Absence of Localization in Two-Dimensional Clifford Circuits

verfasst von

Tom Farshi, Jonas Richter, Daniele Toniolo, Arijeet Pal, Lluis Masanes

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.

Organisationseinheit(en)

Institut für Theoretische Physik

Externe Organisation(en)

University College London (UCL)
University of Bristol
Stanford University

Typ

Artikel

Journal

PRX Quantum

Band

4

Publikationsdatum

06.07.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Elektronische, optische und magnetische Materialien, Informatik (insg.), Mathematische Physik, Physik und Astronomie (insg.), Angewandte Mathematik, Elektrotechnik und Elektronik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2210.10129 (Zugang: Offen)
https://doi.org/10.1103/PRXQuantum.4.030302 (Zugang: Offen)