Entanglement entropy production in Quantum Neural Networks

Year: 2023

Authors: Ballarin M., Mangini S., Montangero S., Macchiavello C., Mengoni R.

Autors Affiliation: Istituto Nazionale di Fisica Nucleare (INFN); University of Pavia; Istituto Nazionale di Fisica Nucleare (INFN); University of Padua; Consiglio Nazionale delle Ricerche (CNR); Istituto Nazionale di Ottica (INO-CNR)

Abstract: Quantum Neural Networks (QNN) are considered a candidate for achieving quantum advantage in the Noisy Intermediate Scale Quantum computer (NISQ) era. Several QNN architectures have been proposed and successfully tested on benchmark datasets for machine learning. However, quantitative studies of the QNNgenerated entanglement have been investigated only for up to few qubits. Tensor network methods allow to emulate quantum circuits with a large number of qubits in a wide variety of scenarios. Here, we employ matrix product states to characterize recently studied QNN architectures with random parameters up to fifty qubits showing that their entanglement, measured in terms of entanglement entropy between qubits, tends to that of Haar distributed random states as the depth of the QNN is increased. We certify the randomness of the quantum states also by measuring the expressibility of the circuits, as well as using tools from random matrix theory. We show a universal behavior for the rate at which entanglement is created in any given QNN architecture, and consequently introduce a new measure to characterize the entanglement production in QNNs: the entangling speed. Our results characterise the entanglement properties of quantum neural networks, and provides new evidence of the rate at which these approximate random unitaries.

Journal/Review: QUANTUM

Volume: 7      Pages from:   to:

More Information: All authors thank CINECA for providing the necessary resources for running the MPS simulations on the High-Performance Computing (HPC) infrastructure GALILEO100, the Quantum Computing and Simulation Center (QCSC) at Padova university, and the ICSC National Center. M.B. thanks Eduardo Gonzalez Lazo for carefully reading the manuscript and his valuable feedback and Daniel Jaschke for valuable discussions. Stefano Mangini thanks Stefan Sack for valuable discussions.
KeyWords: Circuits
DOI: 10.22331/q-2023-05-31-1023

Citations: 4
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