  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 constraints of the physical
system under consideration. We study the expressibility of such constrained
variational circuits for different models and constraints. Our results show
that the encoding of constraints 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 locally-constrained systems and provide an explanation by means
of an restricted lightcone width after incorporating the constraints into the
circuits.
