Verifying Random Quantum Circuits with Arbitrary Geometry Using Tensor Network States Algorithm

The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present tensor network states based algorithm specifically designed compute amplitudes with arbitrary geometry. Singular value decomposition compression together two-sided circuit evolution are used further compress the resulting network. To accelerate simulation, also propose heuristic optimal contraction path. We demonstrate that our up $2$ orders of magnitudes faster than Sch$\ddot{\text{o}}$dinger-Feynman verifying on $53$-qubit Sycamore processor, depths below $12$. larger $104$ qubits, showing this an ideal tool verify relatively shallow near-term computers.