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We report the first experimental demonstration of quantum synchronization. This is achieved by performing a digital simulation of a single spin-1 limit-cycle oscillator on the quantum processors of the IBM Q System. Applying an external signal to the oscillator, we verify typical features of quantum synchronization and demonstrate an interference-based quantum synchronization blockade. Our results show that state-of-the-art noisy intermediate-scale quantum processors are powerful enough to implement realistic open quantum systems. Finally, we discuss limitations of current quantum hardware and define requirements necessary to investigate more complex problems.

Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest state, therefore quenching their oscillation. This phenomenon is termed "amplitude death." Well known and studied in classical self-oscillators, amplitude death was only recently investigated in quantum self-oscillators [Ishibashi and Kanamoto, Phys. Rev. E 96, 052210 (2017)2470-004510.1103/PhysRevE.96.052210]. Quantitative differences between the classical and quantum descriptions were found. Here, we demonstrate that for quantum self-oscillators with anharmonicity in their energy spectrum, multiple resonances in the mean phonon number can be observed. This is a result of the discrete energy spectrum of these oscillators, and is not present in the corresponding classical model. Experiments can be realized with current technology and would demonstrate these genuine quantum effects in the amplitude death phenomenon.

A metamaterial formed by superconducting circuits or quantum dots can serve as active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast to real atoms, variations in their parameters cannot be avoided. In this paper, we examine the influence of disorder on such a multi-atom lasing setup. We find that the lasing process evolves into a selforganized stationary state that is quite robust against disorder. The reason is that photons created by those atoms which are in or close to resonance with the resonator stimulate the emission also of more detuned atoms. Not only the number of photons grows with the number of atoms, but also the width of the resonance as function of the detuning. Similar properties are found for other types of disorder such as variations in the individual coupling. We present relations how the allowed disorder scales with the number of atoms and confirm it by a numerical analysis. We also provide estimates for the sample-to-sample variations to be expected for setups with moderate numbers of atoms.

Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we propose a framework for the automated design of control schemes based on differentiable programming. We apply this approach to the state preparation and stabilization of a qubit subjected to homodyne detection. To this end, we formulate the control task as an optimization problem where the loss function quantifies the distance from the target state, and we employ neural networks (NNs) as controllers. The system’s time evolution is governed by a stochastic differential equation (SDE). To implement efficient training, we backpropagate the gradient information from the loss function through the SDE solver using adjoint sensitivity methods. As a first example, we feed the quantum state to the controller and focus on different methods of obtaining gradients. As a second example, we directly feed the homodyne detection signal to the controller. The instantaneous value of the homodyne current contains only very limited information on the actual state of the system, masked by unavoidable photon-number fluctuations. Despite the resulting poor signal-to-noise ratio, we can train our controller to prepare and stabilize the qubit to a target state with a mean fidelity of around 85%. We also compare the solutions found by the NN to a hand-crafted control strategy.