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arXiv · 2506.11187

Roughening Transition in Quantum Circuits

Hyunsoo Ha·David A. Huse·Grace M. Sommers
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Abstract

We explore a roughening phase transition that occurs in the entanglement dynamics of certain quantum circuits. Viewing entanglement as the free energy of a membrane in a circuit-defined random environment, there is a competition between membrane smoothing due to lattice pinning and roughening due to disorder in the circuit. In particular, we investigate the randomness-induced roughening transition of the entanglement membrane in a (3+1)-dimensional Clifford circuit model, by calculating the entanglement entropy for various bipartitions. We further construct a scaling theory for membranes tilted away from lattice planes, uncovering new scaling forms and a crossover to a previously unexplored critical "tilted regime".

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Hyunsoo Ha, David A. Huse, Grace M. Sommers. 2025-06-12. Roughening Transition in Quantum Circuits. https://doi.org/10.1103/gkwd-8477

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