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

• URL: http://arxiv.org/abs/2504.04769v2
• Date: Thu, 18 Sep 2025 04:09:26 GMT
• Title: Scalable projected entangled-pair state representation of random quantum circuit states
• Authors: Sung-Bin B. Lee, Hee Ryang Choi, Daniel Donghyon Ohm, Seung-Sup B. Lee,
• Abstract summary: We show the update of projected entangled-pair states (PEPSs) in the Vidal gauge that represent random quantum circuit states.<n>We find the universal scaling behaviors of the state fidelity by treating large-scale circuits ofn leq 104$, using $chi leq 128$ on a conventional CPU.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\mathcal{D}_\mathrm{tr}$ = $\beta\log_2\chi$, where $\chi$ is the maximum bond dimension and $2 \lesssim \beta \lesssim 4$ 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 $n \leq 10^{4}$, using $\chi \leq 128$ on a conventional CPU. Our method has a polynomial scaling of computational costs with $n$ for circuit depth $\mathcal{D}=O(\log n)$ 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.

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