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

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.