No Arabic abstract
This paper explains some fundamental ideas of {em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and impulsive dynamics. Topics covered in this paper include open and closed loop control, impulsive control, optimal control, quantum filtering, quantum feedback networks, and coherent feedback control.
This paper is concerned with the concept of {em information state} and its use in optimal feedback control of classical and quantum systems. The use of information states for measurement feedback problems is summarized. Generalization to fully quantum coherent feedback control problems is considered.
A positive P-representation for the spin-j thermal density matrix is given in closed form. The representation is constructed by regarding the wave function as the internal state of a closed-loop control system. A continuous interferometric measurement process is proved to einselect coherent states, and feedback control is proved to be equivalent to a thermal reservoir. Ito equations are derived, and the P-representation is obtained from a Fokker-Planck equation. Langevin equations are derived, and the force noise is shown to be the Hilbert transform of the measurement noise. The formalism is applied to magnetic resonance force microscopy (MRFM) and gravity wave (GW) interferometry. Some unsolved problems relating to drift and diffusion on Hilbert spaces are noted.
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems theoretical perspective and applied to the formulation of quantum gates. Then quantum systems are defined by introducing feedback to the gates. In Part III, quantum gates and systems are reformulated from a quantum field theoretical perspective using S-matrices. We also discuss how gauge fields are related to feedback.
We derive the quantum stochastic master equation for bosonic systems without measurement theory but control theory. It is shown that the quantum effect of the measurement can be represented as the correlation between dynamical and measurement noise. The transfer function representation allows us to analyze a dynamical uncertainty relation which imposes strong constraints on the dynamics of the linear quantum systems. In particular, quantum systems preserving the minimum uncertainty are uniquely determined. For large spin systems, it is shown that local dynamics are equivalent to bosonic systems. Considering global behavior, we find quantum effects to which there is no classical counterparts. A control problem of producing maximal entanglement is discussed as the stabilization of a filtering process.
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum Principle. In a three-level quantum system, we show that the Stimulated Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.