Information Technology Reference
In-Depth Information
Chapter 13
Quantum Control and Manipulation of Systems
and Processes at Molecular Scale
Abstract
Biological systems, at molecular level, exhibit quantum mechanical
dynamics. A question that arises is if the state of such systems can be controlled
by an external input such as an electromagnetic field or light emission (e.g., laser
pulses). The chapter proposes a gradient method for feedback control and stabi-
lization of quantum systems using Schrödinger's and Lindblad's descriptions. The
eigenstates of the quantum system are defined by the spin model. First, a gradient-
based control law is computed using Schrödinger's description. Next, an estimate
of state of the quantum system is obtained using Lindblad's differential equation.
In the latter case, by applying Lyapunov's stability theory and LaSalle's invariance
principle one can compute a gradient control law which assures that the quantum
system's state will track the desirable state within acceptable accuracy levels. The
performance of the control loop is studied through simulation experiments for the
case of a two-qubit quantum system.
13.1
Basics of Quantum Systems Control
Recently, evidence has emerged from several studies that quantum coherence is
playing an important role in certain biological processes [
95
,
100
,
107
]. In [
183
]the
quantization of systems in the quantum theory and their functional roles in biology
has been analyzed. In [
146
] it has been shown that the electron clouds of nucleic
acids in a single strand of DNA can be modeled as a chain of coupled quantum
harmonic oscillators with dipole-dipole interaction between nearest neighbors.
Finally it has been shown that the quantum state of a single base (A, C.G. or T)
contains information about its neighbor, questioning the notion of treating individual
DNA bases as independent bits of information. The next question that arises is if the
state of such systems exhibiting quantum mechanical dynamics can be controlled
by an external input, such as electromagnetic field or light emission (e.g., laser
pulses). To this end this chapter analyzed the basics of quantum systems control and
proposes a systematic method for assuring stability in quantum control feedback
loops.
