Measurement-induced entanglement in noisy 2D random Clifford circuits

Fuente: arXiv
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Autores principales: Wei, Zhi-Yuan, Nelson, Jon, Rajakumar, Joel, Cruz, Esther, Gorshkov, Alexey V., Gullans, Michael J., Malz, Daniel
Formato: Preprint
Publicado: 2025
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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