Non-linear classification capability of quantum neural networks due to emergent quantum metastability

TL;DR

This paper demonstrates that quantum neural networks can achieve effective non-linear classification by leveraging emergent quantum metastability near phase transitions, despite their inherently linear dynamics.

Contribution

It introduces a mechanism for implementing non-linearities in quantum neural networks through metastability and collective behavior in many-body quantum systems.

Findings

Quantum many-body systems exhibit emergent non-linear dynamics near phase transitions.

Metastability enables finite quantum neural networks to perform non-linear classification.

The proposed architecture is inspired by dissipative quantum spin models.

Abstract

The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition. Quantum neural networks, on the other hand, are necessarily linear as they process information via unitary operations. Here we show that effective non-linearities can be implemented in these platforms by exploiting the relationship between information processing and many-body quantum dynamics. The crucial point is that quantum many-body systems can show emergent collective behavior in the vicinity of phase transitions, which leads to an effectively non-linear dynamics in the thermodynamic limit. In the context of quantum neural networks, which are necessarily finite, this translates into metastability with transient non-ergodic behavior. By using a quantum neural network whose architecture is inspired by dissipative many-body quantum spin models, we show that this mechanism indeed allows to realize non-linear data classification, despite the underlying dynamics being local and linear. Our proof-of-principle study may pave the way for the systematic construction of quantum neural networks with emergent non-linear properties.