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Revista Multidisciplinar Epistemología de las Ciencias

Procesamiento morfológico de imágenes binarias mediante circuitos cuánticos: una implementación en qiskit

Leonardi Hernández-Sánchez, Emily Andrea Franco Escudero, R. Arceo

Published Aug 28, 2026• 0 citations
Publisher

Abstract

Erosion and dilation are fundamental mathematical morphology operations used to modify the shape of objects in binary images. This study evaluated their implementation through a quantum circuit simulated in Qiskit, using classical processing in OpenCV as the reference. The Baboon image was analyzed at resolutions of 102×102, 128×128, and 256×256 pixels, with 16, 160, 1600, 16000, and 160000 circuit executions. The comparison included visual inspection, calculation of MSE, PSNR, and SSIM, and measurement of simulation times. The circuit reproduced the expected effect of both operations, although the reconstructed images did not fully match those obtained with OpenCV. Dilation showed more stable similarity than erosion. In addition, increasing the number of executions did not improve the metrics monotonically and substantially increased computation time.

DOI
10.71112/nankke17

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The dilation and erosion operations are the first fundamental step in classical image processing. They are important in many image processing algorithms to extract basic image features, such as geometric shapes; such shapes are then fed to higher level algorithms for object identification and recognition. In this paper, we present an improved quantum method to realize dilation and erosion in imaging processing. Unlike in the classical way, in the quantum version of imaging processing, all of the information is stored in quantum bits (qubits). We use qubits to code the location and other information of each pixel of the images and apply quantum operators (or quantum gates) to accomplish specific functions. Because of quantum entanglement and other nonintuitive features in quantum mechanics, qubits have many advantages over classical bits, but their nature presents challenges in designing quantum algorithms. We first built the quantum circuit theoretically, and then ran it on the IBM Quantum Experience platform to test and process real images. With this algorithm, we are looking forward to more potential applications in quantum computation.
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This study presents a comparative evaluation of three quantum image representation techniques: FRQI, QPIE, and NEQR. The Baboon image is used as a benchmark, and performance is assessed through PSNR, MSE, SSIM, and execution time. Simulations were conducted using a noiseless quantum simulator to ensure fair comparison across methods. Results indicate that QPIE achieves the best reconstruction quality, with PSNR = 117.97, MSE = 1.037, and SSIM = 0.975 for the 8 x 8 image, while maintaining strong performance for larger sizes. In contrast, FRQI shows lower quality and high execution time. NEQR is computationally faster (4.85 s) but delivers moderate quality (PSNR = 79.38, SSIM = 0.859). Additionally, QPIE requires fewer qubits, making it more resource-efficient. Overall, QPIE emerges as the most effective representation, striking a balance between image quality, computational cost, and qubit utilization. These findings highlight QPIE as a promising candidate for future quantum image processing tasks such as compression, edge detection, and negative transformation.
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The Discrete Cosine Transform (DCT) is an integral part of classical image compression, which becomes the basis of the JPEG standard. With advances in quantum computing, there is growing interest in exploring quantum analogues of classical algorithms for such transforms. This paper presents a simulation of the Quantum Discrete Cosine Transform (QDCT) using the Qiskit Python library, applied to standard grayscale images segmented into 8x8 and 4x4 blocks. The QDCT algorithm is formulated as a unitary operator and evaluated using state-vector simulation. Due to the current constraints of quantum hardware and challenges in circuit synthesis, this study focused on simulation results, as direct quantum circuit measurement leads to amplitude collapse and unusable output. The performance of QDCT is quantitative compared to classical DCT using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and compression ratio metrics. The result of this study reveals the feasibility and current limitations of QDCT-based image compression while providing a reproducible benchmark for future quantum image processing research. This study offers a realistic assessment of the potential and technical limitations of QDCT in the context of emerging quantum technologies.