Reinforcement learning has been widely used in many problems including quantum control of qubits. However, such problems can, at the same time, be solved by traditional, non-machinelearning based methods such as stochastic gradient descendent and Krotov algorithms, and it remains unclear which one is most suitable when the control has specific constraints. In this work we perform a comparative study on the efficacy of two reinforcement learning algorithms, Q-learning and deep Q-learning, as well as stochastic gradient descendent and Krotov algorithms, in the problem of preparing a desired quantum state. We found that overall, the deep Q-learning outperforms others when the problem is discretized, e.g. allowing discrete values of control. The Q-learning and deep Q-learning can also adaptively reduce the complexity of the control sequence, shortening the operation time and improving the fidelity. Our comparison provides insights on the suitability of reinforcement learning in quantum control problems.

Aharonov-Bohm interferometry is the most direct probe of anyonic statistics in the quantum Hall effect. The technique involves oscillations of the electric current as a function of the magnetic field and is not applicable to Kitaev spin liquids and other systems without charged quasiparticles. Here, we establish a novel protocol, involving heat transport, for revealing fractional statistics even in the absence of charged excitations, as is the case in quantum spin liquids. Specifically, we demonstrate that heat transport in Kitaev spin liquids through two distinct interferometer's geometries, Fabry-Perot and Mach-Zehnder, exhibits drastically different behaviors. Therefore, we propose the use of heat transport interferometry as a probe of anyonic statistics in charge insulators.

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