Control problems in quantum systems

TzyhJong Tarn,ChunWen Li,ReBing Wu,Jing Zhang,GuiLu Long

doi:10.1007/s11434-012-5193-0

Abstract

The past decade or two has witnessed tremendous progress in theory and practice of quantum control technologies. Bridging different scientific disciplines ranging from fundamental particle physics to nanotechnology, the goal of quantum control has been to develop effective and efficient tools for common analysis and design, but more importantly would pave the way for future technological applications. This article briefly reviews basic quantum control theory from the perspective of modeling, analysis and design, as well as considers future research directions.

Highlights

Quantum control refers to the design of control strategies in systems that obey the principles of quantum mechanics, e.g. microscopic systems with few atoms or photons that were addressed early in the lecture “Plenty of Room at the Bottom” given by Richard Feynman in 1959 [1]
This dream has been pursued since 1960s right after the invention of lasers, which illuminated the hope to coherently control chemical reaction processes, but it was not until the end of 20th century when a burst of successes occurred in controlling ultrafast quantum dynamics
Physical objects in nature are usually classified as either matter or fields; the goal of quantum control can likewise be classified as the control of matter and the control of fields

Summary

Modeling of quantum control systems

Physical objects in nature are usually classified as either matter or fields; the goal of quantum control can likewise be classified as the control of matter and the control of fields. In classical system theory [40], it is natural to treat each component of a composite system as an objective with inputs and outputs: x(t) = f [x(t), u(t)], y(t) = g[x(t), u(t)], where the input u(t) causally affects the evolution of the state x(t) through the dynamical equation, which subsequently influences the variation of the output y(t) as a function of the state and control variables. This general structure needs to be carefully treated in quantum systems when the input and/or output are quantum variables, as they acts on different Hilbert spaces. Readers may look into another paper written by Zhang and James on the topic of coherent feedback control

System analysis

Control design methodologies

Perspectives