetics, charge transfer, and environmental response are strongly coupled.
Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly suited to these computational platforms: they combine high-level calculations on active regions of a molecule with low-level calculations on the surrounding environment, thereby avoiding expensive high-level full-molecule calculations and allowing to distribute computational cost across multiple and heterogeneous computing units. Here, we present the first density matrix embedding theory (DMET) simulations performed in combination with the sample-based quantum diagonalization (SQD) method. We employ the DMET-SQD formalism to compute the ground-state energy of a ring of 18 hydrogen atoms, and the relative energies of the chair, half-chair, twist-boat, and boat conformers of cyclohexane. The full-molecule 41- and 89-qubit simulations are decomposed into 27- and 32-qubit active-region simulations, that we carry out on the ibm_cleveland device, obtaining results in agreement with reference classical methods. Our DMET-SQD calculations mark a tangible progress in the size of active regions that can be accurately tackled by near-term quantum computers, and are an early demonstration of the potential for quantum-centric simulations to accurately treat the electronic structure of large molecules, with the ultimate goal of tackling systems such as peptides and proteins.
Quantum-centric supercomputing (QCSC) approaches, such as sample-based quantum diagonalization (SQD), combine quantum processors with high-performance computers (HPC), offering a promising route toward solving challenging electronic structure problems. However, implementation of QCSC approaches to large active space calculations is constrained by the associated number of qubits, deep quantum circuits, sampling cost, and large-scale Hamiltonian diagonalization. To overcome these limitations, we introduce a distributed QCSC framework that decomposes complex molecular problems into parallel sub-problems requiring fewer qubits, shallower circuits, and reduced shot budgets. A physically motivated, two-step aggregation scheme then reconstructs the global solution: first, a computational bit assignment strategy optimizes a cost function to appropriately map local bit indices to global ones, yielding a mapped tensor product state (MTPS); second, an inter-fragment correlation recovery module restores missing cross-fragment interactions. Herein, we employ a multi-layered generative machine learning architecture, starting with utilizing the recently proposed physics-informed generative SQD (PIGen-SQD) as a distributed QCSC solver, followed by a secondary generative module to model configuration distributions and identify dominant sectors of the global Hilbert space. For water and formamide dimers, our method achieves up to 95% reduction in the diagonalization dimension while enhancing energy accuracy by an order of magnitude over conventional SQD. Furthermore, application to the water hexamer ((H2O)6) cage successfully decomposes a 120-qubit problem into six 20-qubit monomeric subsystems, and stitches the monomers under a dimeric approximation, demonstrating excellent agreement with the reference classical methods.
We provide a systematic evaluation of the sample-based quantum diagonalization (SQD) method for electronic structure based on the W4-11 thermochemistry dataset, comprising 124 total atomization, 83 bond dissociation, 20 isomerization, 505 heavy-atom transfer, and 13 nucleophilic substitution processes, covering diverse bonding situations and reaction mechanisms. This is the largest study assessing the accuracy and precision of a quantum-hybrid algorithm on a digital quantum device across a variety of molecular systems and chemical reactions, using 16.85 hours on the superconducting quantum processor ibm_rensselaer and 724.22 node hours on the supercomputer AiMOS. To ensure a fair comparison, our study employs commensurate resource allocation for both classical and quantum simulations. Although SQD exhibits large statistical deviations from ground-state reference energies, energy extrapolations yield CCSD-level accuracy. While bond-breaking reactions show a systematic improvement as computational resources increase, nucleophilic substitution or heavy atom transfer reactions do not. The limitations quantified in this manuscript indicate opportunities for improvement in SQD-based algorithms. This work provides a benchmark and community resource for exploring new quantum algorithms and devices, supported by an online benchmark challenge and an open-source Python library for direct comparison.