  We present a simple and efficient way to reduce the contraction cost of a
tensor network to simulate a quantum circuit. We start by interpreting the
circuit as a ZX-diagram. We then use simplification and local complementation
rules to sparsify it. We find that optimizing graph-like ZX-diagrams improves
existing state of the art contraction cost by several order of magnitude. In
particular, we demonstrate an average contraction cost 1180 times better for
Sycamore circuits of depth 20, and up to 4200 times better at peak performance.
