Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study

Abstract Exploiting the invariance of the molecular Hamiltonian by unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in Variational Quantum Eigensolver (VQE) approach by using the Wavefunction-Adapted Hamiltonian Through Orbital Rotation (WAHTOR) algorithm.
In this work, we introduce a non-adiabatic version of the WAHTOR algorithm and compare its efficiency with different implementations (two adiabatic and two non-adiabatic) through estimating Quantum Processing Unit (QPU) resources in prototypical benchmarking systems. Calculating first and second order derivatives of the Hamiltonian at fixed VQE parameters does not introduce a significant QPU overload, leading to results on small molecules that indicate the adiabatic Newton-Raphson method as the more convenient choice. On the contrary, we find out that in the case of Hubbard model systems the trust region non-adiabatic optimization is more efficient.
The preset work therefore indicates clearly the best optimization strategies for empirical variational ansatzes, facilitating the optimization of larger variational wavefunctions for quantum computing.