Quantum computation offers a promising path towards efficient calculations of the electronic structure of correlated materials. The properties of iron-based materials, which are key for advancing geological and astrophysical understanding, are notoriously difficult to calculate with classical computers. However, despite the many recent advances in quantum computing on near intermediate scale quantum hardware, a full treatment of the electronic structure of high-$Z$ atoms or molecules remains challenging. Here, we investigate the ground-state properties of molecular FeO and Fe$_2$O$_2$ model Hamiltonians using classical exact diagonalization, Variational Quantum Eigensolver (VQE), and Sample-based Quantum Diagonalization (SQD). The experimental quintet ground state of FeO is recovered classically and with quantum algorithms, while a nonet ground state is recovered for Fe$_2$O$_2$. Although raw VQE does not achieve chemical accuracy for the ground state of FeO or Fe$_2$O$_2$, SQD with two connectivity shells recovers the exact ground energy for both molecules utilizing remarkably few quantum computational resources. Overall, our results indicate that $ab \; initio$-informed low-energy models of correlated materials, combined with SQD, offer a new alternative for scaling up calculations of ground-state properties of strongly correlated solids on existing quantum hardware.
AI Summary
The paper investigates whether DFT-informed low-energy electronic models, combined with quantum sampling and classical diagonalization, can recover correlated iron-oxide ground states. It studies molecular FeO and rhombic Fe$_2$O$_2$ as benchmarks toward bulk FeO, rather than simulating the solid.
Wannier-derived Fe $3d$/O $2p$ Hamiltonians contain 16 and 32 spin orbitals, respectively, with density–density interactions parameterized by $U=4.5$ eV and $J_H=0.9$ eV. Classical exact diagonalization supplies reference energies. One-layer LUCJ circuits are optimized using noiseless classical simulations, then executed on IBM hardware solely to sample determinants. Particle-number-postselected samples define classical Ritz spaces, optionally enlarged by one or two shells of Hamiltonian connectivity.
The FeO model recovers ground-state projections $M_S=\pm2$, consistent with quintet magnetism, and predicts a first excitation of $2167$ cm$^{-1}$ versus approximately $4000$ cm$^{-1}$ experimentally. Its best LUCJ energy remains $0.173$ eV above the ground energy; two-shell diagonalization recovers the ground doublet to numerical precision using 184 determinants. For Fe$_2$O$_2$, two shells yield an error of approximately $2.7\times10^{-2}$ meV at $10^4$ QPU executions, but already retain about $85\%$ of the target spin sector and approach full-sector diagonalization with more samples.
The stated limitations include growing classical diagonalization cost and interaction parameters not independently optimized for Fe$_2$O$_2$, whose predicted nonet differs from the previously reported septet. Bulk applicability remains prospective; no periodic calculation or scaling demonstration is provided.
Little sign of AI-generated textAI use disclosedOverclaimsIncrementalMissing comparisonStrong assumptions
ChatGPT was used for some portions of the literature review, to improve VQE and SQD code, to polish phrasing in the third paragraph of the introduction
Central claim may not hold: Two-shell Fe₂O₂ exact-energy recovery uses approximately 85% to nearly all of its 12,870-dimensional fixed-spin sector, so it does not demonstrate strong compression or scalable classical postprocessing.
The demonstrated workflow trains its sampling circuits using exact classical statevector energy evaluations, leaving end-to-end scalability beyond classical simulation unestablished.
The proposed bulk extension overlooks that local electronic interactions couple individual crystal momenta, so interacting bulk FeO cannot generally be reduced to independent single-k-point diagonalizations.
The reported nondegenerate Fe₂O₂ ground state in a purely spatial symmetry sector contradicts exact spin-reversal symmetry, which requires an equal-energy opposite-magnetization partner in that sector.
The implemented onsite Jastrow layer becomes a one-body phase operation in the fully polarized-spin-register ground sectors, making the ideal ground-sector samplers fermionic Gaussian and efficiently classically sampleable.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
Quantum computation offers a promising path towards efficient calculations of the electronic structure of correlated materials. The properties of iron-based materials, which are key for advancing geological and astrophysical understanding, are notoriously difficult to calculate with classical computers. However, despite the many recent advances in quantum computing on near intermediate scale quantum hardware, a full treatment of the electronic structure of high-Z atoms or molecules remains challenging. Here, we investigate the ground-state properties of molecular FeO and Fe2O2 model Hamiltonians using classical exact diagonalization, Variational Quantum Eigensolver (VQE), and Sample-based Quantum Diagonalization (SQD). The experimental quintet ground state of FeO is recovered classically and with quantum algorithms, while a nonet ground state is recovered for Fe2O2. Although raw VQE does not achieve chemical accuracy for the ground state of FeO or Fe2O2, SQD with two connectivity shells recovers the exact ground energy for both molecules utilizing remarkably few quantum computational resources. Overall, our results indicate that abinitio-informed low-energy models of correlated materials, combined with SQD, offer a new alternative for scaling up calculations of ground-state properties of strongly correlated solids on existing quantum hardware.
The paper investigates whether DFT-informed low-energy electronic models, combined with quantum sampling and classical diagonalization, can recover correlated iron-oxide ground states. It studies molecular FeO and rhombic Fe2O2 as benchmarks toward bulk FeO, rather than simulating the solid.
Wannier-derived Fe 3d/O 2p Hamiltonians contain 16 and 32 spin orbitals, respectively, with density–density interactions parameterized by U=4.5 eV and JH=0.9 eV. Classical exact diagonalization supplies reference energies. One-layer LUCJ circuits are optimized using noiseless classical simulations, then executed on IBM hardware solely to sample determinants. Particle-number-postselected samples define classical Ritz spaces, optionally enlarged by one or two shells of Hamiltonian connectivity.
The FeO model recovers ground-state projections MS=±2, consistent with quintet magnetism, and predicts a first excitation of 2167 cm−1 versus approximately 4000 cm−1 experimentally. Its best LUCJ energy remains 0.173 eV above the ground energy; two-shell diagonalization recovers the ground doublet to numerical precision using 184 determinants. For Fe2O2, two shells yield an error of approximately 2.7×10−2 meV at 104 QPU executions, but already retain about 85% of the target spin sector and approach full-sector diagonalization with more samples.
The stated limitations include growing classical diagonalization cost and interaction parameters not independently optimized for Fe2O2, whose predicted nonet differs from the previously reported septet. Bulk applicability remains prospective; no periodic calculation or scaling demonstration is provided.
Ground-State Energy Estimation of HeH+, ArH+, and H2O via Sample-Based Quantum Diagonalization
Accurate ground-state energies are essential for understanding molecular structure, chemical bonding, and reaction energetics in quantum chemistry. In this work, we investigate the ground-state properties of the molecular systems HeH+, ArH+, and H2O using Sample-Based Quantum Diagonalization (SQD), a hybrid quantum-classical framework designed for near-term quantum devices. Unlike variational approaches such as VQE, which require deep parameterized circuits and repeated expectation-value measurements, SQD reconstructs a low-energy determinant subspace directly from measured bitstrings. For the present calculations, bitstrings were generated on IBM quantum hardware using shallow local unitary cluster Jastrow (LUCJ) circuits whose parameters were constructed from the t1 and t2 amplitudes of coupled-cluster singles and doubles (CCSD) calculations based on restricted Hartree--Fock (RHF) references. From these samples, we compute ground-state potential-energy curves of HeH+, ArH+, and H2O with the 6-31G and cc-pVDZ basis sets. For all three systems, the SQD results obtained with the cc-pVDZ basis closely follow the corresponding same-basis CCSD energies and reproduce the equilibrium-region trends of the potential-energy curves. HeH+ and ArH+ were chosen as simple yet astrophysically important molecular-ion benchmarks, while H2O was included as a representative polyatomic molecule to assess the applicability of SQD beyond diatomic ionic systems. At the adopted equilibrium geometries, the deviations from the same-active-space CASCI references are 0.00, 2.51, and 6.34 mHa for HeH+, ArH+, and H2O, respectively. These results demonstrate the feasibility of hardware-assisted SQD for the present benchmark systems and motivate further studies of its accuracy and computational scaling for larger molecular active spaces.
Quantum chemistry models atoms and molecules using quantum mechanics, with the electronic structure problem at its core. This problem, which determines the energy and properties of electrons in a molecule, is exponentially hard to solve exactly on classical computers. To approximate solutions, effective models introduce layers of simplifications. However, these approximations can fail for strongly correlated systems, necessitating alternative approaches. Quantum computers, capable of processing quantum information natively, offer a promising path to simulate molecular systems beyond classical reach, with potential applications in catalysis, materials science, and photochemistry. Despite rapid advancements in quantum hardware, practical quantum computations remain challenging due to limited resources. This thesis optimizes quantum resource usage in computational chemistry, introducing novel embedding techniques and exploring applications beyond ground-state energies. Chapter 1 establishes the foundation by reviewing quantum chemistry methods, from Hartree-Fock and Density Functional Theory (DFT) to active space approaches. It also provides an introduction to quantum computing for chemistry, focusing on near-term algorithms. The following chapters present novel methods aimed at reducing quantum resource requirements and tackling problems classical methods struggle with. Chapter 2 introduces a technique to reduce the λ-norm of the electronic structure Hamiltonian, a key measure of quantum resource demand. By transforming molecular orbitals, this method enhances sampling efficiency in Noisy Intermediate-Scale Quantum (NISQ) algorithms and reduces runtime in Fault-Tolerant Quantum Computing (FTQC). Localized orbitals outperform canonical ones, and an orbital-optimization scheme is proposed to minimize the λ-norm. Benchmarks on hydrogen chains, FeMoco, and Ruthenium complexes demonstrate its effectiveness. Chapter 3 presents the FragPT2 framework for simulating large systems with multiple interacting fragments. This method embeds each fragment in the mean field of others and applies multi-reference perturbation theory to capture inter-fragment correlations such as dispersion and charge transfer efficiently. The approach reduces computational overhead and enables scalable simulations, as shown in applications to \ce{N2} dimers, aromatic dimers, and butadiene. Chapter 4 focuses on photochemical systems, where multiple electronic states must be treated equally. The state-averaged orbital-optimized variational quantum eigensolver (SAOOVQE) is extended with analytical energy gradients and non-adiabatic couplings, enabling geometry optimizations and simulations of non-adiabatic dynamics on quantum hardware. This is demonstrated by locating the conical intersection in formaldimine, highlighting SAOOVQE’s potential for studying photoisomerization in biomolecules. Building on this, Chapter 5 develops a quantum algorithm to detect conical intersections, where the Born-Oppenheimer approximation breaks down. These intersections are characterized by a discrete Berry phase (0 or π), representing their topological nature. The algorithm extracts this phase as a single bit of information, ensuring resilience to noise. Analytical proof and numerical validation using a toy molecular model illustrate its effectiveness for studying light-perception biochemistry and related photochemical processes. Finally, Chapter 6 explores machine learning density functionals trained on noisy quantum data. While DFT is computationally efficient, its accuracy depends on approximated exchange-correlation functionals. This work proposes a neural network-based approach to learn the exact functional from quantum data, showing that training on noisy outputs from NISQ devices can mitigate sampling errors. Applications to the Fermi-Hubbard model and other systems demonstrate its potential to generalize and provide accurate results under noise. This thesis advances quantum computational chemistry by optimizing quantum resource usage, developing new embedding strategies, and expanding the scope of quantum simulations beyond ground-state properties. These contributions pave the way for practical quantum algorithms that could revolutionize molecular simulations in the near future.
Accurately capturing electron correlation in large-scale molecular systems remains one of the foremost challenges in quantum chemistry and a primary driver for the development of quantum algorithms. Classical configuration-interaction methods, while rigorous, suffer from exponential scaling, rendering them impractical for large or strongly correlated systems. Overcoming this limitation is central to realizing the promise of quantum computing in chemistry. Here, we investigate the pyridine-Li ion complex using three quantum algorithms: the variational quantum eigensolver (VQE), the subspace quantum diagonalization (SQD) method, and the recently introduced handover iterative VQE (HI-VQE). Our results demonstrate how new generations of hybrid quantum-classical frameworks overcome the scalability and noise sensitivity that constrain conventional VQE approaches. SQD and HI-VQE achieve ground-state energy calculations for problem sizes inaccessible to classical computation, marking a clear advance toward quantum advantage. In particular, HI-VQE enables calculations within active spaces as large as (24e,22o), requiring 44 qubits-well beyond the reach of classical CASCI and VQE. This capability provides a systematic pathway for incorporating increasing numbers of electrons into quantum treatment, thereby approaching exact molecular energies. Importantly, both SQD and HI-VQE exhibit robustness against hardware noise, a critical improvement over earlier approaches. By enabling quantum simulations of molecular systems previously deemed intractable, SQD and HI-VQE offer a realistic route toward practical quantum advantage in computational chemistry. The comparison between HI-VQE and SQD shows that optimizing circuit parameters is crucial for accurate simulation.
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.
Describing correlated electron systems has been a major challenge in computational condensed-matter physics. Quantum Monte Carlo, a powerful computational tool for the study of correlated systems, solves electron correlation problems explicitly. It has been taken as a benchmark method for understanding the correlated systems. Instead of making approximations to Hamiltonian, QMC methods work with the wave functions, and the computational cost scales well with the system size. With the development of parallel computing, QMC calculations on large systems are becoming more and more feasible. We have investigated two correlated systems with highly accurate fixed node QMC techniques. The first system is a correlated hydrogen model system near the metal to insulator transition. We have successfully identified the transition point by calculating spin and charge properties and analyzing the low energy Hilbert space. The second one is a strongly correlated Fe/O system. Calculations on the Fe atoms, O atoms, and FeO molecules are conducted with multiple highly accurate many-body techniques. The source of errors has been disentangled by comparing the results of the many body techniques with the experimental results. For the Fe and O atoms, the calculated properties coincide well with previous experimental results. For the basis-based techniques, the performance is mainly limited by the basis set. The calculated equilibrium bond length, excitation energy and vibrational frequency of the FeO molecules are also in close agreement with the known values from previous experiments.
Extending the Handover-Iterative VQE to Challenging Strongly Correlated Systems: N2 and Fe-S Cluster
Accurately describing strongly correlated electronic systems remains a central challenge in quantum chemistry, as electron-electron interactions give rise to complex many-body wavefunctions that are difficult to capture with conventional approximations. Classical wavefunction-based approaches, such as the Semistochastic Heat-bath Configuration Interaction (SHCI) and the Density Matrix Renormalization Group (DMRG), currently define the state of the art, systematically converging toward the Full Configuration Interaction (FCI) limit, but at a rapidly increasing computational cost. Quantum computing algorithms promise to alleviate this scaling bottleneck by leveraging entanglement and superposition to represent correlated states more compactly. We introduced the Handover-Iterative Variational Quantum Eigensolver (HI-VQE) as a practical quantum computing algorithm with an iterative "handover" mechanism that dynamically exchanges information between quantum and classical computers, even using Noisy Intermediate-Scale Quantum (NISQ) computers. In this work, we extend the HI-VQE to benchmark two prototypical strongly correlated systems, the nitrogen molecule N2 and iron-sulfur (Fe-S) cluster, which serve as stringent tests for both classical and quantum electronic-structure methods. By comparing HI-VQE results against Heat-bath Configuration Interaction (HCI) benchmarks, we assess its accuracy, scalability, and ability to capture multireference correlation effects. Achieving quantitative agreement on these canonical systems demonstrates a viable pathway toward quantum-enhanced simulations of complex bioinorganic molecules, catalytic mechanisms, and correlated materials.