On the role of inductive bias in scaling quantum machine learning and variational quantum computing

The rapidly emerging paradigms of quantum machine learning (QML) and variational quantum computing (VQC) promise to combine quantum computational advantages with the powerful capabilities of machine learning and optimization. However, early attempts to naively translate classical machine learning techniques into the quantum domain have encountered severe scalability bottlenecks, both practical and theoretical. This dissertation posits that overcoming these limitations requires a fundamental shift in model and algorithm design: the deliberate integration of inductive bias. By embedding task-specific prior knowledge into quantum models and optimization strategies, this research demonstrates how to achieve the scalability required for near-term real-world applications and long-term success towards quantum advantage. This dissertation demonstrates the power of inductive bias across four methodological contributions. First, fast, gradient-free parameter and ansatz optimizers are developed to bypass costly gradient estimation on quantum computers. By explicitly embedding restriction and implicit biases into the quantum circuit ansatz and optimization method, these algorithms drastically improve resource efficiency, scaling variational quantum eigensolvers for molecular chemistry and quantum feature-map learning for classical data. Second, building on this scalable processing of high-dimensional classical data for discriminative tasks, the dissertation advances generative QML. To achieve high-quality, diverse real-world image generation, a quantum generator is designed with a strong, explicit inductive bias toward visual data, structurally reflecting both spatial image features and distribution characteristics. Third, complementary to learning from classical data, the dissertation advances QML for quantum data, processing inputs directly as quantum states rather than classical vectors. Here, a quantum Gaussian process paradigm is established, deriving a physics-informed inductive bias by encoding quantum information-theoretic assumptions. This bias guarantees provable model faithfulness and theoretical scalability. Finally, to ground this theoretical framework in physical reality, it is demonstrated on regression, classification, and optimization tasks, particularly for physical models. These physical applications close the loop to the initial quantum chemistry research, reinforcing both the overarching necessity and the natural presence of domain-specific inductive bias. Overall, the dissertation delivers timely and relevant findings that advance QML and VQC for near-term practical applications, while laying a foundation for the long-term perspective of quantum computing at scale.