⚛️ quantum physics

Integrated Encoding and Quantization to Enhance Quanvolutional Neural Networks

This paper proposes an enhanced Quanvolutional Neural Network framework that utilizes flexible data quantization with memoization and a novel integrated encoding strategy to improve performance and adaptability while reducing quantum resource requirements compared to existing methods.

Original authors: Daniele Lizzio Bosco, Beatrice Portelli, Giuseppe Serra

Published 2026-08-21

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Daniele Lizzio Bosco, Beatrice Portelli, Giuseppe Serra

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

In the rapidly evolving world of computing, a new frontier is emerging where the laws of quantum mechanics meet the art of teaching machines to see. For decades, artificial intelligence has relied on classical computers to process images, recognizing patterns in everything from medical scans to photographs of distant galaxies. These systems, known as neural networks, are powerful, but they are beginning to hit a wall of complexity. Enter quantum machine learning, a field that seeks to harness the strange, counterintuitive properties of quantum physics to solve problems that are too difficult for today's supercomputers. The most promising application in this realm is the ability to process images using quantum circuits, which can potentially extract hidden features from data that classical methods miss. However, a significant hurdle remains: current quantum computers are fragile, noisy, and have very few building blocks, called qubits, available to them. They cannot yet handle the massive, complex calculations required to process high-quality images without losing information or crashing due to interference. This creates a pressing need for smarter ways to feed data into these delicate machines, ensuring that the limited resources available are used with maximum efficiency.

Researchers at the University of Udine and the University of Naples Federico II have tackled this challenge by developing a new method to prepare and process image data for quantum computers. Their work focuses on a specific type of quantum neural network designed for image recognition, known as a quanvolutional neural network. Unlike traditional quantum models that try to learn and adjust their own internal settings, this approach uses fixed, non-trainable circuits that act as sophisticated filters. The team identified two major bottlenecks in the standard process: the way images are simplified before entering the quantum computer, and the rigid way data is translated into quantum states. They proposed a new pipeline that combines these steps into a single, flexible operation, allowing the system to adapt to the strict limitations of current hardware while retaining more of the original image's detail.

The first innovation addresses the problem of data simplification. To run on a quantum computer, an image must be converted from a continuous range of colors and shades into a format the machine can understand. The standard method involves reducing an image to just two colors, black and white, a process called binary quantization. While this saves computing power, it throws away a vast amount of detail, much like trying to describe a painting using only a handful of primary colors. The researchers introduced a flexible approach that allows for many more levels of gray, preserving the subtle nuances of the original image. To make this practical, they used a technique called memoization, which acts like a smart memory bank. As the system processes the image, it records the results for every unique pattern it encounters. If the same pattern appears again, the system simply recalls the answer instead of recalculating it. This strategy allowed them to use a much higher number of gray levels, keeping the image rich in detail, while simultaneously reducing the number of times the quantum computer had to run its calculations by over 95 percent for certain datasets.

The second, and perhaps more significant, breakthrough involves how the data is actually fed into the quantum circuit. In previous methods, the size of the image patch being analyzed dictated the number of quantum building blocks required. If a researcher wanted to analyze a larger patch of the image, they needed a proportionally larger number of qubits, which quickly exceeded the capacity of available machines. The new method breaks this rigid link. By integrating the data translation and the processing steps into a single circuit, the researchers can choose the number of qubits independently of the image patch size. This means they can use a small, manageable number of qubits to process much larger image patches, or scale up as better hardware becomes available. The system works by using the brightness of the pixels directly to control the rotation of quantum gates, creating a direct and efficient bridge between the classical image and the quantum processor.

To test their ideas, the team applied this new model to two very different real-world problems. The first involved classifying images of galaxies, distinguishing between two specific types of cosmic structures. The second task was to identify different types of subatomic particles based on their energy signatures in a detector. They compared their new integrated model against a standard classical computer program and the traditional quantum method that uses rotational encoding. The results were clear: the new integrated model consistently outperformed the traditional quantum approach across all tested image patch sizes. In the galaxy classification task, it achieved an accuracy of over 80 percent, surpassing both the standard quantum model and the classical computer. In the particle detection task, it also beat the classical computer, whereas the traditional quantum model fell short.

The study also revealed that the specific mathematical function used to translate pixel brightness into quantum settings mattered greatly. Some functions led to stable, high-performing results, while others caused the system to become erratic and unreliable. This suggests that the "personality" of the quantum circuit is just as important as its structure. Furthermore, the researchers found that the ability of their new circuit to explore different possibilities, a property known as expressibility, could be tuned by simply adding more steps to the calculation. This flexibility allows scientists to design circuits that are perfectly matched to the specific constraints of their hardware, a crucial advantage in the current era of noisy, intermediate-scale quantum devices.

Ultimately, this work demonstrates that we do not need to wait for perfect, error-free quantum computers to see benefits in image processing. By rethinking how data is prepared and how it interacts with the quantum circuit, it is possible to build models that are both more accurate and more resource-efficient. The researchers have made their code and methods available to the public, inviting others to build upon this foundation. Their findings suggest that with the right engineering, quantum machine learning can move beyond theoretical experiments and begin to solve practical problems in astronomy, physics, and beyond, even with the imperfect machines we have today.

Technical Summary: Integrated Encoding and Quantization to Enhance Quanvolutional Neural Networks

Problem Statement
Quantum Machine Learning (QML) applied to computer vision faces significant hurdles on current Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, Quanvolutional Neural Networks (QuanvNNs) with non-trainable parameters are preferred to avoid the resource-intensive optimization required by parameter-shift rules. However, existing preprocessing pipelines for QuanvNNs suffer from two main inefficiencies:

Information Loss vs. Efficiency: Standard binary quantization reduces the number of unique input patches, thereby lowering the number of required quantum circuit executions. However, this aggressive binarization often leads to significant information loss, degrading model performance on tasks requiring fine-grained data.
Hardware Constraints in Encoding: Traditional encoding methods, such as rotational encoding, require a number of qubits quadratic to the input patch size ( $k^2$ qubits for a $k \times k$ kernel). This rigid dependency limits the scalability of the model to larger kernel sizes on devices with limited qubit counts and short coherence times.

Methodology
The authors propose a novel preprocessing pipeline and a new encoding strategy to address these limitations.

Flexible Data Quantization with Memoization:
Instead of binary quantization ( $N=2$ ), the authors introduce a flexible quantization approach where the number of levels $N$ is a tunable parameter. The pixel intensity $x \in [0, 1]$ is mapped to $N$ discrete levels using the formula $q(x) = \lfloor x \cdot N \rfloor / (N-1)$ .
- Memoization: A look-up table is constructed to store the output of the quantum circuit for every unique quantized patch encountered. This ensures that identical patches are not processed multiple times.
- Trade-off: This approach allows users to balance information retention (higher $N$ ) against computational load (lower $N$ reduces the number of unique patches and circuit executions).
Integrated Encoding Strategy:
The paper introduces a new encoding method that merges the traditional "encoding" and "processing" steps into a single quantum circuit.
- Mechanism: Classical pixel data from an input patch are used directly as rotation angles for multi-qubit entangling gates. Specifically, gates are constructed as $G(x_i) = \exp(-i\alpha(x_i) \cdot \sigma_1 \otimes \sigma_2)$ , where $x_i$ is a pixel intensity, $\sigma$ are Pauli gates, and $\alpha$ is a mapping function.
- Flexibility: Unlike rotational encoding, which requires exactly $k^2$ qubits for a $k \times k$ kernel, the integrated model allows the number of qubits ( $n$ ) and the number of gates ( $L$ ) to be selected independently of the kernel size. The only constraint is that $L \ge k^2$ to ensure all input features are encoded at least once.
- Mapping Functions: The authors test three mapping functions $\alpha(x)$ : Simple ( $x\pi$ ), Random Multiplication ( $2\beta x\pi$ ), and Random Linear ( $(\beta x + \sigma)\pi$ ).

Key Contributions

Resource Efficiency: The proposed quantization with memoization significantly reduces the number of quantum circuit executions required for training and inference without resorting to destructive binary quantization.
Architectural Decoupling: The integrated encoding strategy decouples the kernel size from the qubit requirement, enabling the use of larger kernels on hardware with limited qubit counts.
Expressibility Control: The method allows for the adjustment of circuit expressibility by varying the number of gates ( $L$ ), providing a mechanism to tune the model's capacity to explore the Hilbert space.

Experimental Results
The proposed model (QNN-Int) was evaluated against a standard rotational encoding QuanvNN (QNN-Rot) and a classical Convolutional Neural Network (CNN) on two datasets:

MiraBest (Binary Classification): QNN-Int models (specifically with Simple and RndMul mapping functions) consistently outperformed both the classical CNN and the QNN-Rot across various kernel sizes ( $k=2, 3, 4$ ). The QNN-Rot model showed performance degradation as kernel size increased.
LArTPC (Multi-class Classification): QNN-Int models again surpassed the classical CNN and QNN-Rot for larger kernel sizes ( $k=3, 4, 5$ ). Notably, while QNN-Rot performance increased with kernel size, it remained below the classical baseline. The QNN-Int-RndLin mapping function performed poorly, highlighting the sensitivity of the integrated model to the choice of mapping function.

Quantization Impact:
Experiments on quantization levels ( $N$ ) demonstrated that setting $N=50$ reduced circuit executions by over 95% for the MiraBest and LArTPC datasets while maintaining negligible Mean Squared Error (MSE) compared to the original images.

Significance and Claims
The paper claims that the proposed integrated encoding and flexible quantization pipeline make QuanvNNs more viable for NISQ devices. The primary significance lies in achieving comparable or superior performance to classical CNNs and traditional QuanvNNs while requiring fewer quantum resources (fewer qubits and fewer circuit executions). The authors emphasize that the integrated model offers greater architectural flexibility, allowing parameters like qubit count and filter size to be adjusted independently based on hardware constraints. They conclude that the choice of the mapping function is critical for maximizing expressivity and classification accuracy, and they suggest future work could explore optimizing these mapping parameters during training.

More like this