• Corpus ID: 10441120

Lie Algebraic Analysis and Control of Quantum Dynamics

@article{DAlessandro2008LieAA,
  title={Lie Algebraic Analysis and Control of Quantum Dynamics},
  author={Domenico D’Alessandro},
  journal={arXiv: Quantum Physics},
  year={2008}
}
In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe their application to the control of two coupled spin 1/2's. 
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References

SHOWING 1-10 OF 27 REFERENCES

Time-optimal Control of Spin Systems

The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system

Notions of controllability for bilinear multilevel quantum systems

In this note, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution

Introduction to Lie Algebras and Representation Theory

Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-

Control of the Evolution of Heisenberg Spin Systems

An algorithm for the control of the unitary evolution operator for the system of two spin 1 2 ’s interacting through Heisenberg interaction is given and it is shown how the result allows to obtain information on the initial state through a series of evolutions and measurements.

Quantum computation and quantum information

  • T. Paul
  • Physics
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal

Optimal control of two-level quantum systems

A comprehensive theory of optimal control for two-level quantum systems is developed, in particular, a classification of normal and abnormal extremals and a proof of regularity of the optimal control functions.

Degrees of controllability for quantum systems and application to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions for each type of controllability are discussed. The results are

Non-stationary quantum walks on the cycle

We consider quantum walks on the cycle in the non-stationary case where the ‘coin’ operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state

Uncontrollable quantum systems: A classification scheme based on Lie subalgebras

It is well known that a finite level quantum system is controllable if and only if the Lie algebra of its generators has full rank. When the rank of the Lie algebra is not full, there is a rich