Resource-Efficient Quantum Circuits for Molecular Simulations: A Case Study of Umbrella Inversion in Ammonia

We conducted a thorough evaluation of various state-of-the-art strategies to prepare the ground state wavefunction of a system on a quantum computer, specifically within the framework of variational quantum eigensolver (VQE). Despite the advantages of VQE and its variants, the current quantum computational chemistry calculations often provide inaccurate results for larger molecules, mainly due to the polynomial growth in the depth of quantum circuits and the number of two-qubit gates, such as CNOT gates. To alleviate this problem, we aim to design efficient quantum circuits that would outperform the existing ones on the current noisy quantum devices. In this study, we designed a novel quantum circuit that reduces the required circuit depth and number of two-qubit entangling gates by about 60 of the ground state energies close to the chemical accuracy. Moreover, even in the presence of device noise, these novel shallower circuits yielded substantially low error rates than the existing approaches for predicting the ground state energies of molecules. By considering the umbrella inversion process in ammonia molecule as an example, we demonstrated the advantages of this new approach and estimated the energy barrier for the inversion process.