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arXiv:2209.04819

Universal Quantum Electron Microscopy: A Small-Scale Quantum Computing Application with Provable Advantage

Hiroshi Okamoto

Published Sep 11, 2022• 0 citations
arXivHTMLPDF

Abstract

We propose a simple design of a quantum electron microscope that ``queries'' a beam-sensitive phase object, such as a biological specimen, as part of quantum computation. Lower quantum query complexity, not the time complexity, of a quantum algorithm means less specimen damage, which translates to more data extracted from the specimen. Hence small-scale quantum computing offers provable quantum advantage in this context. A possible application of the proposed microscope is the Grover search for a true structure, out of a set of candidate structures.

DOI
10.48550/arxiv.2209.04819

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We propose a simple design of a quantum electron microscope that ``queries'' a beam-sensitive phase object, such as a biological specimen, as part of quantum computation. Lower quantum query complexity, not the time complexity, of a quantum algorithm means less specimen damage, which translates to more data extracted from the specimen. Hence small-scale quantum computing offers provable quantum advantage in this context. A possible application of the proposed microscope is the Grover search for a true structure, out of a set of candidate structures.
We show that quantum computational imaging is advantageous in the setting of low-dose electron microscopy of beam-sensitive specimens. Two qudits placed near the electron beam enable full transfer of quantum information between the electron microscope and a quantum computer in the proposed scheme, providing the specimen is a phase object. We present a quantum algorithm that identifies the correct image among n candidate images, where n is larger than the effective dimension of the Hilbert space of the imaging electron.
One of the astounding consequences of quantum mechanics is that it allows the detection of a target using an incident probe, with only a low probability of interaction of the probe and the target. This 'quantum weirdness' could be applied in the field of electron microscopy to generate images of beam-sensitive specimens with substantially reduced damage to the specimen. A reduction of beam-induced damage to specimens is especially of great importance if it can enable imaging of biological specimens with atomic resolution. Following a recent suggestion that interaction-free measurements are possible with electrons, we now analyze the difficulties of actually building an atomic resolution interaction-free electron microscope, or "quantum electron microscope". A quantum electron microscope would require a number of unique components not found in conventional transmission electron microscopes. These components include a coherent electron beam-splitter or two-state-coupler, and a resonator structure to allow each electron to interrogate the specimen multiple times, thus supporting high success probabilities for interaction-free detection of the specimen. Different system designs are presented here, which are based on four different choices of two-state-couplers: a thin crystal, a grating mirror, a standing light wave and an electro-dynamical pseudopotential. Challenges for the detailed electron optical design are identified as future directions for development. While it is concluded that it should be possible to build an atomic resolution quantum electron microscope, we have also identified a number of hurdles to the development of such a microscope and further theoretical investigations that will be required to enable a complete interpretation of the images produced by such a microscope.
Feynman once asked physicists to build better electron microscopes to be able to watch biology at work. While electron microscopes can now provide atomic resolution, electron beam induced specimen damage precludes high resolution imaging of sensitive materials, such as single proteins or polymers. Here, we use simulations to show that an electron microscope based on a multi-pass measurement protocol enables imaging of single proteins, without averaging structures over multiple images. While we demonstrate the method for particular imaging targets, the approach is broadly applicable and is expected to improve resolution and sensitivity for a range of electron microscopy imaging modalities, including, for example, scanning and spectroscopic techniques. The approach implements a quantum mechanically optimal strategy which under idealized conditions can be considered interaction-free.
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
A transmission electron microscope that takes advantage of superconducting quantum circuitry is proposed. The microscope is designed to improve the image contrast of radiation-sensitive weak-phase objects, in particular, biological specimens. The objective in this setting is to measure the phase shift of the probe electron wave to a precision \ensuremath{\Delta}\ensuremath{\theta} within the number of electrons NNN that does not destroy the specimen. In conventional electron microscopy \ensuremath{\Delta}\ensuremath{\theta} scales as \ensuremath{\sim}1/N1/2{N}^{1/2}N1/2, which falls short of the Heisenberg limit \ensuremath{\sim}1/NNN. To approach the latter by using quantum entanglement, we propose a design that involves a Cooper-pair box placed on the surface of an electrostatic electron mirror in the microscope. Significant improvement could be attained if inelastic scattering processes are sufficiently delocalized.