Entanglement entropy production in Quantum Neural Networks

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 not been investigated in details, and 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 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 show a universal behavior for the entanglement entropy production for any given QNN architecture, consequently we introduce a new measure to characterize the entanglement production in QNNs: the entangling speed. Finally, in agreement with known results in the literature, we argue that the most promising regime for quantum advantage with QNNs is defined by a trade-off between high entanglement and expressibility.

Error mitigation of entangled states using brainbox quantum autoencoders

“…It allows delocalizes information in the network and steers the training towards the optimal condition of having a separable output. In order to observe its contribution to the training, some measures of entanglement have been tested, such as entanglement witnesses [50] and von Neumann entropy [51]. Similar to any many-body quantum system, measuring the entropy of different partitions provides a way to probe its entanglement structure.…”