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.