Quantum-optimal-control-inspired ansatz for variational quantum algorithms

TL;DR

This paper introduces Quantum-Optimal-Control-inspired Ans"atze (QOCA), a novel approach for variational quantum algorithms that incorporates symmetry-breaking unitaries, leading to improved convergence and accuracy in simulating complex quantum systems.

Contribution

The paper proposes a new class of ans"atze inspired by quantum optimal control, demonstrating their effectiveness in improving VQA performance for physics and chemistry problems.

Findings

QOCA achieves higher accuracy in approximating the Fermi-Hubbard ground state.

QOCA can handle larger systems than traditional ans"atze.

QOCA improves the ground state estimation for the water molecule.

Abstract

A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. This circuit is most commonly designed to respect the symmetries of the problem Hamiltonian and, in this way, constrain the variational search to a subspace of interest. Here, we show that this approach is not always advantageous by introducing ans\"atze that incorporate symmetry-breaking unitaries. This class of ans\"atze, that we call Quantum-Optimal-Control-inspired Ans\"atze (QOCA), is inspired by the theory of quantum optimal control and leads to an improved convergence of VQAs for some important problems. Indeed, we benchmark QOCA against popular ans\"atze applied to the Fermi-Hubbard model at half-filling and show that our variational circuits can approximate the ground state of this model with significantly higher accuracy and for larger systems. We also show how QOCA can be used to find the ground state of the water molecule and compare the performance of our ansatz against other common choices used for chemistry problems. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans\"atze with applications to physics and chemistry problems.