TY - JOUR

T1 - Absence of Localization in Two-Dimensional Clifford Circuits

AU - Farshi, Tom

AU - Richter, Jonas

AU - Toniolo, Daniele

AU - Pal, Arijeet

AU - Masanes, Lluis

N1 - Funding Information: T.F. acknowledges financial support by the Engineering and Physical Sciences Research Council (Grants No. EP/L015242/1 and No. EP/S005021/1) and is grateful to the Heilbronn Institute for Mathematical Research for support. L.M. and D.T. acknowledge financial support by the UK’s Engineering and Physical Sciences Research Council (Grant No. EP/R012393/1). D.T. also acknowledges support from UK Research and Innovation Grant No. EP/R029075/1. J.R. and A.P. acknowledge funding by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (Grant Agreement No. 853368). J.R. also received funding from the European Union’s Horizon Europe programme under the Marie Sklodowska-Curie grant agreement No. 101060162, and the Packard Foundation through a Packard Fellowship in Science and Engineering.

PY - 2023/7/6

Y1 - 2023/7/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85167865312&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2210.10129

DO - 10.48550/arXiv.2210.10129

M3 - Article

AN - SCOPUS:85167865312

VL - 4

JO - PRX Quantum

JF - PRX Quantum

IS - 3

M1 - 030302

ER -