Problems of quantum control and measurement

H. Ezawa, Yoshimasa Murayama

Alexandre Coutinho Lisboa, José Roberto Castilho Piqueira

The problem concerning the minimum time for an initial state to evolve up to a target state plays an important role in the Classic Optimal Control theory. In the quantum context, as quantum states are so sensitive to environmental influences, the problem is more complex, but its formulation and solution are decisive to implement quantum information processing systems. As is well known, the decoherence phenomenon is unavoidable and the time-energy uncertainty relation must be used to study quantum dynamics. Here, the time-energy uncertainty relations are revisited, being fundamental to propose performance measures based on minimum time evolution. A minimum time performance measure is definedfor quantum control problems. Then, some practical examples are considered and the minimum time performance measure is applied providing results that are supposed to be useful for researchers to pursue strategies to optimize the control of the states of a quantum system.

Alexandre Coutinho Lisboa, José Roberto Castilho Piqueira

The transition time between states plays an important role in designing quantum devices as they are very sensitive to environmental influences. Decoherence phenomenon is responsible for possible destructions of the entanglement that is a fundamental requirement to implement quantum information processing systems. If the time between states is minimized, the decoherence effects can be reduced, thus, it is advantageous to the designer to develop expressions for time performance measures. Quantum speed limit (QSL) problem has been studied from the theoretical point of view, providing general results. Considering the implementation of quantum control systems, as the decoherence phenomenon is unavoidable, it is important to apply these general results to particular cases, developing expressions and performance measures, to assist control engineering designers. Here, a minimum time performance measure is defined for quantum control problems, for time-independent or time-dependent Hamiltonians, and applied to some practical examples, providing hints that may be useful for researchers pursuing optimization strategies for quantum control systems.

Gerard J Milburn

Zhikang Wang

In this thesis, we consider two simple but typical control problems and apply deep reinforcement learning to them, i.e., to cool and control a particle which is subject to continuous position measurement in a one-dimensional quadratic potential or in a quartic potential. We compare the performance of reinforcement learning control and conventional control strategies on the two problems, and show that the reinforcement learning achieves a performance comparable to the optimal control for the quadratic case, and outperforms conventional control strategies for the quartic case for which the optimal control strategy is unknown. To our knowledge, this is the first time deep reinforcement learning is applied to quantum control problems in continuous real space. Our research demonstrates that deep reinforcement learning can be used to control a stochastic quantum system in real space effectively as a measurement-feedback closed-loop controller, and our research also shows the ability of AI to discover new control strategies and properties of the quantum systems that are not well understood, and we can gain insights into these problems by learning from the AI, which opens up a new regime for scientific research.