Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data

• URL: http://arxiv.org/abs/2202.10471v1
• Date: Mon, 21 Feb 2022 19:00:01 GMT
• Title: Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
• Authors: Jack Y. Araz and Michael Spannowsky
• Abstract summary: TNs are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. We show that classical TNs require large bond dimensions and higher Hilbert-space mapping to perform comparably to their quantum counterparts. With increased dimensionality, classical TNs lead to a highly flat loss landscape, rendering the usage of gradient-based optimization methods highly challenging.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum circuits in the context of Machine Learning on highly complex, simulated LHC data. We show that classical TNs require exponentially large bond dimensions and higher Hilbert-space mapping to perform comparably to their quantum counterparts. While such an expansion in the dimensionality allows better performance, we observe that, with increased dimensionality, classical TNs lead to a highly flat loss landscape, rendering the usage of gradient-based optimization methods highly challenging. Furthermore, by employing quantitative metrics, such as the Fisher information and effective dimensions, we show that classical TNs require a more extensive training sample to represent the data as efficiently as TN-inspired quantum circuits. We also engage with the idea of hybrid classical-quantum TNs and show possible architectures to employ a larger phase-space from the data. We offer our results using three main TN ansatz: Tree Tensor Networks, Matrix Product States, and Multi-scale Entanglement Renormalisation Ansatz.

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