Quantum Algorithm Framework for Phase-Contrast Transmission Electron Microscopy Image Simulation

We present a quantum algorithmic framework for simulating phase-contrast transmission electron microscopy (CTEM) image formation using a fault-tolerant, gate-based quantum circuit model. The electron wavefield on an Ntimes N grid is amplitude-encoded into a 2log₂ N-qubit register. Free-space propagation and objective-lens aberrations are implemented via two-dimensional quantum Fourier transforms (QFTs) and diagonal phase operators in reciprocal space, while specimen interaction is modeled under the weak phase object approximation (WPOA) as a position-dependent phase grating. We validate projected potentials, contrast transfer function (CTF) behavior, and image contrast trends against classical multislice simulations for MoS₂ over experimentally relevant parameters, and provide resource estimates and key assumptions that determine end-to-end runtime. While extracting complete Ntimes N intensity images requires O\(N²/ε²\) measurements that preclude advantage for full-image reconstruction, the framework enables quantum advantage for tasks requiring Fourier-space queries, global image statistics, or phase-coherent observables inaccessible to classical intensity-only detection. This framework provides a physics-grounded mapping from CTEM theory to quantum circuits and establishes a baseline for extending toward full multislice and inelastic scattering models.