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Kongzhi yu juece

Optimal preparation of arbitrary quantum state of two-level closed quantum system

Daoyi Dong

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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.
In the presentation of single quantum state on Bloch sphere,a strategy of optimal preparation of arbitrary quantum state of electron spin quantum systems is proposed.By using the mechanical logic gate,the manipulation of quantum system is realized by way of unitary-evolution.In the course,a switch idea for the control systems is presented. The models of quantum systems and the control systems using invariant magnetic field are then established.With the help of the Lie group and the classical control theory,a strategy of optimal preparation of arbitrary quantum state is also realized. Finally,the theoretical analysis and the simulation of the preparation indicate 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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Modelling optimal implementation of an arbitrary NNN-qubit quantum gate within the generalized Bloch vectors formalism
The optimal implementation of quantum gates for closed NNN-qubit systems is one of the key challenges for practical realization of many quantum information processing tasks. In the present article, based on the generalized Bloch vectors formalism [J. Phys. A: Math. Theor. 54, 195301 (2021)] for a finite-dimensional quantum system, we develop a new general model for the optimal implementation of quantum gates, which is formulated in terms of the Bloch vectors for the unitary evolution operator and the system Hamiltonians, drift and control, and has the unified mathematical form, which is standard for the mathematical control theory and applicable for the implementation of an arbitrary NNN-qubit gate within any closed NNN-qubit system, satisfying the controllability conditions. Within the developed optimal model, the cost functional has both the terminal part and also, the integral part with the special scaling, and this allows us to specify the quantum optimal control synthesis via solving the two-point boundary value problem (BVP) for the system of ordinary differential equations (ODEs), which can be explored numerically by any of the known BVP solvers for ODEs. The numerical experiments, conducted for the implementation within the developed optimal model of a variety of N=1,2,3N=1,2,3N=1,2,3 qubit gates, demonstrate the high accuracy of the model-based results.
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.