Optimal compression of constrained quantum time evolution

The time evolution of quantum many-body systems is one of the most promising applications for near-term quantum computers. However, the utility of current quantum devices is strongly hampered by the proliferation of hardware errors. The minimization of the circuit depth for a given quantum algorithm is therefore highly desirable, since shallow circuits generally are less vulnerable to decoherence. Recently, it was shown that variational circuits are a promising approach to outperform current state-of-the-art methods such as Trotter decomposition, although the optimal choice of parameters is a computationally demanding task. In this work, we demonstrate a simplification of the variational optimization of circuits implementing the time evolution operator of local Hamiltonians by directly encoding symmetries of the physical system under consideration. We study the expressibility of such constrained variational circuits for different models and symmetries. Our results show that the encoding of symmetries allows a reduction of optimization cost by more than one order of magnitude and scalability to arbitrary large system sizes, without loosing accuracy in most systems. Furthermore, we discuss the exceptions in constrained systems and provide an explanation by means of an restricted lightcone width after imposing the constraints into the circuits.