Nonparametric learning is able to make reliable predictions by extracting information from similarities between a new set of input data and all samples. Here we point out a quantum paradigm of nonparametric learning which offers an exponential speedup over the sample size. By encoding data into quantum feature space, similarity between the data is defined as an inner product of quantum states. A quantum training state is introduced to superpose all data of samples, encoding relevant information for learning its bipartite entanglement spectrum. We demonstrate that a trained state for prediction can be obtained by entanglement spectrum transformation, using quantum matrix toolbox. We further workout a feasible scheme to implement the quantum nonparametric learning with trapped ions, and demonstrate the power of quantum superposition for machine leaning with a state-of-the-art technology.

Dipolar parity anomaly can be induced by spatiotemporally weak-dependent energy-momentum separation of paired Dirac points in two-dimensional Dirac semimetals. Here we reveal topological currents arising from this kind of anomaly. A corresponding lattice model is proposed to emulate the topological currents by using two-component ultracold atoms in a two-dimensional optical Raman lattice. In our scheme, the topological currents can be generated by varying on-site coupling between the two atomic components in time and tuned via the laser fields. Moreover, we show that the topological particle currents can directly be detected from measuring the drift of the center of mass of the atomic gases. * Electronic address: danweizhang@m.scnu.edu.cn † Electronic address: zwang@hku.hk arXiv:1808.09771v2 [quant-ph]