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Chinese Control Conference (CCC)

Lyapunov Based Control for One Qubit Quantum Gates in Coherence Vector Formulation

Bilal Riaz, Shuang Cong, Shahid Qamar

Published Jul 1, 2018• 1 citation
Publisher

Abstract

The design of one qubit quantum gates with Lyapunov-based method is studied in this paper. Firstly, one qubit quantum control system is described in the coherence vector formation, then two types of Lyapunov functions are selected to implement NOT gate. The performances of control laws derived from both Lyapunov functions are compared and analyzed by means of the simulations for the NOT gate implementation.

DOI
10.23919/chicc.2018.8482596

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The manipulation of gate operators in Non-Markovian open quantum systems are studied in this paper. A Lyapunov function based on operator distance is proposed. An additional adjustable item and the time-dependent control gain in Lyapunov control laws are used to improve control accuracy. In addition, another set of control laws is designed to maintain gate operators within given accuracy as long as possible. The proposed scheme is applied to prepare single qubit NOT gate in a two-level Non-Markovian system by the numerical simulations. The results demonstrate that the error can be limited within the level of 10−4for a significant long time and the system under the proposed control law is robust against the uncertainties of system parameters.
Quantum control is responsible for many key problems in quantum information processing, such as decoherence suppression, quantum state engineering and quantum gate, etc. In recent years quantum control has become a major topic in the fields of quantum optics and quantum information. Fast control of the state of quantum system is effective for both decoherence suppression caused by the environment and information processing in quantum state transfer and tracking. Comparing the standard Lyapunov control function with bang-bang Lyapunov control function, we design an optimized quantum Lyapunov control function, and analyse the influence of control laws on population transfer probability and control time contrastively. The simulation results indicate that the optimized quantum Lyapunov control strategy effectively shortens the control time and avoids high-frequency oscillation that occurs in bang-bang Lyapunov control, therefore, strengthens the robustness against external interference.