Scaling Up Electronic Structure Calculations on Quantum Computers: The Frozen Natural Orbital Based Method of Increments

By Prakash Verma, Lee Huntington, Marc Coons, Yukio Kawashima, Takeshi Yamazaki, & Arman Zaribafiyan
Quantum computing is a new computing paradigm that holds great promise for the efficient simulation of quantum mechanical systems. However, the hardware envelope provided by noisy, intermediate-scale quantum (NISQ) devices is still small compared to the size of molecules that are relevant to industry. In the present paper, the method of increments (MI) is introduced to help expedite the application of NISQ devices for quantum chemistry simulations. The MI approach expresses the electron correlation energy of a molecular system as a truncated many-body expansion in terms of orbitals, atoms, or molecules. Here, the electron correlation is expanded in terms of occupied orbitals. At the same time, the virtual orbital space is reduced based on the frozen natural orbitals (FNO), which are obtained from second-order, many-body perturbation theory. In this way, a method referred to as MI-FNO is constructed for the systematic reduction of both the occupied and the virtual spaces. The subproblems from the MI-FNO reduction can then be solved by any algorithm, including quantum algorithms such as the variational quantum eigensolver, to predict the correlation energies of a molecular system. The accuracy and feasibility of MI-FNO are investigated for the case of small molecules. Then, the efficacy of the proposed framework is investigated using a qubit-count estimation on an industrially relevant catalyst molecule. We show that, even by employing a modest truncation, MI-FNO reduces the qubit requirement by almost a factor of one half. Our approach can facilitate hardware experiments based on smaller, yet more realistic, chemistry problems, assisting in the characterization of NISQ devices. Moreover, reducing the qubit requirement can help scale up the size of molecular systems that can be simulated, which can greatly enhance computational chemistry studies for industrial applications.
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