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 a tensor network states based algorithm specifically designed to compute amplitudes for random quantum circuits with arbitrary geometry. Singular value decomposition based compression together with a two-sided circuit evolution algorithm are used to further compress the resulting tensor network. To further accelerate the simulation, we also propose a heuristic algorithm to compute the optimal tensor contraction path. We demonstrate that our algorithm is up to 2 orders of magnitudes faster than the Schddot{o}dinger-Feynman algorithm for verifying random quantum circuits on the 53-qubit Sycamore processor, with circuit depths below 12. We also simulate larger random quantum circuits up to 104 qubits, showing that this algorithm is an ideal tool to verify relatively shallow quantum circuits on near-term quantum computers.