Counterdiabatic ADAPT-VQE for molecular simulation

TL;DR

This paper introduces a hybrid quantum algorithm that combines ADAPT-VQE with counterdiabatic driving, leading to more efficient molecular simulations with shallower circuits on NISQ devices.

Contribution

It presents a novel integration of ADAPT-VQE and counterdiabatic techniques, enhancing performance and reducing circuit depth in quantum molecular simulations.

Findings

Improved performance over standard ADAPT-VQE and counterdiabatic methods

Reduced circuit depth in molecular ground state estimation

Effective operator selection via approximate adiabatic gauge potential

Abstract

Among variational quantum algorithms designed for NISQ devices, ADAPT-VQE stands out for its robustness against barren plateaus, particularly in estimating molecular ground states. On the other hand, counterdiabatic algorithms have shown advantages in both performance and circuit depth when compared to standard adiabatic approaches. In this work, we propose a hybrid method that integrates the ADAPT-VQE framework with counterdiabatic driving within an adiabatic evolution scheme. Specifically, we map the molecular Hamiltonian to a qubit representation and construct an adiabatic Hamiltonian, from which an approximate adiabatic gauge potential is computed using nested commutators. The resulting operator terms define the operator pool, and the ADAPT-VQE algorithm is applied to iteratively select the most relevant elements for the ansatz. Our results demonstrate improvements in performance and reductions in circuit depth compared to using either counterdiabatic algorithms or ADAPT-VQE with fermionic excitation operators, thus supporting the effectiveness of combining both paradigms in molecular simulations.