Quantum-Enhanced Similarity Measures for Polarimetric Materials Classification

Technical Summary: Quantum-Enhanced Similarity Measures for Polarimetric Materials Classification

Problem Statement
Material classification is a critical perception task for robotics, remote sensing, and industrial inspection. While RGB-based deep learning methods have advanced, they are fundamentally limited by their reliance on color and intensity, which are confounded by illumination conditions, viewpoint, and surface orientation. Polarimetric imaging offers a physically grounded alternative by capturing the Mueller matrix, which encodes reflectance properties (e.g., dielectric constant, roughness) that are largely invariant to illumination color. However, existing polarimetric classifiers trained in a supervised, end-to-end manner remain sensitive to distribution shifts (e.g., changes in azimuth angle or sensor configuration). This paper addresses the need for a representation that is decoupled from acquisition conditions and capable of open-set discrimination, reframing material recognition not as a closed-set classification problem, but as a point-matching problem.

Methodology
The authors propose a quantum-classical hybrid pipeline consisting of two distinct phases:

1. Training Phase (Feature Extraction):

   • Data Representation: The input consists of "polarization cubes" derived from Mueller matrix measurements. These cubes represent intensity variations across 180 analyzer angles, spatial dimensions ($H \times W$), and are generated by simulating various illumination geometries and wavelengths.
   • Encoder Architecture: A polarization cube is processed by an OctGPT encoder (a transformer-based model utilizing octree sparsity) to generate hierarchical embeddings. These embeddings are further processed by a Graph Neural Network (GNN) head.
   • Objective: The full model (OctGPT + GNN + classification head) is trained end-to-end using cross-entropy loss on 23 material classes. The goal is to learn embeddings that are compact within a class and scattered across classes.

2. Inference Phase (Quantum Point Matching):

   • Freezing: The classification head and GNN are discarded; only the frozen OctGPT encoder is retained.
   • Embedding Generation: For a query cube, the encoder produces a $64 \times 32$ embedding matrix (64 leaf nodes from the octree, each with a 32-dimensional vector).
   • Quantum Encoding: The embedding matrix is flattened to a 2048-dimensional vector, $\ell_2$-normalized, and encoded as the probability amplitudes of an 11-qubit quantum state ($|\psi\rangle$).
   • Similarity Estimation: A SWAP-test circuit is used to estimate the fidelity ($F = |\langle \psi | \phi \rangle|^2$) between the query state and a library of "anchor" states (representing known materials). The circuit uses one ancilla qubit, Hadamard gates, and controlled-SWAP gates.
   • Classification: The query is assigned to the class of the anchor(s) yielding the highest aggregated fidelity.

Key Contributions

• Dataset: A polarimetric cube dataset comprising 23 material classes (approx. 800 samples each), generated by varying azimuth angles, light wavelengths, and polarization states over calibrated Mueller matrices.
• Hybrid Pipeline: A novel feature extraction and embedding generation pipeline that produces a rich, fixed-size embedding matrix per material cube, trained discriminatively but frozen for inference.
• Quantum Framework: A quantum-driven point-matching framework that encodes voxel embeddings as quantum amplitude states and utilizes the SWAP test to evaluate material similarities under quantum simulation.
• Comparative Analysis: An extensive evaluation comparing the quantum approach against classical baselines, including Optimal Transport (soft matching), Hungarian distance (hard matching), and Cosine similarity.

Experimental Results
The approach was evaluated on the 23-class KAIST polarimetric dataset (approx. 19,555 samples after filtering).

• Quantum Performance: Under ideal, noiseless statevector simulation, the Quantum SWAP Test achieved 72.7% Top-1 and 90.9% Top-3 accuracy.
• Classical Baselines:
  • Optimal Transport (Normalized): 87.9% Top-1 / 98.5% Top-3.
  • Hungarian Matching (Normalized): 86.4% Top-1 / 95.5% Top-3.
  • Cosine Similarity: 71.2% Top-1 / 93.9% Top-3.
• Analysis: The results indicate that the Quantum SWAP Test provides a valid similarity signal, performing comparably to Cosine similarity. However, structured classical methods (Optimal Transport and Hungarian) outperformed the quantum approach. The authors attribute this gap to the fact that classical methods operate directly on the per-leaf set structure, whereas the current quantum encoding compresses the entire spatial layout into a single global amplitude state.

Significance and Claims
The paper claims that this work establishes a viable path toward NISQ-based (Noisy Intermediate-Scale Quantum) material recognition. By reframing recognition as similarity-based retrieval over local embeddings rather than closed-set classification, the method demonstrates potential for open-set discrimination, successfully distinguishing between known materials and out-of-distribution inputs (random Mueller matrices) with lower confidence.

The authors emphasize that while the current quantum fidelity scores are competitive with simple cosine similarity, the gap with structured classical methods highlights a specific area for improvement: moving from flat amplitude encoding to quantum graph matching that preserves the octree topology. The work serves as a proof-of-concept that quantum fidelity can serve as a meaningful similarity metric for polarimetric data, provided that future iterations address the compression of spatial structure and the overhead of state preparation on real hardware.