Quantum Information Scrambling in Extended Hubbard Models*

This study investigates entanglement and quantum information scrambling (QIS) by the example

of a many-body Extended Hubbard Model (EHM) that described a special type of quantum dot array

(interacting V-shapes). The concept of QIS is used in the framework of quantum information processing

by quantum circuits and quantum channels. In general, QIS is seen as the de-localization of quantum

information over the entire quantum system. Recently, connections of QIS to quantum information

processing and machine learning have been made.

We firstly make an introduction on the concept of quantum information scrambling and its connection

with the 4-point out-of-time-order (OTO) correlators. In order to have a quantitative measure of QIS,

we use the tripartite mutual information, that measures the mutual information between 3

different spacetime partitions of the system; this is used to quantify the dynamical spreading

of quantum entanglement in the system. Then, we investigate scrambling in the quantum many-body Extended Hubbard Model with external

magnetic field Bz for both uniform and thermal quantum channel inputs and show that it

scrambles for specific external tuning parameters (e.g. tunneling amplitudes, on-site potentials, magnetic

field). In addition, we compare different Hilbert space sizes (different number of

qubits) and show the qualitative and quantitative differences in quantum scrambling, as we increase the

number of quantum dots in the system. Moreover, we find a "scrambling phase transition" for a threshold

temperature in the thermal case, that is, the temperature of the model that the channel starts to

scramble quantum information. Finally, we make comparisons with the Transverse Field Ising model

(TFI) and investigate connections to Quantum Machine Learning (QML) and draw potential parallels

between quantum learning and information scrambling.