MicroAlgorithm Technology (NASDAQ: MLGO) employs quantum Fourier transform (QFT) to enhance the efficiency of image compression and filtering.

In the wave of deep integration between artificial intelligence and quantum computing, traditional image processing techniques face efficiency bottlenecks. While classical Fourier Transform (DFT) can convert images from spatial domain to frequency domain for compression and filtering, its computational complexity grows exponentially with data size, making real-time processing difficult. Quantum computing, leveraging superposition and entanglement, offers breakthroughs for high-frequency image processing. Micro Algorithm Technologies (NASDAQ: MLGO) has keenly recognized the potential of Quantum Fourier Transform (QFT)—as the quantum version of classical DFT, QFT can perform frequency domain transformations in polynomial time, exponentially increasing image compression efficiency and optimizing filtering accuracy through quantum parallelism. This technological breakthrough provides efficient solutions for high-resolution remote sensing, medical image analysis, and other scenarios.

Quantum Fourier Transform (QFT) is a core algorithm in quantum computing for implementing time-frequency domain conversions. Its essence is to map the phase information of input quantum states from the spatial domain to the frequency domain through quantum superposition and interference. Mathematically, the transformation of an n-qubit state is defined as:

Compared to traditional DFT, QFT outputs a superposition state, requiring measurement to obtain probability distributions. Its main advantage lies in utilizing quantum parallelism to reduce computational complexity from O(n2^n) in classical DFT to O(n^2), while phase rotation gates enable coherent superposition, breaking through the linear limitations of classical complex multiplication and addition operations. Micro Algorithm Technologies incorporates QFT into image processing by designing quantum circuits that encode image data into quantum states, efficiently performing compression and filtering operations in the frequency domain.

Quantum state encoding: Classical image data must first be converted into quantum states. Micro Algorithm Technologies uses a combination of amplitude encoding and angle encoding to map pixel values to the amplitudes or rotation angles of qubits. For example, a 256×256 medical image, after dimensionality reduction via principal component analysis, is encoded into an 8-qubit quantum state, with each qubit carrying part of the image features.

QFT circuit construction: The encoded quantum states enter a parameterized quantum circuit (PQC). Micro Algorithm Technologies’ PQC adopts a layered variational structure, with each layer containing single-qubit rotation gates (Rx, Ry, Rz) and two-qubit controlled phase gates (CROT). The rotation gate parameters are dynamically adjusted through classical optimization to achieve adaptive feature space transformation; CROT gates enhance feature correlations via entanglement. For example, when processing satellite remote sensing images, the PQC can automatically capture the periodic features of ground textures, which are difficult to explicitly model in classical space.

Frequency domain operations and filtering: After QFT transforms the quantum state from spatial to frequency domain, Micro Algorithm Technologies performs frequency filtering through quantum measurement. For compression, the system identifies and removes high-frequency noise components, preserving low-frequency structural information; for edge enhancement, high-pass filters are used to strengthen high-frequency details. For instance, in industrial quality inspection scenarios, QFT can precisely separate micron-level defect signals on chip surfaces from background noise, improving image signal-to-noise ratio by 40% after filtering.

Quantum-classical hybrid decoding: The filtered quantum state must be measured to convert it into classical data. Micro Algorithm Technologies employs repeated sampling, running the quantum circuit multiple times on the same input, and averaging the probability distributions for the final prediction. Additionally, the design reduces the number of two-qubit gates, lowering the complexity of a 16-qubit circuit from O(n^2) to O(n). Experiments on IBM superconducting quantum hardware show that this design achieves a fidelity exceeding 50%.

Micro Algorithm Technologies’ Quantum Principal Component Analysis (QPCA) leverages quantum parallelism to achieve exponential speedup, extracting principal components of high-dimensional images in polynomial time, outperforming classical PCA by several orders of magnitude. Its quantum Hilbert space properties enable capturing complex features that are difficult for classical models, maintaining high stability even with limited samples or noisy data. Through dynamic circuit optimization and error correction coding, it significantly reduces computational complexity, enhancing noise resistance and robustness.

Looking ahead, as quantum hardware performance improves and algorithms innovate, Micro Algorithm Technologies’ (NASDAQ: MLGO) QPCA technology will accelerate toward practical and widespread use. The expansion of qubit numbers and enhanced error correction will enable real-time processing of 4K/8K ultra-high-definition images, supporting quantum-level computing power for autonomous driving perception and industrial robot decision-making. When integrated with generative models, it can achieve self-supervised feature extraction in medical multimodal analysis and financial fraud detection with limited samples. Building a universal quantum image platform will promote technology adoption, combining edge computing to form a cloud-edge collaborative network, ultimately establishing a quantum intelligence infrastructure across multiple industries and leading the global shift into a “quantum-first” era.