WiMi Develops Variational Quantum Algorithm-Driven Multi-Dimensional Data Pooling Optimization Technology

WiMi Hologram Cloud Inc., a leading global Hologram Augmented Reality (“AR”) Technology provider, announces the proposal of a multi-dimensional pooling optimization scheme based on Variational Quantum Algorithms (VQA), which, by integrating the Quantum Haar Transform (QHT) with quantum partial measurement technology, constructs a quantum pooling mechanism that simultaneously possesses local feature preservation capability and dimension compression efficiency.

Quantum Haar Transform’s High-Dimensional Data Mapping Mechanism: The Haar transform, as an orthogonal transformation method in the classical signal processing field, achieves multi-scale feature extraction and data compression of signals through decomposition by orthogonal basis functions. Its core advantage lies in its sensitive capture of local abrupt features. The Quantum Haar Transform (QHT), as an extended implementation of the classical Haar transform under the quantum computing framework, is constructed based on the universal quantum circuit of the quantum Fourier transform and utilizes the superposition property of quantum states to achieve efficient orthogonal transformation of high-dimensional data. In technical implementation, QHT maps high-dimensional classical data to the quantum state space through parameterized quantum gate groups, where each qubit corresponds to one feature dimension of the data, and the superposition coefficients of the quantum state encode the feature intensity information. This mapping process constructs correlations between feature dimensions through quantum entanglement, preserving the global structural information of the data while reinforcing the correlations of local features through the local action domain constraints of quantum gates, thereby solving the problem of exponentially increasing computational complexity that classical Haar transform faces in high-dimensional data processing.

Quantum Partial Measurement Pooling Implementation Mechanism: Unlike classical pooling strategies that achieve dimension compression through hard discarding of data, quantum partial measurement realizes selective extraction of key feature information in the quantum state based on the probabilistic interpretation of quantum states. After QHT completes the quantum mapping of high-dimensional data, partial measurement is performed on the qubits by designing specific measurement bases (matched with preset pooling strategies): if the max-pooling strategy is adopted, the construction of the measurement basis aims to maximize the collapse probability of the quantum state corresponding to the maximum feature intensity; if the average-pooling strategy is adopted, the probabilistic weighted average of feature intensities is achieved through the orthogonality constraints of the measurement basis. During this process, unmeasured qubits remain in superposition states, ensuring the continuity of local feature correlations, while the measurement results are output as low-dimensional classical feature vectors, realizing the synergistic optimization of “feature preservation–dimension compression” and effectively avoiding the information loss problem inherent in classical pooling.

Variational Quantum Algorithm Parameter Optimization Framework: VQA, as a class of quantum-classical hybrid optimization algorithms, consists of a core architecture comprising a Parameterized Quantum Circuit (PQC) and a classical optimizer. The classical optimizer iteratively adjusts the parameters of the PQC to minimize a preset loss function (such as feature reconstruction error or classification accuracy loss), thereby achieving precise control of the quantum state transformation process. In the multi-dimensional pooling optimization task, the core role of VQA is embodied in its ability to optimize the quantum gate parameters of QHT, ensuring that when high-dimensional data is mapped to the quantum state space, the correlations of local features are maximally preserved; to optimize the measurement basis parameters of quantum partial measurement, making the pooling output features optimally adapted to downstream tasks (quantum classification, quantum regression); and to mitigate errors caused by quantum state decoherence through iterative optimization, thereby improving the stability of the pooling process.

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Compared with traditional pooling methods and existing QML schemes, this VQA-driven multi-dimensional pooling technology possesses high-dimensional adaptation capability, without the need to reduce high-dimensional data to one-dimensional space, and can directly complete pooling operations on multi-dimensional data in the quantum state space, fully preserving the local structural information of the data; at the same time, it also exhibits efficient computational characteristics. Leveraging quantum parallelism and the efficient orthogonality of QHT, it achieves polynomial-level reduction in computational complexity compared to classical high-dimensional data pooling algorithms, significantly improving the processing efficiency for large-scale data; additionally, by adjusting the quantum gate structure and parameters of the PQC, it can flexibly adapt to the processing needs of unstructured data of different dimensions and types, such as one-dimensional audio, two-dimensional images, three-dimensional point clouds, and hyperspectral data.

The multi-dimensional pooling optimization technology under the variational quantum algorithm framework studied by WiMi effectively breaks through the locality preservation limitations of traditional pooling methods in high-dimensional data processing, fully unleashes the inherent advantages of quantum computing in feature representation and computational efficiency, and provides key technical support for the practical application of QML in complex multi-dimensional data tasks. With the iteration of quantum hardware technology and the continuous optimization of quantum algorithms, in the future it will build efficient and precise quantum machine learning models in fields such as computer vision, remote sensing detection, biomedicine, etc., driving QML from theoretical research toward real-world applications.