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arXiv:2504.17453 · AIP Advances

Quantum simulation of CO2 chemisorption in an amine-functionalized metal–organic framework

Jonathan R. Owens, Marwa H. Farag, Pooja Rao, Annarita Giani

Published Jan 1, 2026• 2 citations
arXivHTMLPDF

Abstract

We perform a series of calculations using simulated quantum processing units (QPUs), accelerated by the NVIDIA CUDA-Q platform, focusing on a molecular analog of an amine-functionalized metal–organic framework, a promising class of materials for CO2 capture. The variational quantum eigensolver (VQE) technique is employed, utilizing both the unitary coupled-cluster method with singles and doubles and adaptive Ansätze within active spaces extracted from the larger material system. We explore active spaces of (6e, 6o), (8e, 8o), and (10e, 10o), corresponding to 12, 16, and 20 qubits, respectively, and simulate them using CUDA-Q’s graphics processing unit-accelerated state-vector simulator. Gate fusion is shown to decrease the circuit evaluation time by 2–3×, while parameter shift decreases the number of epochs required for variational convergence. The ADAPT-VQE method decreases both the number of epochs required for convergence and the number of circuit parameters across all active spaces, at the cost of an increased number of circuit evaluations. Combining ADAPT-VQE with the one- and two-electron integrals from a classical complete-active space self-consistent field calculation recovers more correlation energy, at the cost of increased computational time. The CO2 binding energy is computed, and we observe and discuss how just increasing the active space size can lead to uneven recovery of correlation energy, making the predicted binding energies variable, even positive (i.e., energetically unfavorable) in some instances. This can be partially remedied by using an alternative approach to computing the binding energy that more evenly spreads the active space. This work explores the application of VQE to a novel material system using large-scale simulated QPUs and provides some insight into various important considerations when performing these types of calculations, ultimately highlighting the challenges of studying chemisorption on near-term quantum machines, simulated or not.

DOI
10.1063/5.0277568

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We perform a series of calculations using simulated quantum processing units (QPUs), accelerated by the NVIDIA CUDA-Q platform, focusing on a molecular analog of an amine-functionalized metal–organic framework, a promising class of materials for CO2 capture. The variational quantum eigensolver (VQE) technique is employed, utilizing both the unitary coupled-cluster method with singles and doubles and adaptive Ansätze within active spaces extracted from the larger material system. We explore active spaces of (6e, 6o), (8e, 8o), and (10e, 10o), corresponding to 12, 16, and 20 qubits, respectively, and simulate them using CUDA-Q’s graphics processing unit-accelerated state-vector simulator. Gate fusion is shown to decrease the circuit evaluation time by 2–3×, while parameter shift decreases the number of epochs required for variational convergence. The ADAPT-VQE method decreases both the number of epochs required for convergence and the number of circuit parameters across all active spaces, at the cost of an increased number of circuit evaluations. Combining ADAPT-VQE with the one- and two-electron integrals from a classical complete-active space self-consistent field calculation recovers more correlation energy, at the cost of increased computational time. The CO2 binding energy is computed, and we observe and discuss how just increasing the active space size can lead to uneven recovery of correlation energy, making the predicted binding energies variable, even positive (i.e., energetically unfavorable) in some instances. This can be partially remedied by using an alternative approach to computing the binding energy that more evenly spreads the active space. This work explores the application of VQE to a novel material system using large-scale simulated QPUs and provides some insight into various important considerations when performing these types of calculations, ultimately highlighting the challenges of studying chemisorption on near-term quantum machines, simulated or not.
Carbon capture is vital for decarbonizing heavy industries such as steel and chemicals. Metal-organic frameworks (MOFs), with their high surface area and structural tunability, are promising materials for CO2 capture. This study focuses on Fe-MOF-74, a magnetic Mott insulator with exposed metal sites that enhance CO2 adsorption. Its strongly correlated electronic structure challenges standard DFT methods, which often yield inconsistent predictions. We initially benchmark adsorption energies using various DFT functionals, revealing substantial variability and underscoring the need for more accurate approaches, such as those provided by quantum computing. However, practical quantum algorithms are far less established for simulations of periodic materials, particularly when the plane-wave basis set, often comprising tens of thousands of basis vectors, is used. To address this, we employ an active space reduction strategy based on Wannier functions and natural orbital selection. Localized orbitals around the adsorption site are identified, and MP2 natural orbitals are used to improve convergence of correlation energies. Adsorption energies are then computed using a quantum number-preserving ansatz within the variational quantum eigensolver framework. In addition to classical simulations, we conduct quantum experiments using the sample-based quantum diagonalization method. Although current hardware limits the size of feasible simulations, our approach offers a more efficient and scalable path forward. These results advance the applicability of quantum algorithms to realistic models of carbon capture and periodic materials more broadly.
Direct air capture (DAC) of carbon dioxide is a promising method for mitigating climate change. Solid sorbents, such as metal–organic frameworks, are currently being tested for DAC application. However, their potential for deployment at scale has not been fully realized. The computational discovery of solid sorbents is challenging, given the vast chemical search space and the DAC requirements for molecular selectivity. Quantum computing can potentially accelerate the discovery of solid sorbents for DAC by predicting molecular binding energies. In this work, we explore algorithms for predicting gas adsorption in metal–organic frameworks using a quantum computer. In particular, we simulate the potential energy surfaces of CO2, N2, and H2O molecules at the Mg+2 metal center that represents the binding sites of typical metal–organic frameworks. We apply the qubit-ADAPT-VQE technique to run simulations on both classical and quantum computing hardware and achieve reasonable accuracy while maintaining hardware efficiency.
CO2 capture is critical to solving global warming. Amine-based solvents are extensively used to chemically absorb CO2. Thus, it is crucial to study the chemical absorption of CO2 by amine-based solvents to better understand and optimize CO2 capture processes. Here, we use quantum computing algorithms to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3. Molecular vibrational properties are important to understanding kinetics of reactions. However, the molecule size correlates with the strength of anharmonicity effect on vibrational properties, which can be challenging to address using classical computing. Quantum computing can help enhance molecular vibrational calculations by including anharmonicity. We implement a variational quantum eigensolver (VQE) algorithm in a quantum simulator to calculate ground state vibrational energies of reactants and products of the CO2 and NH3 reaction. The VQE calculations yield ground vibrational energies of CO2 and NH3 with similar accuracy to classical computing. In the presence of hardware noise, Compact Heuristic for Chemistry (CHC) ansatz with shallower circuit depth performs better than Unitary Vibrational Coupled Cluster. The “Zero Noise Extrapolation” error-mitigation approach in combination with CHC ansatz improves the vibrational calculation accuracy. Excited vibrational states are accessed with quantum equation of motion method for CO2 and NH3. Using quantum Hartree–Fock (HF) embedding algorithm to calculate electronic energies, the corresponding reaction profile compares favorably with Coupled Cluster Singles and Doubles while being more accurate than HF. Our research showcases quantum computing applications in the study of CO2 capture reactions.
We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C 5 H 5 ) 2 ], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.
In recent years, the Variational Quantum Eigensolver (VQE) has emerged as one of the most popular algorithms for solving the electronic structure problem on near-term quantum computers. The utility of VQE is often hindered by the limitations of current quantum hardware, including, but not limited to, short qubit coherence times and low gate fidelities. These limitations become particularly pronounced when VQE is used along with deep quantum circuits, such as those required by the ”Unitary Coupled Cluster Singles and Doubles” (UCCSD) ansatz, often resulting in significant errors. To address these issues, we propose a low-depth ansatz based on parallelized Givens rotations, which can recover substantial correlation energy while drastically reducing circuit depth and two-qubit gate counts for an arbitrary active space (AS). Also, considering the current hardware architectures with low qubit counts, we introduce a systematic way to select molecular orbitals to define active spaces (ASs) that retain significant electron correlation. We validate our approach by computing bond dissociation profiles of water and strongly correlated systems, such as molecular nitrogen and oxygen, across various ASs. Noiseless simulations using the new ansatz yield ground-state energies comparable to those from the UCCSD ansatz while reducing circuit depth by 50–70%. Moreover, in noisy simulations, our approach achieves energy error rates an order of magnitude lower than that of UCCSD. Considering the efficiency and practical usage of our ansatz, we hope that it becomes a potential choice for performing quantum chemistry calculations on near-term quantum devices.
In this work, we combine the recently developed double unitary coupled cluster (DUCC) theory with the adaptive, problem-tailored variational quantum eigensolver (ADAPT-VQE) to explore the accuracy of unitary downfolded Hamiltonians for quantum simulation of chemistry. We benchmark the ability of DUCC effective Hamiltonians to recover dynamical correlation energy outside of an active space. We consider the effects of strong correlation, commutator truncation, higher-body terms, and approximate external amplitudes on the accuracy of these effective Hamiltonians. When combining these DUCC Hamiltonians with ADAPT-VQE, we observe similar convergence of the ground state as compared with bare active space Hamiltonians, demonstrating that DUCC Hamiltonians provide increased accuracy without increasing the load on the quantum processor.