Hybrid quantum-classical algorithms for solving quantum chemistry in Hamiltonian-wavefunction space

TL;DR

This paper introduces hybrid quantum-classical algorithms that optimize both Hamiltonian and wavefunction spaces to improve efficiency in solving quantum chemistry problems, demonstrating rapid convergence and potential for faster energy surface calculations.

Contribution

It develops novel algorithms incorporating Hamiltonian derivatives into VQE, enabling simultaneous optimization in Hamiltonian and wavefunction spaces for quantum chemistry.

Findings

Mutual gradient descent accelerates molecular geometry optimization.

Differential equations describe how variational parameters evolve with Hamiltonian changes.

Algorithms improve efficiency in calculating energy potential surfaces.

Abstract

Variational quantum eigensolver~(VQE) typically optimizes variational parameters in a quantum circuit to prepare eigenstates for a quantum system. Its applications to many problems may involve a group of Hamiltonians, e.g., Hamiltonian of a molecule is a function of nuclear configurations. In this paper, we incorporate derivatives of Hamiltonian into VQE and develop some hybrid quantum-classical algorithms, which explores both Hamiltonian and wavefunction spaces for optimization. Aiming for solving quantum chemistry problems more efficiently, we first propose mutual gradient descent algorithm for geometry optimization by updating parameters of Hamiltonian and wavefunction alternatively, which shows a rapid convergence towards equilibrium structures of molecules. We then establish differential equations that governs how optimized variational parameters of wavefunction change with intrinsic parameters of the Hamiltonian, which can speed up calculation of energy potential surface. Our studies suggest a direction of hybrid quantum-classical algorithm for solving quantum systems more efficiently by considering spaces of both Hamiltonian and wavefunction.