Large-scale sparse wave function circuit simulator for applications with the variational quantum eigensolver

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 the sparse wave function 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.