Hilbert-Space Quantum Neural Representation Learning for NISQ-Era Quantum Computing
Yijie Zhu
The convergence of quantum computing and machine learning offers significant potential for processing complex data distributions. However, the realization of this potential in the Noisy Intermediate-Scale Quantum (NISQ) era is constrained by physical hardware limitations, particularly restricted qubit counts and system noise. This thesis addresses the challenge of the ”Representation Bottleneck” by establishing a framework for resource-efficient quantum representation learning. The research demonstrates that effective learning on near-term devices can be achieved by optimizing circuit architectures and objective functions to align with hardware constraints. First, to address resource limitations in high-dimensional visual recognition, we propose the Multi-Gate Quantum Convolutional Neural Network (MG-QNN). By employing a Multi-Gate strategy, this architecture optimizes the utilization of quan tum resources within the circuit design. Empirical evaluations on face recognition benchmarks indicate that this approach maintains competitive recognition accuracy while reducing the qubit requirement compared to standard quantum convolutional methods. Second, extending the framework to non-Euclidean data, we introduce the Single-Qubit Graph Neural Network (sQGNN). Utilizing Discrete-Time Quantum Walks, this method encodes graph topologies and relational patterns onto a single qubit. This approach circumvents the need for multi-qubit entangling gates, thereby reducing the computational overhead and noise sensitivity typically associated with processing graph-structured data. Third, in the domain of generative modeling, we present the Single-Qubit Quan tum Convolutional Variational Autoencoder (QCVAE). Addressing the difficulty of generative tasks on constrained devices, this model integrates the Information Bottleneck principle with efficient data re-uploading techniques. The study demonstrates that a single qubit possesses sufficient expressivity to model and reconstruct image distributions effectively when guided by appropriate information theoretic constraints. Finally, to resolve the fundamental limitations of classical loss functions in quantum learning, we establish the Hilbert-Schmidt Information Bottleneck (HSIB). We identify that standard Euclidean metrics often fail to respect the geometric structure of the Hilbert space. The HSIB framework employs the Hilbert Schmidt distance as a tractable geometric measure, providing a learning objective that maximizes information retention while adhering to the intrinsic geometry of quantum states. Collectively, these contributions illustrate that practical quantum machine learning advantage in the NISQ era does not rely solely on scaling hardware, but on the strategic design of resource-efficient architectures and geometrically valid metrics.
•Aug 17, 2026•0 citations