Quantum simulation of CO$_2$ chemisorption in an amine-functionalized metal-organic framework

TL;DR

This work demonstrates GPU-accelerated VQE on simulated quantum processing units to study CO$_2$ chemisorption in an amine-functionalized MOF analogue, benchmarking UCCSD-VQE, parameter-shift, and ADAPT-VQE across active spaces from $(6e,6o)$ to $(10e,10o)$ (12–20 qubits). It shows that gate fusion can substantially reduce runtimes for larger active spaces, and that ADAPT-VQE offers faster convergence with far fewer parameters than fixed-form UCCSD-VQE, though at the cost of more circuit evaluations; parameter shift accelerates convergence but may underperform the CCSD reference. Binding-energy predictions reveal strong sensitivity to how the active space is distributed, with standard definitions sometimes yielding unfavorable energies as the space grows, while alternative formulations and ADAPT-VQE+CASSCF recover more correlation but remain uneven, highlighting the need for balanced correlation recovery and embedding strategies. The study identifies practical challenges in applying VQE-based chemisorption calculations to near-term quantum hardware and points to future directions such as quantum CASSCF, embedding methods, and improved active-space selection to enable reliable, scalable predictions for MOF-based CO$_2$ capture.

Abstract

We perform a series of calculations using simulated QPUs, accelerated by the NVIDIA CUDA-Q platform, focusing on a molecular analog of an amine-functionalized metal-organic framework (MOF), a promising class of materials for CO$_2$ capture. The variational quantum eigensolver (VQE) technique is employed, utilizing both the unitary coupled-cluster method with singles and doubles (UCCSD) 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 GPU-accelerated state-vector simulator. Gate fusion is shown to decrease circuit evaluation time by 2-3$\times$, 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 reduces the number of circuit parameters across all active spaces, at the cost of an increased number of circuit evaluations. Combining ADAPT-VQE with the 1- and 2-electron integrals from a CASSCF calculation recovers more correlation energy, at the cost of increased computational time. The CO$_2$ binding energy is computed, and we observe and discuss how increasing the active space size can lead to uneven recovery of correlation energy, making the predicted binding energies variable, even positive (\textit{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 simulated QPUs and provides some insight into various consideration when performing these types of calculations, ultimately highlighting the challenges of studying chemisorption on near-term quantum machines.

Figures (6)

• Figure 1: (a) View of the ampd amine-functionalized metal-organic framework Mg$_2$(dobpdc) looking down the pore direction. The black lines mark the boundaries of one unit cell, with a super cell shown to illustrate the pore structure. (b) A view along the crystallographic c-axis, showing the ammonium carbamate chain formation, mapped to the proxy chain model. Gray atoms are carbon, green are magnesium, blue are nitrogen, red are oxygen, and white are hydrogen.
• Figure 2: The natural orbitals treated in the active space in our simulations. The active space orbitals, computed from the MP2 theory, where chosen based on the natural orbital occupation number (NOON). The visualized orbitals on the left are for the system before the CO$_2$ has been adsorbed, and the orbitals on the right show the active space for the post-adsorbed structure. The colored lines indicate the orbitals included in simulations of the number of qubits $N$. In all cases, the active space consisted of an equal number of orbitals and electrons, meaning that the $N=8$ case had 4 orbitals and 4 electrons, $N=12$ had 6 orbitals and 6 electrons, and so on. The orbitals clearly correspond to chemically relevant regions of the adsorption process. Gray atoms are carbon, green are magnesium, blue are nitrogen, red are oxygen, and white are hydrogen.
• Figure 3: The impact of the gate fusion hyperparameter, referred to as the degree of gate fusion, on the computation time of a single (averaged) expectation value call in CUDA-Q for UCCSD-VQE. The optimal gate fusion degree is problem-dependent, with peak performance typically observed at degrees 3 to 4.
• Figure 4: Energy vs. VQE epoch for 12, 16, and 20 qubit simulations. The y-axes are the same for all the runs. The blue lines represent the UCCSD-VQE run, the orange lines represent the UCCSD-VQE runs with parameter shift used for gradient computation, the green lines represent the ADAPT-VQE approach, and the red dotted lines show the classical CCSD energies. The insets focus on the region where UCCSD-VQE+PS and ADAPT-VQE approach the classical result. In all three active space sizes, UCCSD-VQE and ADAPT-VQE reach chemical accuracy compared to CCSD, with ADAPT-VQE saturating the energy value much more rapidly. UCCSD-VQE+PS, however, does not quite converge to the classical CCSD results.
• Figure 5: The CO$_2$ binding energy for different active space sizes, as well as the amount of correlation recovered in the different terms that go into computing the binding energy, as defined by eq. \ref{['eq:be']}. Increasing the active space size