Measurement-induced entanglement in noisy 2D random Clifford circuits
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912810491969536 |
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| author | Wei, Zhi-Yuan Nelson, Jon Rajakumar, Joel Cruz, Esther Gorshkov, Alexey V. Gullans, Michael J. Malz, Daniel |
| author_facet | Wei, Zhi-Yuan Nelson, Jon Rajakumar, Joel Cruz, Esther Gorshkov, Alexey V. Gullans, Michael J. Malz, Daniel |
| contents | We study measurement-induced entanglement generated by column-by-column sampling of noisy 2D random Clifford circuits of size $N$ and depth $T$. Focusing on the operator entanglement $S_{\rm op}$ of the sampling-induced boundary state, first, we reproduce in the noiseless limit a finite-depth transition from area- to volume-law scaling. With on-site probablistic trace noise at any constant rate $p>0$, the maximal $S_{\rm op}$ attained along the sampling trajectory obeys an area law in the boundary length and scales approximately linearly with $T/p$. By analyzing the spatial distribution of stabilizer generators, we observe exponential localization of stabilizer generators; this both accounts for the scaling of the maximal $S_{\rm op}$ and implies an exponential decay of conditional mutual information across buffered tripartitions, which we also confirm numerically. Together, these results indicate that constant local noise destroys long-range, volume-law measurement-induced entanglement in 2D random Clifford circuits. Finally, based on the observed scaling, we conjecture that a tensor-network-based algorithm can efficiently sample from noisy 2D random Clifford circuits (i) at sub-logarithmic depths $T = o(\log N)$ for any constant noise rate $p = Ω(1)$, and (ii) at constant depths $T = O(1)$ for noise rates $p = Ω(\log^{-1}N)$. Finally, we turn to Haar-random circuits of depth $T = 4$, where we observe numerically the same qualitative behavior as in the Clifford circuit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measurement-induced entanglement in noisy 2D random Clifford circuits Wei, Zhi-Yuan Nelson, Jon Rajakumar, Joel Cruz, Esther Gorshkov, Alexey V. Gullans, Michael J. Malz, Daniel Quantum Physics We study measurement-induced entanglement generated by column-by-column sampling of noisy 2D random Clifford circuits of size $N$ and depth $T$. Focusing on the operator entanglement $S_{\rm op}$ of the sampling-induced boundary state, first, we reproduce in the noiseless limit a finite-depth transition from area- to volume-law scaling. With on-site probablistic trace noise at any constant rate $p>0$, the maximal $S_{\rm op}$ attained along the sampling trajectory obeys an area law in the boundary length and scales approximately linearly with $T/p$. By analyzing the spatial distribution of stabilizer generators, we observe exponential localization of stabilizer generators; this both accounts for the scaling of the maximal $S_{\rm op}$ and implies an exponential decay of conditional mutual information across buffered tripartitions, which we also confirm numerically. Together, these results indicate that constant local noise destroys long-range, volume-law measurement-induced entanglement in 2D random Clifford circuits. Finally, based on the observed scaling, we conjecture that a tensor-network-based algorithm can efficiently sample from noisy 2D random Clifford circuits (i) at sub-logarithmic depths $T = o(\log N)$ for any constant noise rate $p = Ω(1)$, and (ii) at constant depths $T = O(1)$ for noise rates $p = Ω(\log^{-1}N)$. Finally, we turn to Haar-random circuits of depth $T = 4$, where we observe numerically the same qualitative behavior as in the Clifford circuit. |
| title | Measurement-induced entanglement in noisy 2D random Clifford circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.12743 |