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  • Open Access

Measurement-Induced Entanglement in Noisy 2D Random Circuits

Zhi-Yuan Wei (魏志远)1,*, Jon Nelson1, Joel Rajakumar1, Esther Cruz2,3, Alexey V. Gorshkov1, Michael J. Gullans1,4, and Daniel Malz5

  • *Contact author: zywei@umd.edu
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PRX Quantum 7, 033023 – Published 5 August, 2026

DOI: https://doi.org/10.1103/yfzm-5rr6

Abstract

We study measurement-induced entanglement (MIE) generated by column-by-column sampling of noisy 2D random circuits of size N and depth T. Focusing primarily on Clifford circuits and using the operator entanglement Sop of the sampling-induced boundary state as a proxy for computational complexity, first, we reproduce in the noiseless limit a finite-depth transition from area- to volume-law scaling at a threshold depth Tc=6. In contrast, in the presence of single-qubit depolarizing noise at any constant rate p>0, we find that the operator entanglement Sop obeys an area law, with its maximum value scaling approximately linearly with T/p in the regime T>Tc. By analyzing the spatial distribution of stabilizer generators, we observe exponential localization of stabilizer generators; these both account for the scaling of the maximal Sop and imply 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 MIE in 2D random Clifford circuits, and that a tensor-network-based algorithm can efficiently sample from noisy 2D random Clifford circuits (i) at sub-logarithmic depths T=o(logN) for any constant noise rate p=Ω(1), and (ii) at constant depths T=O(1) for noise rates p=Ω(log−1N). Finally, we turn to depth T=4 Haar-random and measurement-based quantum computing-type circuits, providing evidence that MIE in noisy 2D Haar-random circuits exhibits the same qualitative behavior as in random Clifford circuits, and that noise destroys the volume-law scaling of MIE in non-Clifford circuits.

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Popular Summary

Random quantum circuits are a leading route for testing when quantum computers can outperform classical computers, but real devices are never perfectly isolated from noise. In this work, we study how noise affects measurement-induced entanglement, a type of entanglement that can appear when a two-dimensional quantum circuit is sampled piece by piece. We find that measurements can induce entanglement that grows with system size in ideal noiseless circuits. However, even a small constant amount of local noise cuts off this growth and keeps the entanglement limited. We demonstrate this effect in large-scale simulations of noisy random Clifford circuits and provide evidence that the same qualitative behavior appears in more general random circuits. These findings clarify how we should think about the classical hardness of noisy quantum sampling experiments. They suggest that noise can make some two-dimensional quantum circuits easier to simulate classically, even when their noiseless versions may be hard. More broadly, our results help explain how sampling, entanglement, and noise shape the computational power of near-term quantum devices.

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PRX Quantum 7, 033023– Published 5 August, 2026
  • Received 16 January 2026
  • Revised 15 May 2026
  • Accepted 17 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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