Scalable projected entangled-pair state representation of random quantum circuit states

Classical simulation of a programmable quantum processor is crucial in identifying the threshold of a quantum advantage. We demonstrate the simple update of projected entangled-pair states (PEPSs) in the Vidal gauge that represent random quantum circuit states, which center around recent quantum advantage claims. Applied to square lattices of qubits akin to state-of-the-art superconducting processors, the PEPS representation is exact for circuit depths less than Dtr=βlog2χ, where χ is the maximum bond dimension and 2≲β≲4 depends on the choice of two-qubit gates, independent of the qubit number n. We find the universal scaling behaviors of the state fidelity by treating large-scale circuits of n≤104, using χ≤128 on a conventional CPU. Our method has a polynomial scaling of computational costs with n for circuit depth D=O(logn) and is more advantageous than matrix product state approaches if n is large. This work underscores PEPSs as a scalable tool for benchmarking quantum algorithms with future potential for sampling applications using advanced contraction techniques.