Transfer Learning in Hybrid Classical-Quantum Neural Networks

Paper Information

Title: Transfer Learning in Hybrid Classical-Quantum Neural Networks

Authors: Andrea Mari, Thomas R. Bromley, Josh Izaac, Maria Schuld, Nathan Killoran

Published: Quantum 4, 340 (2020)

DOI: 10.22331/q-2020-10-09-340

Reproduction Status: Complete

Reproducer: Benjamin Stott (benjamin.stott@quandela.com)

Abstract

This paper extends the concept of transfer learning to hybrid classical-quantum neural networks. The key contribution is a framework for combining pre-trained classical feature extractors with variational quantum circuits, introducing four transfer learning paradigms (CC, CQ, QC, QQ) depending on whether the source and target networks are classical or quantum. The paper focuses on the CQ paradigm, in which a frozen pre-trained CNN extracts compact feature representations from high-dimensional inputs, which are then processed by a trainable variational quantum circuit for final classification.

The paper introduces the concept of a dressed quantum circuit, which augments a bare variational quantum circuit with classical pre- and post-processing layers, making the input and output dimensions independent of qubit count. Proof-of-concept experiments are demonstrated on 2D spiral classification, image recognition (ants vs bees), and CIFAR-10 binary classification, with hardware validation on IBM and Rigetti quantum processors.

Significance

This paper is significant for the quantum ML field because it provides a practical blueprint for applying near-term quantum devices to real-world tasks without requiring quantum hardware to process raw high-dimensional data. By delegating feature extraction to a classical pre-trained network and using the quantum circuit only for the final classification step, the approach is compatible with the limited qubit counts of current NISQ devices. The dressed quantum circuit abstraction is a general design pattern that has since been widely adopted in hybrid quantum-classical architectures.

MerLin Implementation

MerLin is used to implement the variational quantum circuit component of the dressed quantum circuit. The QuantumLayer uses beam splitter meshes as the variational ansatz, with phase shifters providing angle encoding of the classical input features. The beam splitters have fixed angles; the phase shifters are the trainable parameters, optimised via PyTorch gradient descent through the full hybrid pipeline. A PennyLane qubit-based backend is also provided, implementing the paper’s original RY + CNOT architecture for direct comparison.

Key Contributions

Example 1: 2D Spiral Classification

  • We have trained a dressed quantum circuit (4 modes, depth 5) on the 2D spiral dataset and achieved 100% test accuracy, exceeding the paper’s reported ~97% for the quantum model. The classical baseline (two 4-neuron hidden layers) reached 76% accuracy, consistent with the paper’s ~85% and confirming that the quantum model outperforms a comparably-sized classical network on this non-linear task.

Example 2: CQ Transfer Learning - Ants vs Bees

  • We have reproduced the CQ transfer learning pipeline using a frozen ResNet18 as feature extractor (11,176,512 frozen parameters) and a dressed 4-mode quantum circuit as the trainable classifier (2,606 trainable parameters, 0.02% of total). We achieved 90.8% test accuracy compared to the paper’s 96.7% simulator result.

Example 3: CIFAR-10 Binary Classification

  • We have reproduced both CIFAR-10 binary experiments using CQ transfer learning. Dogs vs Cats reached 83.0% accuracy (paper: 82.7%) and Planes vs Cars reached 96.6% accuracy (paper: 96.1%), closely matching the paper’s reported results.

Implementation Details

The dressed quantum circuit wraps MerLin’s QuantumLayer with classical linear layers for flexible input/output dimensionality:

import torch.nn as nn
from merlin import QuantumLayer, ComputationSpace, MeasurementStrategy
from lib.circuits import create_merlin_circuit

n_modes = 4
circuit = create_merlin_circuit(n_modes, q_depth=6)

quantum_layer = QuantumLayer(
    input_size=n_modes,
    circuit=circuit,
    trainable_parameters=["phi"],
    input_parameters=["theta"],
    computation_space=ComputationSpace.UNBUNCHED,
    measurement_strategy=MeasurementStrategy.probs(),
)

# Dressed quantum circuit: classical -> quantum -> classical
dressed_circuit = nn.Sequential(
    nn.Linear(512, n_modes),   # ResNet18 features -> quantum input
    quantum_layer,
    nn.Linear(quantum_layer.output_size, 2),  # quantum output -> classes
)

# Full CQ transfer learning model: frozen ResNet18 + dressed circuit
model = nn.Sequential(resnet18_frozen, dressed_circuit)

Extensions and Future Work

The MerLin implementation extends beyond the original paper:

Enhanced Capabilities

  • A PennyLane qubit-based backend is included alongside MerLin, implementing the paper’s original RY + CNOT ladder circuit, enabling direct comparison of photonic and qubit-based quantum transfer learning.

  • The dressed quantum circuit abstraction is implemented as a reusable module, configurable via JSON for different qubit/mode counts, circuit depths, and computation spaces (fock, unbunched, dual_rail).

Experimental Extensions

  • All three paper examples are reproduced with both backends, allowing quantitative comparison of photonic vs qubit approaches on the same datasets.

  • The MerLin photonic backend provides results competitive with the paper’s simulator results, particularly on CIFAR-10 where Dogs vs Cats and Planes vs Cars match to within 0.5 percentage points.

Hardware Considerations

  • All experiments run on CPU. The CIFAR-10 experiments are the most expensive, taking approximately 6 minutes per training run.

  • Examples 4 (QC) and 5 (QQ) from the paper involve continuous-variable quantum networks using Strawberry Fields and are not reproduced here.

Future Work

  • Reproducing Examples 4 and 5 (QC and QQ transfer learning with continuous-variable quantum circuits) would complete the full set of paradigms introduced in the paper.

  • Extending the CQ pipeline to larger backbone networks (e.g., ResNet50, ViT) and more modes would test the scalability of the approach.

Citation

@article{mari2020transfer,
  title={Transfer learning in hybrid classical-quantum neural networks},
  author={Mari, Andrea and Bromley, Thomas R. and Izaac, Josh and Schuld, Maria
          and Killoran, Nathan},
  journal={Quantum},
  volume={4},
  pages={340},
  year={2020},
  publisher={Verein zur F{\"o}rderung des Open Access Publizierens in den
             Quantenwissenschaften},
  doi={10.22331/q-2020-10-09-340}
}