⚛️ quantum physics

Practical insights on the effect of different encodings, ansätze and measurements in quantum and hybrid convolutional neural networks

This study systematically evaluates nearly 500 configurations of quantum and hybrid convolutional neural networks for satellite image classification, revealing that data encoding is the dominant performance factor in hybrid models while measurement protocols and data-to-amplitude mappings are most critical for purely quantum architectures.

Original authors: Jesús Lozano-Cruz, Albert Nieto-Morales, Oriol Balló-Gimbernat, Adan Garriga, Antón Rodríguez-Otero, Alejandro Borrallo-Rentero

Published 2026-01-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jesús Lozano-Cruz, Albert Nieto-Morales, Oriol Balló-Gimbernat, Adan Garriga, Antón Rodríguez-Otero, Alejandro Borrallo-Rentero

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a very special, futuristic robot how to recognize different types of landscapes (like forests, rivers, or cities) from satellite photos. This robot doesn't think like a human or a standard computer; it thinks using the strange rules of quantum physics.

This paper is essentially a "cookbook test" where the researchers tried thousands of different recipes to see which one made the robot learn best. They didn't just want to see if the robot could learn; they wanted to know which ingredients in the recipe mattered the most.

Here is a breakdown of their findings using simple analogies:

The Three Main Ingredients

To build this quantum robot, the researchers had to choose three specific things:

The Encoding (How to feed the data): Imagine you have a photo. How do you translate that photo into the robot's language? Do you turn every pixel into a specific angle of a spinning wheel? Or do you squeeze the whole photo into the "volume" of a wave? This is the Encoding.
The Ansatz (The robot's brain structure): Once the data is inside, how does the robot process it? Does it let the different parts of the image talk to each other (entanglement), or does it keep them separate? This is the Ansatz.
The Measurement (How to get the answer): At the end, how does the robot tell you what it thinks? Does it look at the result in a specific way (like checking if a coin is heads or tails)? This is the Measurement.

The Experiment: Hybrid vs. Pure Quantum

The researchers tested two types of robots:

Hybrid Robots: These are like a team where a standard computer does the heavy lifting (looking at the big picture), and the quantum robot steps in to do a specific, tricky task.
Pure Quantum Robots: These are robots that do everything using quantum physics, with no help from standard computers.

The Big Discoveries

1. For Hybrid Robots: "How you feed the data is everything."

When the quantum robot worked alongside a standard computer, the most important thing was how the image was translated (Encoding).

The Analogy: Imagine trying to teach a student. If you write the lesson in a language they don't understand (a bad encoding), they will fail no matter how smart they are. If you write it in their native language (a good encoding), they can learn quickly.
The Result: Changing the encoding changed the robot's success rate by over 30%. However, changing the robot's internal brain structure (Ansatz) or how it checked its work (Measurement) barely made a difference (less than 5%).
The Catch: Some encodings worked great in one hybrid setup but failed miserably in another. For example, trying to squeeze the whole image into a tiny quantum wave (Amplitude Encoding) worked well when the robot looked at the whole picture, but failed when the robot was looking at tiny patches of the image.

2. For Pure Quantum Robots: "How you look at the answer matters most."

When the robot had to do the whole job alone, the rules changed.

The Result: Here, the Measurement strategy was the boss. Changing how the robot "read" the final result changed its success rate by up to 30%.
The Insight: It also mattered how the pixels were arranged before the robot started. If you arranged the pixels so that neighbors were next to each other in the quantum system, the robot understood the "shape" of the image better.

3. The "Entanglement" Question

Entanglement is a quantum superpower where particles are linked together.

The Finding: For the hybrid robot that looked at small patches of the image (like a convolutional layer), having these particles linked (entangled) helped it learn better. However, for the hybrid robot that looked at the whole picture later in the process, linking them didn't seem to matter as much.

The "Secret Sauce" of Efficiency

One of the most exciting findings was about efficiency.

The Analogy: Imagine two students taking a test. Student A (the standard computer) has a massive textbook with 900,000 pages to memorize. Student B (the quantum robot) only has a tiny 300-page booklet.
The Result: Even though Student B had way fewer pages to memorize (parameters), they still got a decent score. In fact, the quantum robot achieved a much higher "score per page memorized" than the standard computer. This suggests that in the future, quantum computers could solve complex problems using a tiny fraction of the memory and energy that current computers need.

What They Didn't Say

It is important to note what this paper didn't claim:

They did not say these robots are ready to replace your phone's camera app today.
They did not test these robots on real, noisy quantum hardware (they used a perfect simulation). In the real world, "noise" might ruin the delicate quantum links (entanglement) that helped them in the simulation.
They did not claim these robots are the absolute best at recognizing satellites; they just wanted to understand how to build them better.

The Bottom Line

If you are building a quantum AI for image recognition:

Don't obsess over the brain structure (Ansatz) or the final check (Measurement) first.
Focus intensely on how you translate the image (Encoding) into the quantum world. Getting that translation right is the difference between a robot that learns and one that fails.
Pure quantum models are incredibly efficient, needing far fewer "memories" (parameters) than classical models, but they require very specific ways of reading the final result to work well.

Technical Summary: Practical Insights on PQCs in Quantum and Hybrid CNNs

Problem Statement

The integration of Parameterized Quantum Circuits (PQCs) into machine learning architectures offers a flexible paradigm for Quantum Machine Learning (QML). However, the efficacy of these models is highly sensitive to design choices, specifically data encoding techniques, variational ansätze, and measurement strategies. While existing literature often focuses on hyperparameter scaling or theoretical entanglement implications, there is a lack of systematic empirical analysis regarding the structural composability of QML architectures. This study addresses the gap by investigating how these core design elements influence model behavior and efficacy in the context of satellite image classification, without necessarily claiming state-of-the-art performance or immediate quantum utility.

Methodology

The authors conducted a systematic evaluation of approximately 500 distinct model configurations using the EuroSAT dataset (27,000 RGB satellite images across 10 land-cover classes). To ensure computational tractability within the Noisy Intermediate-Scale Quantum (NISQ) era, images were downscaled to $32 \times 32$ and $16 \times 16$ resolutions. All experiments were performed via simulation using the CTIC Quantum Testbed (QUTE) platform, implementing PQCs with PennyLane and classical layers with PyTorch.

The study evaluated three architectural paradigms:

Hybrid "Quantum-First" (HQNN-Parallel): PQCs act as a quantum linear layer following classical convolutional feature extraction.
Hybrid "Quantum-Later" (HQNN-Quanv): PQCs replace the initial classical convolutional layer, acting as a weight-tied quantum kernel (quanvolution) on image patches.
Purely Quantum Models: Standalone architectures including a QCNN (inspired by classical CNNs with pooling), a Shaped Embedding Quantum Neural Network (SEQNN), and a Fully Connected (FC) baseline.

Variables Tested:

Encodings: Angle (RX, RY, RZ, QAOA variants), Amplitude, Instantaneous Quantum Polynomial-time (IQP), Ring, and Waterfall.
Variational Ansätze: No entanglement, Full entanglement (StronglyEntanglingLayers), Ring, NQ, and QCNN structures.
Measurements: Z-basis, X-basis, Y-basis, Histogram (state frequency), and Pauli strings.

Each hybrid architecture was benchmarked against a "structural twin" classical baseline (replacing quantum layers with equivalent classical layers) to isolate the performance impact of the PQC components. Models were trained using the AdamWScheduleFree optimizer with fixed hyperparameters to ensure fair comparison.

Key Contributions and Results

1. Hierarchy of Influence in Hybrid Architectures

The study reveals a clear hierarchy of influence on model performance for hybrid models:

Data Encoding is Dominant: The choice of encoding strategy is the primary determinant of performance. Validation accuracy varied by over 30% depending on the embedding. For instance, in HQNN-Parallel, IQP encoding combined with a non-entangled ansatz achieved 75.1% accuracy, outperforming the classical baseline (67.1%). Conversely, RZ-based angle encoding consistently failed (10% accuracy) due to the addition of irrelevant global phases.
Ansatz and Measurement are Marginal: In contrast to encoding, the selection of variational ansätze and measurement bases had a comparatively minor effect, with validation accuracy variations remaining below 5%. For HQNN-Parallel, all tested ansätze yielded similar performance, suggesting that for this specific problem, the specific entangling structure is not a critical factor.

2. Architecture-Specific Findings

HQNN-Parallel: Performed slightly better than its classical counterpart when using specific encodings (e.g., IQP, QAOA Z). The model benefits from increasing qubit allocation per circuit to access long-range correlations.
HQNN-Quanv: None of the quantum configurations surpassed the classical baseline. However, entanglement was found to be necessary for top performance in this architecture; non-entangled circuits performed worse than entangled ones. Amplitude encoding failed in this context, likely because normalizing small pixel patches dilutes the gradients essential for early-layer learning.
Purely Quantum Models: Restricted to amplitude encoding, these models showed the highest dependence on the measurement protocol and data-to-amplitude mapping.
- Measurement: The choice of measurement strategy varied validation accuracy by up to 30%. Pauli Z measurements generally performed best, while Pauli strings offered flexibility but with high dispersion.
- Input Ordering: The ordering of pixels in the amplitude embedding significantly impacted performance. Arranging neighboring pixels to be acted upon by two-qubit gates (mimicking spatial proximity) improved results, effectively implementing "shaped kernels."
- Parameter Efficiency: Purely quantum models achieved comparable operating points with orders of magnitude fewer parameters (e.g., QCNN with ~300 parameters vs. classical models with ~900,000).

3. Robustness to Resolution

Image size ( $32 \times 32$ vs. $16 \times 16$ ) did not significantly impact model accuracy in the hybrid models, suggesting that reduced-resolution images retain sufficient discriminative information for this task.

Significance and Claims

The authors explicitly state that the primary objective of this work is not to achieve state-of-the-art performance or claim immediate quantum utility, but to provide practical insights into how core PQC design elements influence model behavior.

Design Guidance: The study offers a "clear hierarchy of influence," guiding researchers to prioritize data encoding strategies over ansatz selection when designing hybrid QML models.
Parameter Efficiency: The results highlight that purely quantum models can achieve high accuracy-parameter ratios, suggesting a potential memory advantage for future quantum accelerators, even if current simulation wall-clock times are slower.
Limitations: The authors acknowledge that these findings are based on ideal, noiseless simulations. They caution that the theoretical advantages of entanglement may be compromised in real-world NISQ environments due to decoherence and gate errors. The study does not generalize to all datasets or hardware constraints, and future work is needed to validate these findings under realistic noise models and to explore hyperparameter sensitivity.

In summary, the paper establishes that while quantum components can match or slightly exceed classical baselines in specific hybrid configurations, the success of these models is heavily contingent on the correct selection of data encoding and, for purely quantum models, the measurement strategy and input mapping.