Synalgebraic Reasoning for Automation of Photonic Quantum Learning

This paper presents a framework for automated reasoning about photonic quantum machine learning algorithms. At its core, the approach models photonic quantum circuits using a new mathematical theory called synalgebra. A synalgebraic formulation of the Variational Quantum Eigensolver (VQE) is introduced, enabling a specification - referred to as SVQE - of the traditional estimation of molecular ground states based on Hartree-Fock theory. Unlike previous works, the classical optimization stage of SVQE, using the Nelder-Mead method, is also implemented within the synalgebraic framework. This suggests the potential for fully automated analysis of VQE in quantum chemistry.