Efficient Hamiltonian-aware Quantum Natural Gradient Descent for Variational Quantum Eigensolvers

TL;DR

This paper introduces Hamiltonian-aware Quantum Natural Gradient Descent (H-QNG), a new optimizer for VQE that leverages Hamiltonian structure to improve convergence speed and reduce quantum resource requirements.

Contribution

The paper proposes H-QNG, which combines the benefits of QNG and classical gradient descent by using a Hamiltonian-informed metric to enhance VQE optimization.

Findings

H-QNG converges faster to chemical accuracy in molecular Hamiltonians.

H-QNG requires fewer quantum resources than standard QNG.

H-QNG maintains reparameterization-invariance and low computational cost.

Abstract

The Variational Quantum Eigensolver (VQE) is one of the most promising algorithms for current quantum devices. It employs a classical optimizer to iteratively update the parameters of a variational quantum circuit in order to search for the ground state of a given Hamiltonian. The efficacy of VQEs largely depends on the optimizer employed. Recent studies suggest that Quantum Natural Gradient Descent (QNG) can achieve faster convergence than vanilla gradient descent (VG), but at the cost of additional quantum resources to estimate Fubini-Study metric tensor in each optimization step. The Fubini-Study metric tensor used in QNG is related to the entire quantum state space and does not incorporate information about the target Hamiltonian. To take advantage of the structure of the Hamiltonian and address the limitation of additional computational cost in QNG, we propose Hamiltonian-aware Quantum Natural Gradient Descent (H-QNG). In H-QNG, we propose to use the Riemannian pullback metric induced from the lower-dimensional subspace spanned by the Hamiltonian terms onto the parameter space. We show that H-QNG inherits the desirable features of both approaches: the low quantum computational cost of VG and the reparameterization-invariance of QNG. We also validate its performance through numerical experiments on molecular Hamiltonians, showing that H-QNG achieves faster convergence to chemical accuracy while requiring fewer quantum computational resources.