Supramolecular approach-based intermolecular interaction energy calculations using quantum phase estimation algorithm

TL;DR

The paper tackles the challenge of accurately computing intermolecular non-covalent energies with quantum computers by engineering a resource-efficient QPE-CASCI workflow, underpinned by MP2-based active-space selection and Boys orbital localization. It demonstrates that, for a hydrogen-bonded water dimer, QPE-CASCI with algorithmic error mitigation can reproduce CASCI-level interaction energies within about 0.02 kcal mol$^{-1}$ using only 12 qubits, and it discusses circuit compression prospects. The study integrates orbital localization, active-space design, and controlled time evolution to manage size-consistency and resource demands, while highlighting the limitations of Hamiltonian truncation and the need for future fault-tolerant techniques. Overall, the work provides a concrete, scalable pathway for applying quantum phase estimation to supramolecular interaction problems and outlines practical routes to extend to larger systems and more complex inter-molecular interactions.

Abstract

Accurate computation of non-covalent, intermolecular interaction energies is important to understand various chemical phenomena, and quantum computers are anticipated to accelerate it. Although the state-of-the-art quantum computers are still noisy and intermediate-scale ones, development of theoretical frameworks those are expected to work on a fault-tolerant quantum computer is an urgent issue. In this work, we explore resource-efficient implementation of the quantum phase estimation-based complete active space configuration interaction (QPE-CASCI) calculations, with the aid of the second-order Møller--Plesset perturbation theory (MP2)-based active space selection with Boys localized orbitals. We performed numerical simulations of QPE for the supramolecular approach-based intermolecular interaction energy calculations of the hydrogen-bonded water dimer, using 6 system and 6 ancilla qubits. With the aid of algorithmic error mitigation, the QPE-CASCI simulations achieved interaction energy predictions with an error of 0.02 kcal mol$^{-1}$ relative to the CASCI result, demonstrating the accuracy and efficiency of the proposed methodology. Preliminary results on quantum circuit compression for QPE are also presented to reduce the number of two-qubit gates and depth.

Figures (12)

• Figure 1: Quantum circuit for QPE.
• Figure 2: Steps for the MP2-based active space selection with Boys localized orbitals.
• Figure 3: Overlap between the localized orbitals of monomer and dimer in the dimer equilibrium geometry and contour plots of the localized orbitals. MO means dimer molecular orbital, and the following number indicates the index.
• Figure 4: Orbital-wise MP2 correlation energy contribution.
• Figure 5: Excitation-wise MP2 correlation energy contribution.