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IEEE International Conference on Information and Automation (ICIA)

Manipulations of quantum state for a two-level closed or open quantum system

Juju Hu, Qiang Ke, Yinghua Ji

Published Jul 1, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1109/icinfa.2017.8078965

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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.
Based on analyzing the presentation of the single quantum state on Bloch sphere,a strategy of optimal preparation of arbitrary quantum state of two-level closed quantum systems is proposed.With the help of quantum mechanical logic gate,manipulation of quantum system is realized,on unitary-evolution.The models of two-level quantum systems and its control systems are set up.Then,by using the Lie group,and with classical control theory and dynamics of quantum system,a strategy of optimal preparation of arbitrary quantum state is developed.The theoretical analysis and the simulation of the preparation show the advantage of the idea.
We study the manipulation of two-level quantum systems. This research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two-level quantum system, a quantum bit. We consider the problem of driving the evolution operator to a desired state, while minimizing the energy-type cost. Mathematically, this problem translates into an optimal control problem for systems varying on the Lie group of special unitary matrices, with cost that is quadratic in the control. We develop a comprehensive theory of optimal control for two-level quantum systems. In particular, we prove the 'normality' of the given problem and the 'regularity' of the optimal control functions. The impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed.
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A general scheme is presented for controlling quantum systems using evolution driven by nonselective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a two-level quantum system controlled by nonselective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive nonselective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.