Multislice method is widely used to simulate the elastic interaction of an electron beam with matter in electron microscopy. In this paper, we propose a quantum algorithm of multislice method. With the use of quantum circuit this quantum version of multislice method costs less storage space and less runtime than the classical algorithm by taking advantage of the feature of quantum computing. We have used a classical supercomputer to simulate a quantum circuit, and successfully carried out the quantum multislice computation and obtained the expected result on a virtual quantum circuit, which proves the feasibility and correctness of the quantum algorithm. This work demonstrates the potential application prospect of quantum computing to the research of computational physics as a good example.
Multislice method is widely used to simulate the elastic interaction of an electron beam with matter in electron microscopy. In this paper, we propose a quantum algorithm of multislice method. With the use of quantum circuit this quantum version of multislice method costs less storage space and less runtime than the classical algorithm by taking advantage of the feature of quantum computing. We have used a classical supercomputer to simulate a quantum circuit, and successfully carried out the quantum multislice computation and obtained the expected result on a virtual quantum circuit, which proves the feasibility and correctness of the quantum algorithm. This work demonstrates the potential application prospect of quantum computing to the research of computational physics as a good example.
The multislice method is an important algorithm for electron diffraction and image simulations in transmission electron microscopy (TEM). We have proposed a quantum algorithm of the multislice method based on quantum circuit model previously. In this work, we have developed an improved quantum algorithm. We reconstruct the phase-shifting quantum circuit without using the multi-controlled quantum gates, thereby significantly improve the computation efficiency. The improved quantum circuit also allows further gate count reduction at the cost of a controllable error. We have simulated the quantum circuit on a classical supercomputer and analyzed the result to prove the feasibility and correctness of the improved quantum algorithm. We also provide proper parameter settings through testing, allowing the minimization of the necessary number of quantum gates while limiting the relative error within 1%. This work demonstrates the potential of applying quantum computing to electron diffraction simulations and achieving quantum advantages.
In the field of microscopy and microanalysis, technological advancements continually push the boundaries of what is possible in data analysis and simulation. Quantum computing, with its ability to perform complex calculations at unprecedented speeds, represents a promising frontier in this ongoing evolution. By harnessing the principles of quantum mechanics, such as superposition and entanglement, quantum computing offers a novel approach to processing and analyzing vast and complex datasets more efficiently than traditional computing methods [1,2]. In this context, our work focuses on leveraging quantum algorithms to enhance the processing, simulation, and analysis of image and spectroscopic data in microscopy. The primary goal is to utilize the unique capabilities of quantum computing to achieve not only faster but also more precise analysis of microscopy data. Our work primarily involves developing and applying quantum machine learning (QML) [3,4] techniques that are specifically tailored to address the challenges faced in microscopic analysis, such as handling complex data structures and improving the accuracy of simulations. Through this approach, we aim to open new pathways for advancements in microscopy, contributing to more detailed and faster analysis processes that can support a wide range of scientific investigations. Figure 1A illustrates the key parts of QML designed for the analysis and processing of microscopy data. It outlines the steps from data acquisition through preprocessing, quantum feature extraction, and quantum-enhanced machine learning. In addition, we have explored the potential incorporation of quantum algorithms into traditional image and electron diffraction pattern simulations. This approach aims to harness the unique capabilities of quantum computing to perform calculations at exponentially faster rates than classical computing. To this end, Figure 1B illustrates the methodologies we have developed, providing a visual representation of how quantum algorithms can be integrated into the image simulation process, leading to significant improvements in both accuracy and efficiency. This diagram outlines the sequential steps involved in simulating electron microscopy images and diffraction patterns through the application of quantum computing. Starting from the initialization of sample and beam parameters, it progresses through quantum state preparation, the application of quantum algorithms (including Hamiltonian evolution and Quantum Fourier Transform), measurement and data retrieval, post-processing and analysis, and concludes with the visualization of simulation results. A critical aspect of this work is the performance comparison between classical and quantum methodologies. Benchmarking against traditional methods indicates significant performance improvements when utilizing quantum algorithms. These improvements are not limited to computational speed but also include enhanced accuracy and the ability to handle complex data sets, which are often challenging for classical computing methods. Figure 2 summarizes key quantum algorithms, their associated subroutines, the theoretical speedup they offer over classical algorithms, and the main equations underlying each algorithm. These algorithms represent advanced quantum computing techniques aimed at enhancing data processing, analysis, and machine learning tasks, showcasing the potential for exponential and quadratic speedups in specific computational domains. Furthermore, we have conducted quantum cost estimations to compare the resource efficiency of quantum simulations with classical simulations, particularly in the context of electron scattering simulations. This analysis provides valuable insights into the scalability and practicality of quantum computing in microscopy, laying the groundwork for future developments in quantum-enhanced microscopy. In summary, our work demonstrates the feasibility and benefits of integrating quantum computing into the analysis pipeline of microscopy data. By leveraging the power of quantum algorithms, including quantum machine learning, we open the door to new capabilities in microscopy data analysis, promising significant advancements in the field [5-6] A) Quantum Machine Learning (QML) workflow for microscopy data analysis. B) Outlines the steps involved in simulating electron microscopy images and diffraction patterns through the application of quantum computing Overview of quantum algorithms and their applications in electron microscopy data analysis
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×N grid is amplitude-encoded into a 2log2N-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 N×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.
Quantum computing, or quantum computation, has garnered increasing attention within the computational community in recent years, owing to its remarkable efficacy in addressing large-scale problems. In specific scenarios, quantum algorithms exhibit exponential enhancements over their classical counterparts executed on classical computing platforms. Quantum computing introduces myriad opportunities for simulating intricate physical systems, including but not limited to electromagnetic (EM) structures. Despite the extensive research devoted to quantum computing in contemporary literature, the exploration of quantum simulation techniques for EM structures remains relatively limited. In this paper, we will describe a quantum computing method for solving EM problems through finite element equations. The performance of this method will be verified by an EM example.
Image formation in transmission electron microscopy (TEM) is governed by the coherent evolution of the electron wavefunction through the specimen and the objective lens. This physics maps naturally onto the gate model of quantum computation. We present QuScope, an open-source Python framework that expresses the complete TEM image-formation pipeline as quantum circuits. The N×N electron wavefunction is amplitude-encoded in 2log2N qubits, and every optical element, including phase-grating transmission, Fresnel propagation between specimen slices, and the aberrated objective lens, is implemented as a diagonal unitary conjugated by quantum Fourier transforms. On this foundation, QuScope v0.2.0 implements validated imaging pipelines, covering conventional TEM under the phase-object approximation, full multislice CTEM and STEM for thick specimens. All quantum results reported here come from exact, noise-free statevector simulation of the circuits on classical hardware, and every result is validated against a classical twin implementation. Quantum and classical multislice exit waves agree to unit fidelity, and all physical constants are verified against standard references. We provide transpiled quantum-resource estimates for each algorithm, an analysis of the diagonal-synthesis bottleneck that governs near-term hardware execution, and a fully tested, documented, and pip-installable package. QuScope v0.2.0 is available at https://github.com/QuScope/QuScope.
The numerical analysis of the diffraction features rendered by transmission electron microscopy typically relies either on classical approximations (Monte Carlo simulations) or quantum paraxial tomography (the multislice method and any of its variants). Although numerically advantageous (relatively simple implementations and low computational costs), they involve important approximations and thus their range of applicability is limited. To overcome such limitations, an alternative, more general approach is proposed, based on an optimal combination of wave-packet propagation with the on-the-fly computation of associated Bohmian trajectories. For the sake of clarity, but without a loss of generality, the approach is used to analyze the diffraction of an electron beam by a thin aluminum slab as a function of three different incidence (working) conditions which are of interest in electron microscopy: the probe width, the tilting angle, and the beam energy. Specifically, it is shown that, because there is a dependence on particular thresholds of the beam energy, this approach provides a clear description of the diffraction process at any energy, revealing at the same time any diversion of the beam inside the material towards directions that cannot be accounted for by other conventional methods, which is of much interest when dealing with relatively low energies and/or relatively large tilting angles.