Satellite image classification with neural quantum kernels

TL;DR

The paper tackles real-world satellite image classification by marrying classical preprocessing with neural quantum kernels (NQKs) derived from data-reuploading quantum neural networks. It introduces two NQK constructions, 1-to-n and n-to-n, and demonstrates that with $p\in\{2,3\}$ features and up to $n=8$ qubits, the approach achieves near-90% accuracy, while remaining robust under suboptimal QNN training. The study compares against classical benchmarks (SVC and Random Forest) and shows competitive performance, highlighting the potential of quantum-inspired techniques in earth observation tasks. The work also discusses limitations, including feature bottlenecks and hardware noise, and points to future directions such as qudit-based encodings to scale feature dimensionality and practical deployment on quantum hardware.

Abstract

Achieving practical applications of quantum machine learning for real-world scenarios remains challenging despite significant theoretical progress. This paper proposes a novel approach for classifying satellite images, a task of particular relevance to the earth observation (EO) industry, using quantum machine learning techniques. Specifically, we focus on classifying images that contain solar panels, addressing a complex real-world classification problem. Our approach begins with classical pre-processing to reduce the dimensionality of the satellite image dataset. We then apply neural quantum kernels (NQKs)-quantum kernels derived from trained quantum neural networks (QNNs)-for classification. We evaluate several strategies within this framework, demonstrating results that are competitive with the best classical methods. Key findings include the robustness of or results and their scalability, with successful performance achieved up to 8 qubits.

Figures (12)

• Figure 1: (a) Positive image sample with solar panels ($\hat{y} = +1$) and (b) negative image sample without solar panels ($\hat{y} = -1$), each accompanied by their respective binary segmentation masks. The negative sample illustrates a case where the proportion of white pixels is $\gamma = 0$.
• Figure 2: Flowchart of the image processing workflow. The input dataset for the classification model is prepared, and features are extracted to meet the requirements for encoding the information into a quantum model.
• Figure 3: Diagram illustrating the complete architecture, from the input image to the construction of the NQK. Starting with large, complex images, a dataset $X$ of $M$ data points is generated, consisting of 2- or 3-dimensional points, through classical preprocessing. The upper branch represents the $1$-to-$n$ NQK construction, while the lower branch illustrates the $n$-to-$n$ NQK, which is built using an $n$-qubit QNN. This QNN is trained iteratively to ensure scalability. $\vec{\theta}$ and $\vec{\varphi}$ denote the trainable parameters.
• Figure 4: Detailed NQK construction process. The diagram begins with the training of a single-qubit QNN, from which the optimal parameters $\vec{\theta}^*$ are obtained. Using these parameters, two types of NQKs can be constructed. The first is the $1$-to-$n$ NQK, which is shown in the upper part of the figure, illustrating the specific case where $n=2$. The second is the $n$-to-$n$ NQK, where we iteratively add qubits to construct an $n$-qubit QNN. The first step in constructing the 2-qubit QNN is shown in the lower-left part of the figure. This $n$-qubit QNN is then used directly as the embedding to create the $n$-to-$n$ NQK, as shown in the lower-right part.
• Figure 5: Numerical results for the $1$-to-$n$ NQKs approach. $1q$, $2q$, and $3q$ refer to one-qubit, two-qubit, and three-qubit constructions, respectively. In $(a)$ and $(b)$, we consider the $1$-to-$2$ NQK, while in $(c)$ we examine the $1$-to-$3$ NQK. The results are displayed for $p=2$ features. The training and test accuracies are drawn from the 10-fold process using the described "$1$-to-$n$ set" of 2000 samples. In the box plots, the upper and lower parts of the boxes represent the 25th and 75th percentiles of the accuracies obtained by evaluating the accuracy of the classifiers using 10-fold. The horizontal line inside the box indicates the median, while the whiskers extend from the box to the most distant evaluation score that lies within 1.5 times the interquartile range (IQR) from the box. Score values beyond the whiskers are considered outliers.