Entanglement Signatures of Random Quantum Circuits

Beatriz Cardoso Dias

Key information

Authors:

Beatriz Cardoso Dias (Beatriz Cardoso Dias)

Supervisors:

Paul Alexander McClarty; Pedro José Gonçalves Ribeiro (Pedro José Gonçalves Ribeiro)

Published in

June 9, 2021

Abstract

We study the non-equilibrium dynamics of one-dimensional quantum systems, generated by random unitary circuits, i.e. random unitary gates acting on nearest neighbour bonds. While studying different circuit models, including those formed by Haar-distributed unitaries and Clifford gates, we focus on circuits proxy to random free fermion evolution. In particular, we quantify information scrambling in the form of operator spreading for random free fermion dynamics and study the crossover from integrable-like to chaotic dynamics within random circuits. We present an exact calculation of time-ordered and out-of-time-ordered correlators measuring operator spreading for free fermion dynamics. Within this, we consider three distinct cases: the random circuit with spatio-temporal disorder (i) with and (ii) without particle number conservation and (iii) the particle non-conserving case with purely temporal disorder. In all three cases, temporal disorder causes diffusive operator spreading and sqrt(t) entanglement growth. This is in sharp contrast to Anderson localization for the case of static disorder and the ballistic behaviour observed in both the clean case of Hamiltonian evolution and in fully random unitary quantum circuits. Moreover, we perform a numerical study of the entangling properties of different circuits, with emphasis on the entanglement entropy and spectrum. This numerical analysis is extended to studying the effects of adding occasional non-free fermion gates (i.e. intruders) amidst free fermion circuits. We observe that this leads the initial integrable-like dynamics to become chaotic and obtain bounds on the number of intruders needed to reach the chaotic regime, which is extensive with system size.