The growing societal demand for privacy, driven by rapid advances in information technologies and machine learning, motivates the development of approaches that reconcile privacy preservation with computational efficiency. This thesis addresses this challenge by bridging two seemingly disparate paradigms: universal blind quantum computation (UBQC), based on measurement-based quantum computation, and quantum machine learning (QML) algorithms such as the Harrow–Hassidim–Lloyd (HHL) algorithm and quantum recommendation systems.

To this end, we developed a transpiler that maps Qiskit quantum circuits into computational brickwork graphs (Graphix Pattern objects), the underlying resource states of UBQC. This enables systematic evaluation of the depth and cost incurred by blind implementations. From these constructions, we established a general upper bound on the depth scaling of the computational graph corresponding to blind algorithms as O(mn), where m is the circuit width and n its original complexity. Building on this framework, we provide detailed analyses of blind implementations of the quantum Fourier transform, HHL, recommendation systems, and quantum transformers.

Finally, the thesis proposes a minimal experimental design for Blind Quantum Machine Learning with resource estimates requiring a total of 750 remotely prepared qubit states, but with only 12 coherent qubits in memory at any time using a conveyor-belt architecture, making the resource requirements compatible with near-term implementations on a quantum internet.
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