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)

We study how quantum and thermal noise affects synchronization of two optomechanical limit-cycle oscillators. Classically, in the absence of noise, optomechanical systems tend to synchronize either inphase or anti-phase. Taking into account the fundamental quantum noise, we find a regime where fluctuations drive transitions between these classical synchronization states. We investigate how this 'mixed' synchronization regime emerges from the noiseless system by studying the classical-toquantum crossover and we show how the time scales of the transitions vary with the effective noise strength. In addition, we compare the effects of thermal noise to the effects of quantum noise. OPEN ACCESS RECEIVED

In this paper, we study cavity optomechanical systems in which the position of a mechanical oscillator modulates both the resonance frequency (dispersive coupling) and the linewidth (dissipative coupling) of a cavity mode. Using a quantum noise approach, we calculate the optical damping and the optically induced frequency shift. We find that dissipatively coupled systems feature two parameter regions providing amplification and two parameter regions providing cooling. To investigate the strong-coupling regime, we solve the linearized equations of motion exactly and calculate the mechanical and optical spectra. In addition to signatures of normal-mode splitting that are similar to the case of purely dispersive coupling, the spectra contain a striking feature that we trace back to the Fano line shape of the force spectrum. Finally, we show that purely dissipative coupling can lead to optomechanically induced transparency which will provide an experimentally convenient way of observing normal-mode splitting.

Mechanical oscillators can be cooled by coupling them to an optical or microwave cavity. Going beyond the standard quantum noise approach, we find an analytic expression for the steady-state phonon number in systems where the position of the mechanical oscillator modulates the cavity frequency as well as the cavity line width. We trace the origin for the quantum limit of cooling to fluctuations in the optical force both at and away from the mechanical frequency. Finally, we calculate the minimal phonon number for the different types of coupling. Our study elucidates how to beneficially combine dispersive and dissipative optomechanical coupling.

Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped and therefore incoherent. We show that there exist regimes of underdamped and even quantum-coherent phase motion, opening up new possibilities to study quantum synchronization dynamics. To this end, we investigate the Van der Pol oscillator (a paradigm for a self-oscillating system) synchronized to an external drive. We derive an effective quantum model which fully describes the regime of underdamped phase motion and additionally allows us to identify the quality of quantum coherence. Finally, we identify quantum limit cycles of the phase itself.Comment: 6 pages + Supplemental Materia