Speeding up quantum circuits simulation using ZX-Calculus

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.