Bridge the Gap between Classical and Quantum Neural Networks with Residual Connections

TL;DR

This paper introduces a Hybrid Quantum Residual Network (HQRN) that links classical and quantum neural networks, enabling transfer of classical optimization benefits and leveraging quantum correlations for advanced feature processing.

Contribution

The work establishes an exact correspondence between quantum and classical residual networks and demonstrates their effectiveness in practical classification tasks.

Findings

HQRN reduces to classical networks with basis-restricted inputs.

HQRN leverages quantum correlations for feature resolution.

HQRN achieves high accuracy on digit recognition and entanglement classification.

Abstract

We introduce a Hybrid Quantum Residual Network (HQRN) and establish an exact functional correspondence between its state evolution and the dynamics of classical networks with residual connections. When inputs are restricted to the computational basis, the HQRN reduces to its classical analog, enabling the direct translation of optimized classical weights into quantum unitary operations, effectively inheriting the landscape benefits of classical optimization. Conversely, when processing general mixed states, the HQRN leverages off-diagonal quantum correlations to resolve features inaccessible to its classical analog. We validate this framework through digit recognition and bipartite entanglement classification. Notably, HQRN achieves high classification accuracy even for adversarial separable states that mimic the marginal measurement statistics of entangled pairs. Our results bridge the gap between classical and quantum residual learning, paving a scalable pathway for deep quantum architectures.