Nonlinear classification capability of quantum neural networks due to emergent quantum metastability
Mario Boneberg, Federico Carollo, Igor Lesanovsky · Physical Review A · 2025
The power and expressivity of deep classical neural networks can be attributed to nonlinear input-output relations. Such nonlinearities 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 nonlinearities 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 nonlinear dynamics in the thermodynamic limit. In the context of quantum neural networks, which are necessarily finite, this translates into metastability with transient nonergodic behavior. By using a quantum neural network the architecture of which is inspired by dissipative many-body quantum spin models, we show that this mechanism indeed allows one to realize nonlinear 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 nonlinear properties.