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

A central component of variational quantum algorithms (VQAs) is the state-preparation circuit, also known as ansatz or variational form. This circuit is most commonly designed such as to exploit 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 ansatzes that incorporate symmetry-breaking unitaries. This class of ansatzes, that we call quantum-optimal-Control-inspired ansates (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 variational forms applied to the Fermi-Hubbard model at half-filling and show that our variational circuits can approximate the ground state of this model with high accuracy. 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 ansatzes with applications to physics and chemistry problems.