Efficient and quantum-adaptive machine learning with fermion neural networks

TL;DR

This paper introduces fermion neural networks (FNNs), a quantum-adaptive machine learning model that leverages quantum properties for efficient learning and analysis of complex quantum systems and phases.

Contribution

The paper presents fermion neural networks that integrate quantum properties into machine learning, enabling direct analysis of quantum systems and novel insights into network connectivity and interpretability.

Findings

FNNs achieve competitive performance on machine-learning benchmarks.

FNNs can accurately determine topological phases and charge orders.

Quantum features enhance network connectivity and interpretability.

Abstract

Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional conductance, serve as outputs, once the inputs are incorporated as an initial layer. Comparable to back-propagation, we establish an efficient optimization, which entitles FNNs to competitive performance on challenging machine-learning benchmarks. FNNs also directly apply to quantum systems, including hard ones with interactions, and offer in-situ analysis without preprocessing or presumption. Following machine learning, FNNs precisely determine topological phases and emergent charge orders. Their quantum nature also brings various advantages: quantum correlation entitles more general network connectivity and insight into the vanishing gradient problem, quantum entanglement opens up novel avenues for interpretable machine learning, etc.