Machine learning with artificial neural networks is revolutionizing science. The most advanced challenges require discovering answers autonomously. This is the domain of reinforcement learning, where control strategies are improved according to a reward function. The power of neural-networkbased reinforcement learning has been highlighted by spectacular recent successes, such as playing Go, but its benefits for physics are yet to be demonstrated. Here, we show how a network-based "agent" can discover complete quantum-error-correction strategies, protecting a collection of qubits against noise. These strategies require feedback adapted to measurement outcomes. Finding them from scratch, without human guidance, tailored to different hardware resources, is a formidable challenge due to the combinatorially large search space. To solve this, we develop two ideas: two-stage learning with teacher/student networks and a reward quantifying the capability to recover the quantum information stored in a multi-qubit system. Beyond its immediate impact on quantum computation, our work more generally demonstrates the promise of neural-network-based reinforcement learning in physics. arXiv:1802.05267v3 [quant-ph] 31 Aug 2018 stabilizer codes decoherence-free subspaces noise measurement qubits RL-environment neural network RL-agent action (gate)

Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an important quantity in this field. Another example of topology, in polarization physics, are polarization singularities, called L lines and C points. By establishing a connection between these two theories, we develop a novel technique to visualize and potentially measure the Chern number: it can be expressed either as the winding of the polarization azimuth along L lines in reciprocal space, or in terms of the handedness and the index of the C points. For mechanical systems, this is directly connected to the visible motion patterns.

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A 35-year-old woman was receiving warfarin sodium therapy for a prosthetic aortic valve. She sustained a myocardial infarction five weeks after beginning a diet of lettuce, broccoli, and turnip greens to lose weight. Excess dietary vitamin K can cause life-threatening consequences in patients on warfarin treatment.