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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2504.04769 |
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| _version_ | 1866908544524091392 |
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| author | Lee, Sung-Bin B. Choi, Hee Ryang Ohm, Daniel Donghyon Lee, Seung-Sup B. |
| author_facet | Lee, Sung-Bin B. Choi, Hee Ryang Ohm, Daniel Donghyon Lee, Seung-Sup B. |
| contents | 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 $\mathcal{D}_\mathrm{tr}$ = $β\log_2χ$, where $χ$ is the maximum bond dimension and $2 \lesssim β\lesssim 4$ 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 $χ\leq 128$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable projected entangled-pair state representation of random quantum circuit states Lee, Sung-Bin B. Choi, Hee Ryang Ohm, Daniel Donghyon Lee, Seung-Sup B. Quantum Physics Computational Physics 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 $\mathcal{D}_\mathrm{tr}$ = $β\log_2χ$, where $χ$ is the maximum bond dimension and $2 \lesssim β\lesssim 4$ 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 $χ\leq 128$ 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. |
| title | Scalable projected entangled-pair state representation of random quantum circuit states |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2504.04769 |