Beyond Classical Limits: Quantum Algorithms for Transmission Electron Microscopy

Classical transmission electron microscopy simulation faces three fundamental barriers: the phase problem where detectors cannot measure phase directly, the exponential scaling of many-body quantum systems, and the non-convex optimization landscape of phase retrieval algorithms. We present a quantum algorithm framework that overcomes all three limitations through intrinsically quantum computational advantages. Rather than treating electron waves as classical complex numbers, our approach maintains quantum coherence throughout the calculation. Phase information, lost in classical detection, is preserved through quantum entanglement and extracted via quantum measurement. The framework maps electron-specimen interactions to unitary evolution on quantum processors. Classical computers must simulate numerically; quantum computers execute natively. We implement this on IBM quantum processors, demonstrating that current NISQ devices can handle the required quantum circuits. Most significantly, quantum superposition enables simultaneous exploration of exponentially many phase configurations, transforming intractable classical searches into efficient quantum algorithms. Scaling analysis identifies ~100 qubits as the advantage of threshold-precisely matching near-term hardware targets. This work establishes quantum computing not as an alternative but as the natural computational paradigm for microscopy of quantum matter, with open-source implementation enabling immediate community engagement.