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

Sung-Bin B. Lee1,*, Hee Ryang Choi2, Daniel Donghyon Ohm1, and Seung-Sup B. Lee1,3,4,†

  • *Contact author: tomsb.lee@gmail.com
  • †Contact author: sslee@snu.ac.kr
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Phys. Rev. Research 7, 033252 – Published 15 September, 2025

DOI: https://doi.org/10.1103/rzgm-cywf

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 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.

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Phys. Rev. Research 7, 033252– Published 15 September, 2025
  • Received 21 April 2025
  • Accepted 20 August 2025
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