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Tuberculosis (TB) is the world’s deadliest infectious disease, with over 1.5 million deaths and 10 million new cases reported anually. The causative organismMycobacterium tuberculosis(Mtb) can take nearly 40 d to culture, a required step to determine the pathogen’s antibiotic susceptibility. Both rapid identification and rapid antibiotic susceptibility testing of Mtb are essential for effective patient treatment and combating antimicrobial resistance. Here, we demonstrate a rapid, culture-free, and antibiotic incubation-free drug susceptibility test for TB using Raman spectroscopy and machine learning. We collect few-to-single-cell Raman spectra from over 25,000 cells of the Mtb complex strain Bacillus Calmette-Guérin (BCG) resistant to one of the four mainstay anti-TB drugs, isoniazid, rifampicin, moxifloxacin, and amikacin, as well as a pan-susceptible wildtype strain. By training a neural network on this data, we classify the antibiotic resistance profile of each strain, both on dried samples and on patient sputum samples. On dried samples, we achieve >98% resistant versus susceptible classification accuracy across all five BCG strains. In patient sputum samples, we achieve ~79% average classification accuracy. We develop a feature recognition algorithm in order to verify that our machine learning model is using biologically relevant spectral features to assess the resistance profiles of our mycobacterial strains. Finally, we demonstrate how this approach can be deployed in resource-limited settings by developing a low-cost, portable Raman microscope that costs <$5,000. We show how this instrument and our machine learning model enable combined microscopy and spectroscopy for accurate few-to-single-cell drug susceptibility testing of BCG. 

Given a loop or more generally 1-cycle r r of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks whether or not it is homologous to zero. We frame and tackle this problem in the quantum setting. Given an oracle that one can use to query the inclusion of edges on a closed curve, we design a quantum algorithm for such a homology detection with a constant running time, with respect to the size or the number of edges on the loop r r , requiring only a single usage of oracle. In contrast, classical algorithm requires \Omega(L) Ω ( L ) oracle usage, followed by a linear time processing and can be improved to logarithmic by using a parallel algorithm. Our quantum algorithm can be extended to check whether two closed loops belong to the same homology class. Furthermore, it can be applied to a specific problem in the homotopy detection, namely, checking whether two curves are not homotopically equivalent on a closed two-dimensional manifold.