Exploring the role of parameters in variational quantum algorithms

The prospect of achieving quantum advantage by running variational algorithms on near-term devices is very exciting. However many challenges remain before these near-term devices can be used reliably to solve different problems in different areas of science. In this talk, I will explain a way to analyze the impact of the parametrization in variational quantum algorithms (VQAs) on the size of the solution space spanned by their parameters. Focusing on quantum circuits whose structure is patterned on alternating unitaries, I will present a connection between VQAs and the theory of quantum control that has been recently established. I will show how our proposed analysis gives insight into the most efficient way to parametrize a quantum circuit in order to span a sector of interest in the Hilbert space. Finally, I will present some numerical results to show the improvements that can be made using the proposed analysis.