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EE 290O. Advanced Topics in Control:
Introduction to Quantum Dynamics and Control
Instructor: Alireza Shabani
Contact : [email protected]
Office: Gilman, Room 19
Cory 278
Office Hours: Wednesdays 3-4 pm
All announcements will be posted on bspace.
http://inst.eecs.berkeley.edu/~ee290o/
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Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
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Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
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Physical theories, a historical/intuitive chart
Object Speed
Newtonian
Mechanics
faster
Electromagnetic
Relativity
Theory
smaller
Object Size
larger
slower
Quantum
Mechanics
Quantum Field
Theory, ...
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Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
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Birth of Quantum Mechanics
Classical physics (existing theories of the 19th century) failed to explain a number of
experiments:
Black-body radiation and ultra-violate catastrophe (Gustav Kirchhoff, 1877):
Thermodynamics predict infinite radiation power. Planck solved the problem in 1901
by introducing the concept of discrete energy elements: energy quanta.
Non-classical feature: Light behaves like a particle rather than a wave.
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Birth of Quantum Mechanics
Photoelectric Effect (Heinrich Hertz 1887):
Classical Maxwell wave theory of light:
The more intense the incident light the
greater the energy with which the electrons
should be ejected from the metal.
Non-classical feature:
Light behaves like a particle rather
than a wave.
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Birth of Quantum Mechanics
Electron Diffraction (Thomson and Davisson-Germer 1927)
Wave diffraction phenomenon
Non-classical feature:
Electrons behave like a wave rather than a particle.
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Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
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Quantum Mechanics
Quantum mechanics provides a mathematical description of the dual particle-like and
wave-like nature behavior and interactions of matter and energy.
In principle quantum mechanics applies to any object of any size. However the
quantum effects (wave-particle behavior) is most noticeable for very small objects.
Largest manmade quantum object:
A piezoelectric resonator cooled down to 0.1 K,
A. D. O’Connell et al., Nature 464, 697 (2010).
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Relationship between classical mechanics and
quantum mechanics
All physics you learned in high school and college as mechanics and electromagnetic laws
are just approximations to quantum mechanics.
Classical mechanics is just an approximation to quantum mechanics. It provides good
description of phenomena if the object under studied is not well isolated from its
environment.
1 nm
Quantum
1 mm
1 μm
Classical
Quantum- Classical
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1m
Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
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First Quantum Revolution
20th Century: Formulation of quantum mechanics and technological revolution.
Particle nature of light
Wave nature of electrons
Atoms and molecules structure
Photovoltaic
LASER
Semiconductors physics
Solar cells, CD, photocopy machines,
surgeries ...
Integrated circuits
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Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
Second Quantum Revolution
In the 20th century quantum mechanics revealed the secrets of the nature at atomic scales.
Then we used this knowledge do design some classical machines either novel or with
significantly higher efficiency in compare to their old ancestors.
In the 21st century, we are going to make quantum machines, complex systems governed
by the laws of quantum physics.
- Miniaturization is the dominant trend in modern technology. The electronic, optical and
mechanical devices are reaching to the length scales that need design based on quantum
principles.
- The principles of quantum mechanics offer the promise of exceptional performance over
what classical physics has offered to us.
J.P.Dowling and G.J.Milburn, Phil. Trans. R. Soc. A 361, 3655 (2003).
G.J.Milburn , Schrödinger's machines:the quantum technology reshaping everyday life,
W.H. Freeman & Co., Jun 30, (1997).
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Quantum Technologies
Spintronics
Coherent quantum electronics
Molecular coherent quantum electronics
Solid-state quantum computers
Quantum photonics
Quantum optics
Quantum sensor
Quantum lithography and microscopy
Quantum teleportation
Coherent matter technology
Atom optics
Atom lasers
Quantum information technology:
Quantum algorithms
Quantum cryptography
Quantum coding
Quantum circuit design
Quantum Computer
Quantum electromechanical systems
Single-spin magnetic resonance force
microscopy
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Transistors reach quantum regime
The evolution of transistor gate length (minimum
feature size) and the density of transistors in
microprocessors over time.
2 Gate MOSFET
AIST, Japan
M. Ferain etc, Nature 479, 310 (2011).
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Few-electron single-crystal silicon quantum dot transistor
Quantum tunneling
M. Fuechsle etc, Nature Nano. 5, 502 (2010).
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Quantum Technology Tools
Quantum Metrology: High precision measurement of quantum systems.
Quantum Control: Classical control theory is complete to guide a quantum machine.
Quantum Communication: Quantum-based protocols more powerful than their classical
counterparts in order to inter-connect components of a quantum complex.
Quantum Computation: Quantum mechanics enables exponentially more efficient
algorithms than can be implemented on a classical computer. Building a quantum
computer is the ultimate goal of quantum technology.
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Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
Control Theory of Quantum Systems
Design of a machine becomes complete when it is accompanied with the knowledge of
how to control it for the purpose it is built for.
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Everyday Feedback Control system
Cold Water
Hot Water:
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Control Theory
Open loop control:
Input
Controller
(Actuator)
System
(Plant)
Input
Output
Closed-loop (feedback) control:
InputReference
Controller
(Actuator)
System
(Plant)
Input
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Output
Measurement
(Monitor)
Control Theory
InputReference
Controller
(Actuator)
System
(Plant)
Input
Output
Measurement
(Monitor)
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Quantum Technology:
Physical theories, a historical chart
Birth of Quantum Mechanics
Quantum Mechanics versus classical mechanics
First Quantum Revolution
Second Quantum Revolution
Control Theory:
Classical Classical Control Theory
Modern Classical Control Theory
Quantum Control Theory
Classical Classical Control Theory
Classical classical control theory is based on frequency domain analysis of the system
and controller.
A linear system P is controlled by a linear controller C while being monitored by the a
linear sensor F.
A laplace domain
characterization and
analysis of all components:
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Modern Classical Control Theory
Modern classical control theory utilizes the time domain state-space representation.
The state of the system P is parameterized
by a number of variables
∂Y
= g (X, u)
∂t
∂X
= f (X, u)
∂t
∂Y
= g (X, u)
∂t
∂X
= f (X, u)
∂t
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X = {xi }
.. ..
∂Y
= g (X, u)
∂t
∂X
= f (X, u)
∂t
Quantum Control Theory
Classical approach:
Open loop (coherent control)
Measurement-based feedback control (real-time)
Quantum approach:
Coherent feedback control (not-covered in this course)
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Open-Loop Control
Quantum control theory is base on the modern classical theory.
Open loop quantum problems are among the bilinear control problems:
∂X
∂X
= AX + uF X
= F X + Gu
∂t
∂t
Population control:
dP
dt
= (rbirth − rdeath )P
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Feedback Control
Closed loop quantum control is totally different from its classical
counterpart for two reasons:
1- Quantum states cannot be copied.
2- In contrast to classical realm, a quantum system cannot measured without
destroying the system state.
A feedback quantum control problems turns into a stochastic control problem.
∂X
= AX + uF X + G(X)ξ
∂t
Better control necessitates deeper understanding of natural laws, so
quantum control can help us to better understand quantum physics.
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Next Session:
Linear Algebra for Quantum Mechanics
or Linear algebra with Dirac Notations
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