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IEEE International Conference on Information and Automation (ICIA)

Optimal Lyapunov-based states transfer for superconducting qubits

Yinghua Ji, Jianhua Huang, Juju Hu

Published Aug 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1109/icinfa.2016.7831937

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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.
Quantum Lyapunov control was developed in order to transform a quantum system from arbitrary initial states to a target state. The idea is to find control fields that steer the Lyapunov function to zero as $t\ensuremath{\rightarrow}\ensuremath{\infty}$, meanwhile the quantum system is driven to the target state. In order to shorten the time required to reach the target state, we propose two designs to optimize Lyapunov control in this paper. The first design makes the Lyapunov function decrease as fast as possible with a constraint on the total power of control fields, and the second design has the same purpose but with a constraint on each control field. Examples of a three-level system demonstrate that the evolution time for Lyapunov control can be significantly shortened, especially when high control fidelity is required. Besides, this optimal Lyapunov-based quantum control is robust against uncertainties in the free Hamiltonian and decoherence in the system compared to conventional Lyapunov control. We apply our optimal design to cool a nanomechanical resonator where a shorter cooling time is found with respect to the cooling time by the conventional Lyapunov design.
Lyapunov-based quantum control has the advantage that it is free from the measurement-induced decoherence and it includes the instantaneous information of the system in the control. The Lyapunov control is often confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time delay on the Lyapunov control and explore the possibility of replacing the control field with a pulse train or a bang–bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the system. These results suggest that the Lyapunov control is robust against time delay, easy to realize and effective for high-dimensional quantum systems.
By using a quadratic Lyapunov function with un-known parameters and a particle swarm optimization (PSO) algorithm, this paper proposes a new Lyapunov control scheme for quantum systems. This approach can achieve high-probability population transfer to a given target state. For the case when the target state is an eigenstate of the internal Hamiltonian, we introduce a virtual control law into the system model and design corresponding control law. The stability of the system under the action of the Lyapunov control law is analyzed via the LaSalle invariance principle. For the case when the target state is a superposition state, we design a control law by performing a unitary transformation for the quantum system model under consideration. To achieve desired state transfer, we further introduce a PSO algorithm to search for the unknown parameters contained in the control law. Numerical results on a five-level quantum system and a three-qubit system are presented to demonstrate the effectiveness of the proposed approaches.
One main problem of quantum control in quantum systems is the manipulation of states including state transfer and state tracking. We design control fields to realize arbitrary state transfer for open quantum system by Lyapunov stability theory, and investigate the state transfer for non-Markovian system with phase relaxation and energy dissipative relaxation. The numerical simulations illustrate that arbitrary state (eigenstate, superposition state or mixed state) transfer and maintenance for non-Markovian system can be realized under Lyapunov control function by an external steady control field of proper amplitude, with a success rate of more than 98%. When the right control field and function are implemented, not only the decoherence is compensated completely but also the purity of quantum states is maintained in the process of state transfer.
By means of the design method for bilinear systems in the macroscopic field in association with the characteristic that the mathematical model of pure state quantum system is bilinear,and of selecting the performance index of the controlled system,the optimal control strategy in quantum systems was proposed based on the Lyapunov stability theorem.The detailed design process of optimal control law was derived.Some simulation experiments were performed on a spin-1/2 particle system.Experimental results demonstrate the effectiveness of the method proposed.At the same time,the influence of different parameters on the system control effects is analyzed.
This paper addresses the critical objective of achieving rapid state transfer in quantum systems. Increasing control gain to achieve fast convergence can result in poor convergence. To circumvent this, a novel continuous, nonsmooth control is devised, exploiting Lyapunov conditions for quantum systems described by von Neumann equations. This approach ensures swift convergence to the target eigenstate while minimizing control effort and enhancing fidelity compared to prevalent techniques such as bang-bang control, approximate bang-bang control, and standard Lyapunov control. Several illustrative examples are provided to corroborate and validate the efficacy of the proposed methodology.