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Quantum Visual Fields with Neural Amplitude Encoding
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Proposes Quantum Visual Field (QVF), a quantum implicit neural representation using learnable Boltzmann-based neural amplitude encoding and a real-unitary entangled ansatz, evaluated on a PennyLane simulator for 2D images and 3D SDFs.
Problem
Quantum implicit neural representations (QINRs) for 2D image and 3D shape fields suffer from hand-crafted data encodings, heavy classical post-processing, trainability issues, and limited scale.
Approach
Encode coordinates and latent codes into quantum states via a learnable energy-based Gibbs distribution (neural amplitude encoding), process them with a fully entangled ansatz restricted to real-valued unitaries built from Pauli-Y rotations and entangling gates, and read out signals directly from Pauli-Z measurements without classical decoders.
Key results
- QVF with Siren outperforms QIREN by about 30% on MSE for single 2D images at n=5 qubits.
- QVF maintains about 30 dB PSNR on images with no noise and about 25.8 dB at gate perturbation sigma=0.1 (MLP-style ReLU variant).
- QVF adds only about 170 parameters over its classical energy-inference module and yields a smaller total parameter count (0.52e5) than QIREN (0.74e5).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase circuit perturbation noise from no noise to σ = 0.1 (ablation) | QVF with Gaussian initialization and ReLU · Selected 2D images | PSNR: 30.06 ± 0.1 -> 25.78 ± 0.2 | Hurt |
| Increase circuit perturbation noise from no noise to σ = 0.1 (ablation) | QVF with identity initialization and ReLU · Selected 2D images | PSNR: 30.02 ± 0.2 -> 25.96 ± 0.2 | Hurt |
| Increase circuit perturbation noise from no noise to σ = 0.1 (ablation) | QVF with Gaussian initialization and Sin · Selected 2D images | PSNR: 32.59 ± 0.2 -> 27.94 ± 0.2 | Hurt |
| Increase circuit perturbation noise from no noise to σ = 0.1 (ablation) | QVF with identity initialization and Sin · Selected 2D images | PSNR: 32.67 ± 0.3 -> 28.12 ± 0.2 | Hurt |
| Use Sin instead of ReLU activation (ablation) | QVF · Selected 2D images | PSNR: 30.06 ± 0.1 -> 32.59 ± 0.2 | Helped |
| Use identity instead of Gaussian initialization (ablation) | QVF with Sin activation · Selected 2D images | PSNR: 32.59 ± 0.2 -> 32.67 ± 0.3 | No clear effect |
| Use identity instead of Gaussian initialization (ablation) | QVF with ReLU activation · Selected 2D images | PSNR: 30.06 ± 0.1 -> 30.02 ± 0.2 | No clear effect |
| Use a hand-crafted amplitude encoding instead of learnable energy embedding (ablation) | QVF · 2D image representation | representation quality | Hurt |
| Increase circuit depth and qubit width (ablation) | QVF · 2D image representation | representation performance | Helped |
| Increase hidden dimension p of the classical encoding module (ablation) | QVF · 2D image representation | representation performance | Helped |
| Add the quantum ansatz to the classical energy inference module (ablation) | QVF · 2D image representation | PSNR | Helped |
| Constrain the ansatz to real-valued unitary operations (ablation) | QVF · Circuit trainability | gradient variance | Helped |
Surprising findings
- Hand-crafted amplitude encoding from Rathi et al. does not yield a recognisable image after convergence, indicating the learnable encoding is necessary.
Limitations
- Experimental scale is limited by exponentially costly classical simulation of quantum circuits.
- Results are only on a noiseless simulator; noisy evaluation is a perturbation proxy rather than real hardware.
- Authors state they do not aim to beat well-engineered classical models in absolute terms.
Experimental setup
Datasets: CIFAR-10 high-resolution images with rich spectral details ShapeNet
Benchmarks: CIFAR-10 ShapeNet
Metrics: PSNR MSE gradient variance
Baselines: QIREN MLP with ReLU Siren DeepSDF-style MLP Rathi et al. hand-crafted encoding
Builds on: QIREN 3D-QAE Siren DeepSDF Solovay-Kitaev theorem
Closest papers by meaning
- Quantum Implicit Neural Representations (ICML 2024 · similarity 0.86)
- Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding (NeurIPS 2026 · similarity 0.85)
- Reinforced Learning Explicit Circuit Representations for Quantum State Characterization from Local Measurements (ICML 2025 · similarity 0.84)
- Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations (NeurIPS 2026 · similarity 0.84)
- HDQMF: Holographic Feature Decomposition Using Quantum Algorithms (CVPR 2024 · similarity 0.84)
- Exploring channel distinguishability in local neighborhoods of the model space in quantum neural networks (ICLR 2025 · similarity 0.84)
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