Year: 2025
Type: article
Abstract: 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 D tr = β log 2 χ , 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 ≤ 10 4 , using χ ≤ 128 on a conventional CPU. Our method has a polynomial scaling of computational costs with n for circuit depth D = O ( log n ) 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.
Source: Physical Review Research
DOI: 10.1103/rzgm-cywf
Institution: Seoul National University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
OpenAlex ID: W4414258735