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IEEE/CAA Journal of Automatica Sinica

Manipulations between eigenstates of 2-level quantum system based on optimal measurements

Jingbei Yang, Shuang Cong, Feng Shuang, HERSCHEL A. RABITZ

Published Jan 10, 2016• 2 citations
Publisher

Abstract

This paper explores the manipulation between eigenstates in a two-level system by a sequence of instantaneous projective measurements. Three cases of the manipulations are studied: the manipulation of optimal measurement-based control; the optimal measurement-based manipulation with the effect of free evolution of system; and the external control fields being used to compensate for the effect caused by the free evolution. Numerical simulations are conducted to verify the results obtained from the theoretically analytical solutions. The optimal parameters for each manipulation case are obtained. The experimental results indicate that the external control fields can make the optimal measurement-based control more effective.

DOI
10.1109/jas.2016.7373760

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This paper explores the manipulation between eigenstates in a two-level system by a sequence of instantaneous projective measurements. Three cases of the manipulations are studied: the manipulation of optimal measurement-based control; the optimal measurement-based manipulation with the effect of free evolution of system; and the external control fields being used to compensate for the effect caused by the free evolution. Numerical simulations are conducted to verify the results obtained from the theoretically analytical solutions. The optimal parameters for each manipulation case are obtained. The experimental results indicate that the external control fields can make the optimal measurement-based control more effective.
Summary This paper explores the optimal control of quantum state transfer in a two‐dimensional quantum system by a sequence of non‐selective projection measurements. We show that for a given initial state, one can always find the corresponding projection operator that can effectively drive the given initial state to any arbitrary target pure state. An external control field is proposed to compensate the effect of the free evolution of system. Numerical simulations and characteristics analysis are given in three cases: without considering free evolution, considering free evolution, and with the action of external control field. The simulating experimental results show that the optimal measurement control is more effective by using proposed external control field. Copyright © 2016 John Wiley & Sons, Ltd.
A general scheme of state transfer is presented for controlling the quantum system with or without an additional electromagnetic field in this paper. As an example, a two-level closed quantum system controlled by the electromagnetic field is considered. The relation between the realization of quantum logic gates and resonance magnetic field pulse is studied. Meanwhile, for a two-level open quantum system, state transfer is achieved by instantaneous projective measurements. We focus on discussing the relation between the state transfer probability and the times of measurement based on instantaneous projective measurement. The results suggest a new way to design control strategies of optimal quantum dynamics by quantum measurement.
Quantum measurements are considered for optimal control of quantum dynamics with instantaneous and continuous observations utilized to manipulate population transfer. With an optimal set of measurements, the highest yield in a two-level system can be obtained. An analytical solution is given for the problem of population transfer by measurement-assisted coherent control in a three-level system with dynamical symmetry. The anti-Zeno effect is recovered in the controlled processes. Demonstrations show that suitable observations can be powerful tools in the manipulation of quantum dynamics.
There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal controls in numerical and laboratory experiments, and for this reason the analysis of traps attracts considerable attention. In this paper we prove that for a wide range of control problems for two-level quantum systems all locally optimal controls are also globally optimal. Hence we conclude that two-level systems in general are trap-free. In particular, manipulating qubits—two-level quantum systems forming a basic building block for quantum computation—is free of traps for fundamental problems such as the state preparation and gate generation.
Taking a two-level system as an example, we show that a strong control field may enhance the efficiency of optimal Lyapunov quantum control in [Hou et al., Phys. Rev. A \textbf{86}, 022321 (2012)] but could decrease its control fidelity. A relationship between the strength of the control field and the control fidelity is established. An extended technique, which combines free evolution and external control, is proposed to improve the control fidelity. We analytically demonstrate that the extended technique can be used to design a control law for steering a two-level system exactly to the target state. In such a way, the convergence of the extended optimal Lyapunov quantum control can be guaranteed.
Abstract A systematic scheme is proposed to numerically estimate the quantum speed limit and temporal shape of optimal control in two-level and three-level quantum systems with bounded amplitude. For the two-level system, two quantum state transitions are studied as illustration. Comparisons between numerical and analytical results are made, and deviations are significantly small. For the three-level system, two critical time points are determined with high accuracy, and optimal controls are obtained for different durations. The shape of optimized control field is simple and does not switch frequently, thus are easy to implement in experiment. In addition, we compare our method with the chopped random basis (CRAB), and the performance of our method is much better than that of CRAB. Our scheme is of importance in estimating the quantum speed limit and optimal control for cases in which analytical solution is absent.