Measurement-induced entanglement in noisy 2D random Clifford circuits

• URL: http://arxiv.org/abs/2510.12743v1
• Date: Tue, 14 Oct 2025 17:21:55 GMT
• Title: Measurement-induced entanglement in noisy 2D random Clifford circuits
• Abstract summary: We study measurement-induced entanglement generated by column-by-column sampling of noisy 2D random Clifford circuits.<n>We find that constant local noise destroys long-range, volume-law measurement-induced entanglement.<n>We conjecture that a tensor-network-based algorithm can efficiently sample from noisy 2D random Clifford circuits.
• Score: 1.915364393561725
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $p = \Omega(1)$, and (ii) at constant depths $T = O(1)$ for noise rates $p = \Omega(\log^{-1}N)$.

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