Holographic Quantum Neural Networks

TMLR Paper5366 Authors

Abstract: We introduce Holographic Quantum Neural Networks (HQNNs), a novel quantum machine learning architecture that leverages principles from holographic encoding and tensor networks to efficiently process high-dimensional quantum data. By embedding neural network operations within a holographic framework, HQNNs naturally implement multi-scale feature extraction while providing inherent error correction capabilities. We mathematically formalize the HQNN structure and prove its advantages in representational capacity, showing that HQNNs require only $\mathcal{O}(N_{\text{log}}\log N_{\text{log}})$ physical qubits to process $N_{\text{log}}$-qubit logical input states while tolerating error rates up to a threshold of $1-\frac{2}{z}$, where $z$ is the tensor network coordination number. Furthermore, we demonstrate how the geometric structure of HQNNs enables efficient learning of quantum data with hierarchical features, offering a promising approach for quantum machine learning in the noisy intermediate-scale quantum (NISQ) era and beyond.

Submission Length: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Steffen_Udluft1

Submission Number: 5366