Enhancing the Expressivity of Variational Neural, and Hardware-Efficient Quantum States Through Orbital Rotations

TL;DR

This paper demonstrates that jointly optimizing the single-particle basis with variational quantum states significantly enhances their expressivity and optimization, leading to improved results in quantum chemistry and condensed matter simulations.

Contribution

It introduces a method for joint optimization of the basis and variational states in VMC and VQE, improving their expressiveness and optimization landscape.

Findings

Joint optimization improves variational state expressivity.

Active-space neural quantum state calculations are achieved.

Significant improvements in chemistry and condensed matter systems.

Abstract

Variational approaches, such as variational Monte Carlo (VMC) or the variational quantum eigensolver (VQE), are powerful techniques to tackle the ground-state many-electron problem. Often, the family of variational states is not invariant under the reparametrization of the Hamiltonian by single-particle basis transformations. As a consequence, the representability of the ground-state wave function by the variational ansatz strongly dependents on the choice of the single-particle basis. In this manuscript we study the joint optimization of the single-particle basis, together with the variational state in the VMC (with neural quantum states) and VQE (with hardware-efficient circuits) approaches. We show that the joint optimization of the single-particle basis with the variational state parameters yields significant improvements in the expressive power and optimization landscape in a variety of chemistry and condensed matter systems. We also realize the first active-space calculation using neural quantum states, where the single-particle basis transformations are applied to all of the orbitals in the basis set.