When Quantum Meets AI: Quantum Methods for Machine Learning and Machine Learning Methods for Quantum Systems

A thesis exploring bidirectional advances between quantum computing and artificial intelligence

Tak Hur· 2026· DOI 10.48550/arXiv.2609.25641

The core problem

The intersection of quantum computing and artificial intelligence is a rapidly growing field with potential to enhance both domains. This thesis, by Tak Hur, explores two complementary directions: quantum methods for machine learning (QML) and machine learning methods for quantum systems (ML4QS). In QML, the focus is on developing quantum algorithms that improve machine learning tasks, particularly in noisy environments. In ML4QS, the goal is to leverage classical machine learning to tackle challenges in quantum computing, such as error correction and state estimation. The work is unified by themes of learned representations, statistical control, and hardware constraints. The thesis presents novel contributions in each direction, validated through theoretical analysis and experiments on quantum hardware and simulators.

In QML, NQE improves classification accuracy on noisy quantum hardware by increasing the trace distance between class ensembles. The DQC1 extension is successfully demonstrated on an NMR quantum processor, showing the feasibility of the approach on near-term devices. Margin-based analysis reveals that margin distributions predict generalization more reliably than parameter-count metrics in the studied benchmarks. For ML4QS, the Mamba-based neural decoder matches the performance of a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, multi-shift SR reduces checkpoint-local validation residuals and update variance compared to fixed-shift SR, at additional computational cost. These results highlight the benefits of learned representations and adaptive statistical control in quantum-AI systems.

The intersection of quantum computing and artificial intelligence is a rapidly growing field with potential to enhance both domains. This thesis, by Tak Hur, explores two complementary directions: quantum methods for machine learning (QML) and machine learning methods for quantum systems (ML4QS). In QML, the focus is on developing quantum algorithms that improve machine learning tasks, particularly in noisy environments. In ML4QS, the goal is to leverage classical machine learning to tackle challenges in quantum computing, such as error correction and state estimation. The work is unified by themes of learned representations, statistical control, and hardware constraints. The thesis presents novel contributions in each direction, validated through theoretical analysis and experiments on quantum hardware and simulators.

The thesis employs a combination of theoretical derivations, algorithm design, and empirical validation. For QML, the Neural Quantum Embedding (NQE) is proposed to learn data representations that maximize the trace distance between embedded class ensembles. This is formalized by minimizing an embedding-dependent bound on empirical risk. The approach is extended to deterministic quantum computation with one qubit (DQC1) using a training objective based on the Hilbert-Schmidt inner product, and demonstrated on an NMR quantum processor. A margin-based generalization analysis connects quantum neural network performance to quantum state discrimination. For ML4QS, a Mamba-based neural decoder for surface codes is developed and compared against a Transformer baseline. The decoder's inference cost scaling is analyzed, and its performance under decoder-induced noise is evaluated. Additionally, stochastic reconfiguration (SR) for neural quantum states is reinterpreted as tangent-space ridge regression, leading to a multi-shift SR variant that balances bias and variance. The methodology integrates quantum information theory, statistical learning theory, and deep learning architectures.

The findings demonstrate that learned representations can significantly enhance quantum machine learning, particularly in noisy environments where traditional methods struggle. The margin-based generalization analysis provides a new perspective on why quantum neural networks generalize, linking performance to quantum state discrimination. The Mamba-based decoder's improved scaling and error rates suggest that classical machine learning can effectively address quantum error correction challenges, potentially enabling more scalable quantum computing. The reinterpretation of SR as tangent-space ridge regression offers a principled way to control the bias-variance trade-off in variational quantum algorithms, with multi-shift SR providing a practical improvement. However, the additional computational cost of multi-shift SR and the need for further validation on larger quantum systems remain open challenges. Overall, the thesis underscores the importance of statistical control and hardware constraints in shaping the exchange between quantum computing and machine learning.

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