Q-SORT introduces a revolutionary concept whereby the TEM is employed as a Quantum Sorter. All TEM techniques are in fact limited to the imaging and energy spectroscopy of the electron wavefunction. Moreover, when a single sample property is sought, most of the image information is useless, a waste that cannot be afforded in dose-sensitive materials. The Quantum Sorter leverages the recently-acquired capacity to structure e-beams, which implies that if, in a quantum experiment (tunable state preparation, interaction, analysis), the analysis is performed over the ‘optimal’ basis of quantum states, very few electrons are necessary for the full characterisation of a sought property, i.e. the TEM can be tuned to answer a single question but with maximum efficiency. To this end, Q-SORT introduces a new parallel analysis strategy, based on a suitable conformal mapping of the wavefunction: the starting point is the analysis of orbital angular momentum (OAM), but building a recipe for diagonalising a wider range of observables is one of the planned Breakthroughs of Q-SORT. This will in turn allow Q-SORT to achieve three other high-risk Breakthroughs of vast applicability: assessing the OAM of plasmonic resonances in select nanoparticles, achieving atomic-resolution magnetic dichroism, identifying different proteins based on selected properties. We believe that the Quantum Sorter will become so important that it will eventually be part of every state-of-the-art TEM, since the new technology is easy to integrate with energy-loss spectrometry. The project consortium includes some of the world leaders in optical and electronic vortex beams, as well as in protein cryoTEM. A major industrial partner in TEM is included, so as to secure market penetration of technological outcomes. The project avails itself of established resource and IPR management techniques. Gender balance and equal opportunities will be ensured. A comprehensive outreach and dissemination strategy is foreseen.