Entanglement entropy production in Quantum Neural Networks
- URL: http://arxiv.org/abs/2206.02474v3
- Date: Wed, 24 May 2023 10:21:50 GMT
- Title: Entanglement entropy production in Quantum Neural Networks
- Authors: Marco Ballarin, Stefano Mangini, Simone Montangero, Chiara
Macchiavello and Riccardo Mengoni
- Abstract summary: Quantum Neural Networks (QNN) are considered a candidate for achieving quantum advantage in the Noisy Intermediate Quantum computer (NISQ) era.
We show a universal behavior for the rate at which entanglement is created in any given QNN architecture.
We introduce new measure to characterize the entanglement production in QNNs: the entangling speed.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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
QNN-generated 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.
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