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Absence of Localization in Two-Dimensional Clifford Circuits

Farshi, Tom; Richter, Jonas; Toniolo, Daniele; Pal, Arijeet; Masanes, Lluis; (2023) Absence of Localization in Two-Dimensional Clifford Circuits. PRX Quantum , 4 (3) , Article 030302. 10.1103/prxquantum.4.030302. Green open access

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Abstract

We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using random graphs and methods from percolation theory, we prove in the two-dimensional (2D) setting that some local operators grow at a ballistic rate, which implies the absence of localization. In contrast, the one-dimensional model displays a strong form of localization, characterized by the emergence of left- and right-blocking walls in random locations. We provide additional insights by complementing our analytical results with numerical simulations of operator spreading and entanglement growth, which show the absence (presence) of localization in two dimensions (one dimension). Furthermore, we unveil how the spectral form factor of the Floquet unitary in 2D circuits behaves like that of quasifree fermions with chaotic single-particle dynamics, with an exponential ramp that persists up to times scaling linearly with the size of the system. Our work sheds light on the nature of disordered Floquet Clifford dynamics and their relationship to fully chaotic quantum dynamics.

Type: Article
Title: Absence of Localization in Two-Dimensional Clifford Circuits
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/prxquantum.4.030302
Publisher version: https://doi.org/10.1103/PRXQuantum.4.030302
Language: English
Additional information: © 2023 American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0/).
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology
URI: https://discovery.ucl.ac.uk/id/eprint/10174403
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