Quantum Self-Supervised Learning (QSSL)

Paper Information

Title: Quantum Self-Supervised Learning

Authors: B. Jaderberg, L. W. Anderson, W. Xie, S. Albanie, M. Kiffner, D. Jaksch

Published: Quantum Science and Technology, Volume 7, Number 3 (2022)

DOI: 10.1088/2058-9565/ac6825

Paper URL: arXiv:2103.14653

Reproduction Status: ✅ Complete

Reproducer: Cassandre Notton (cassandre.notton@quandela.com)

Project Repository

Run the QSSL model

Complete code reproduction of the QSSL (classical, qiskit and Merlin)

Reproduced papersqSSLQiskit

Abstract

This reproduction studies the qSSL framework proposed by Jaderberg et al., where a quantum representation layer is trained inside a self-supervised SimCLR-style pipeline. The model uses two augmented views, InfoNCE contrastive loss, and linear evaluation on frozen representations.

The MerLin reproduction keeps the same high-level design and compares three representation backends under a shared training loop: Qiskit gate-model QNN, MerLin/Perceval photonic QNN, and a classical MLP baseline.

Significance

The original paper highlights self-supervised learning as a promising regime for practical quantum advantage because of the representational capacity required by SSL objectives. This reproduction validates that claim in the MerLin ecosystem and extends it with a photonic implementation that is competitive or better than the compared baselines in short-training settings.

MerLin Implementation

The implementation follows the standard qSSL recipe:

• ResNet18 encoder (non-pretrained)

• Linear compression from 512 features to width

• Representation block selected among merlin, qiskit, and classical

• 2-layer projection head with BatchNorm

• InfoNCE training on two augmented views, followed by frozen-encoder linear probing

How QuantumLayer is used (MerLin backend)

In papers/qSSL/lib/model.py, QuantumLayer is used as the MerLin representation_network:

# __init__: build the MerLin representation block
self.circuit = create_quantum_circuit(modes=self.modes, feature_size=self.width)
input_state = [(i + 1) % 2 for i in range(args.modes)]

self.representation_network = QuantumLayer(
    input_size=self.width,
    circuit=self.circuit,
    trainable_parameters=[
        p.name for p in self.circuit.get_parameters()
        if not p.name.startswith("feature")
    ],
    input_parameters=["feature"],
    input_state=input_state,
    computation_space=ComputationSpace.UNBUNCHED,
    measurement_strategy=MeasurementStrategy.PROBABILITIES,
)

# forward: encoder -> quantum layer -> projection head
x1 = self.comp(self.backbone(y1))
x1 = torch.sigmoid(x1) * (1 / torch.pi)  # MerLin scaling
z1 = self.representation_network(x1)
z1 = self.proj(z1)

Minimal reading of this flow:

• feature-* circuit parameters receive the compressed image features.

• Non-feature parameters are trainable variational parameters.

• QuantumLayer output (probability features) is the representation used by InfoNCE after the projection head.

Default training settings used in reproduction runs:

• Batch size: 256

• Optimizer: Adam (betas=(0.9, 0.999), lr=1e-3, weight_decay=1e-5)

• Temperature: tau=0.07

qSSL architecture used in the reproduction (shared encoder + selectable representation network + projection head).

Key Contributions Reproduced

Unified backend comparison

• Reproduced qSSL with Qiskit, MerLin photonic, and classical representations under the same training/evaluation stack.

• Preserved the CIFAR-10 restricted-label setup used in the original work.

Photonic qSSL implementation

• Replaced the gate-model quantum layer with a photonic interferometer implementation in MerLin.

• Evaluated multiple mode counts and both no_bunching settings.

End-to-end reproducibility

• Produced SSL losses, linear-probe accuracies, checkpoints, and summary metrics for each run.

• Added pretrained checkpoint support and linear-probing utilities.

Experimental Results

Note

The original paper reports additional batch-level diagnostics (recorded every 256-image batch) beyond the main loss curve: average Hilbert-Schmidt distance between positive and negative pairs, mean positive-pair clustering, mean negative-pair clustering, and ensemble inter-cluster overlap. These diagnostics are not yet included in this reproduction page and will be added in a future update.

Original paper headline results (5 CIFAR-10 classes)

Setting	Classical SSL	Quantum SSL (statevector)	Quantum SSL (sampling)
Simulation	43.49 ± 1.31	46.51 ± 1.37	46.34 ± 2.07 (100 shots)
IBM QPU (27 qubits)	.	.	47.00

Reproduced results

CIFAR10 (5 classes), linear probing accuracy

Epochs	Classes	Qiskit based	Classical SSL	Quantum SSL (no_bunching=False)	Quantum SSL (no_bunching=True)
2	5	48.37, #32, x0.08/x0.008	48.08, #144, x1/x1	8 modes: 49.22 (#184, x0.97/x0.95); 10 modes: 47.28 (#320, x0.89/x0.88); 12 modes: 46.46 (#488, x0.83/x0.65)	8 modes: 45.58 (#184, x0.97/x0.97); 10 modes: 45.58 (#320, x0.97/x0.93); 12 modes: 45.76 (#488, x0.94/x0.82)
5	5	47.88	49.04	8 modes: 49.9; 10 modes: 51.12; 12 modes: 50.64	8 modes: 49.3; 10 modes: 48.86; 12 modes: 51.74

Legend:

• #...: number of parameters in the representation network

• x.../...: forward/backward speed-up relative to the classical baseline

Additional 10-epoch benchmark results

CIFAR10 classes	Classical SSL	Quantum SSL (no_bunching=False)	Quantum SSL (no_bunching=True)
2	81.4	88.65 (= param); with batch norm: 89.7 (= param); 14 modes: 90.35; 12 modes: 89.95; 10 modes: 87.8	with batch norm: 14 modes: 50.6; 12 modes: 53.3; 10 modes: 51.7; 14 modes: 80.35; 12 modes: 86.7; 10 modes: 84.15
5	58.3 and 48.64	61.22 (= param); 14 modes: 56.78; 12 modes: 58.94; 10 modes: 61.56	14 modes: 64.14; 12 modes: 59.7; 10 modes: 62.44

Parameter counts (representation network)

Modes	Classical baseline	no_bunching=False	no_bunching=True
10	11,182,034	11,202,150 (diff 0.18%)	11,184,650 (diff 0.02%)
12	11,182,034	11,306,058 (diff 1.11%)	11,191,538 (diff 0.08%)
14	11,182,034	11,957,698 (diff 6.94%)	11,216,818 (diff 0.30%)

Training curves

SSL training losses over epochs.

Fine-tuning losses and linear-probe accuracies.

Citation

@article{jaderberg2022quantum,
  title={Quantum self-supervised learning},
  author={Jaderberg, Ben and Anderson, Lewis W and Xie, Weidi and Albanie, Samuel and Kiffner, Martin and Jaksch, Dieter},
  journal={Quantum Science \& Technology},
  volume={7},
  number={3},
  pages={035005},
  year={2022},
  publisher={IOP Publishing}
}

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