In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems; however, the complexity of multilevel quantum systems make the development of analogous control methods extremely challenging. Here we exploit the equivalence between multilevel systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multilevel control methods. As a demonstration of this technique, we develop adiabatic and composite multilevel quantum control methods and experimentally realize these methods using a $^{171}\mathrm{Yb}^{+}$ ion system. We measure the average infidelity of the process in both cases to be around ${10}^{\ensuremath{-}4}$, demonstrating that this technique can be used to develop high-fidelity multilevel quantum control methods and can, for example, be applied to a wide range of quantum computing protocols, including implementations below the fault-tolerant threshold in trapped ions.In recent decades there has been a rapid development of methods to experimentally control individual quantum systems. A broad range of quantum control methods has been developed for two-level systems; however, the complexity of multilevel quantum systems make the development of analogous control methods extremely challenging. Here we exploit the equivalence between multilevel systems with SU(2) symmetry and spin-1/2 systems to develop a technique for generating new robust, high-fidelity, multilevel control methods. As a demonstration of this technique, we develop adiabatic and composite multilevel quantum control methods and experimentally realize these methods using a $^{171}\mathrm{Yb}^{+}$ ion system. We measure the average infidelity of the process in both cases to be around ${10}^{\ensuremath{-}4}$, demonstrating that this technique can be used to develop high-fidelity multilevel quantum control methods and can, for example, be applied to a wide range of quantum computing protocols, including implementations below the fault-tolerant threshold in trapped ions.

arXiv:1708.02634Physical Review AOct 8, 201839 citations

Advances in Quantum Control Theory

Jeffrey L. Krause

APSMar 1, 20010 citations

Control of Quantum Systems

Manoj Kumar

Jan 1, 20190 citations

Quantum optimal control of multilevel dissipative quantum systems with reinforcement learning

Zheng An, Hai-Jing Song, Qi-Kai He +1 more

Manipulation and control of the complex quantum system with high precision are essential for achieving universal fault-tolerant quantum computing. For a physical system with restricted control resources, it is a challenge to control the dynamics of the target system efficiently and precisely under disturbances. Here we propose a multilevel dissipative quantum control framework and show that deep reinforcement learning provides an efficient way to identify the optimal strategies with restricted control parameters of the complex quantum system. This framework can be generalized to be applied to other quantum control models. Compared with the traditional optimal control method, this deep reinforcement learning algorithm can realize efficient and precise control for multilevel quantum systems with different types of disturbances.Manipulation and control of the complex quantum system with high precision are essential for achieving universal fault-tolerant quantum computing. For a physical system with restricted control resources, it is a challenge to control the dynamics of the target system efficiently and precisely under disturbances. Here we propose a multilevel dissipative quantum control framework and show that deep reinforcement learning provides an efficient way to identify the optimal strategies with restricted control parameters of the complex quantum system. This framework can be generalized to be applied to other quantum control models. Compared with the traditional optimal control method, this deep reinforcement learning algorithm can realize efficient and precise control for multilevel quantum systems with different types of disturbances.

arXiv:2007.00838Physical Review AJan 11, 202148 citations

Lorentz Transformation and Its Generalizations in Problems of Precisely Controlling the States of Multilevel Quantum Systems

Yu. I. Bogdanov, Nadezhda A. Bogdanova, Yu. A. Kuznetsov +1 more

Abstract A method of precision quantum measurements is proposed, which makes it possible to accurately track the states of multilevel quantum systems in Hilbert spaces of various dimensions. The developed quantum control algorithms are based on the use of the spinor representation of the Lorentz transformation group and its generalizations to the case of multilevel quantum systems. It is shown that feedback through weakly perturbing adaptive quantum measurements is capable of providing precise control of the quantum system, while introducing only weak perturbations in the initial quantum state.Abstract A method of precision quantum measurements is proposed, which makes it possible to accurately track the states of multilevel quantum systems in Hilbert spaces of various dimensions. The developed quantum control algorithms are based on the use of the spinor representation of the Lorentz transformation group and its generalizations to the case of multilevel quantum systems. It is shown that feedback through weakly perturbing adaptive quantum measurements is capable of providing precise control of the quantum system, while introducing only weak perturbations in the initial quantum state.

Russian MicroelectronicsApr 1, 20220 citations

Control of quantum systems

G. Huang

Mar 1, 198013 citations

^{171}\mathrm{Yb}^{+}

ion system. We measure the average infidelity of the process in both cases to be around ${10}^{\ensuremath{-}4}$, demonstrating that this technique can be used to develop high-fidelity multilevel quantum control methods and can, for example, be applied to a wide range of quantum computing protocols, including implementations below the fault-tolerant threshold in trapped ions.