  The standard paradigm for state preparation on quantum computers for the
simulation of physical systems in the near term has been widely explored with
different algorithmic methods. One such approach is the optimization of
parameterized circuits, but this becomes increasingly challenging with circuit
size. As a consequence, the utility of large-scale circuit optimization is
relatively unknown. In this work we demonstrate that purely classical resources
can be used to optimize quantum circuits in an approximate but robust manner
such that we can bridge the resources that we have from high performance
computing and see a direct transition to quantum advantage. We show this
through sparse wavefunction circuit solvers, which we detail here, and
demonstrate a region of efficient classic simulation. With such tools, we can
avoid the many problems that plague circuit optimization for circuits with
hundreds of qubits using only practical and reasonable classical computing
resources. These tools allow us to probe the true benefit of variational
optimization approaches on quantum computers, thus opening the window to what
can be expected with near term hardware for physical systems. We demonstrate
this with a unitary coupled cluster ansatz on various molecules up to 64 qubits
with tens of thousands of variational parameters.
