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

TL;DR

This paper introduces a quantum algorithmic framework for simulating phase-contrast transmission electron microscopy images, enabling potential quantum advantages in specific Fourier-space and phase-coherent tasks over classical methods.

Contribution

It develops a physics-grounded quantum circuit model for CTEM image formation, including validation against classical simulations and resource estimation for quantum implementation.

Findings

Validated quantum simulation against classical models for MoS2

Identified quantum advantage in Fourier-space and phase-coherent tasks

Provided resource estimates and key assumptions for quantum implementation

Abstract

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 $N\times N$ grid is amplitude-encoded into a $2\log_2 N$-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 MoS$_2$ over experimentally relevant parameters, and provide resource estimates and key assumptions that determine end-to-end runtime. While extracting complete $N\times N$ intensity images requires $O(N^2/\epsilon^2)$ 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.