EE 290O. Advanced Topics in Control:
Introduction to Quantum Dynamics and Control
Instructor: Alireza Shabani
Contact : [email protected]
Office: Gilman, Room 19Cory 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 chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
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Quantum Technology:Physical theories, a historical chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
Physical theories, a historical/intuitive chart
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Object Speed
Obj
ect S
ize
fasterslower
smal
ler
larg
er Newtonian Mechanics
Quantum Mechanics
Quantum Field Theory, ...
Relativity
TheoryElectromagnetic
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Quantum Technology:Physical theories, a historical chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
Birth of Quantum Mechanics
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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.
Birth of Quantum Mechanics
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Photoelectric Effect (Heinrich Hertz 1887):
Non-classical feature: Light behaves like a particle rather than a wave.
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.
Birth of Quantum Mechanics
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Electron Diffraction (Thomson and Davisson-Germer 1927)
Non-classical feature: Electrons behave like a wave rather than a particle.
Wave diffraction phenomenon
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Quantum Technology:Physical theories, a historical chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
Quantum Mechanics
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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).
All physics you learned in high school and college as mechanics and electromagnetic laws are just approximations to quantum mechanics.
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Relationship between classical mechanics and quantum mechanics
1 m1 mm1 μm1 nm
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.
ClassicalQuantum- ClassicalQuantum
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Quantum Technology:Physical theories, a historical chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
First Quantum Revolution
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20th Century: Formulation of quantum mechanics and technological revolution.
Wave nature of electrons
Atoms and molecules structure
Semiconductors physics
Integrated circuits
Particle nature of light
Photovoltaic
Solar cells, CD, photocopy machines, surgeries ...
LASER
Quantum Technology:Physical theories, a historical chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
Second Quantum Revolution
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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).
Quantum Technologies
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Quantum photonics Quantum opticsQuantum sensorQuantum lithography and microscopy Quantum teleportation
SpintronicsCoherent quantum electronics Molecular coherent quantum electronics Solid-state quantum computers
Coherent matter technology Atom optics Atom lasers
Quantum electromechanical systems
Single-spin magnetic resonance forcemicroscopy
Quantum information technology:Quantum algorithmsQuantum cryptography Quantum codingQuantum circuit designQuantum Computer
Transistors reach quantum regime
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The evolution of transistor gate length (minimum feature size) and the density of transistors in microprocessors over time.
AIST, Japan
2 Gate MOSFET
M. Ferain etc, Nature 479, 310 (2011).
Few-electron single-crystal silicon quantum dot transistor
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M. Fuechsle etc, Nature Nano. 5, 502 (2010).
Quantum tunneling
Quantum Technology Tools
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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.
Quantum Technology:Physical theories, a historical chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
Control Theory of Quantum Systems
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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.
Everyday Feedback Control system
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Cold Water
Hot Water:
Control Theory
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Open loop control:
System(Plant)Input
Controller(Actuator) Output
Closed-loop (feedback) control:
System(Plant)Input
Controller(Actuator)
Measurement(Monitor)
Input
Output
Input-Reference
Control Theory
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System(Plant)Input
Controller(Actuator)
Measurement(Monitor)
Output
Input-Reference
Quantum Technology:Physical theories, a historical chartBirth of Quantum MechanicsQuantum Mechanics versus classical mechanicsFirst Quantum RevolutionSecond Quantum Revolution
Control Theory:Classical Classical Control TheoryModern Classical Control TheoryQuantum Control Theory
Classical Classical Control Theory
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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:
Modern Classical Control Theory
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Modern classical control theory utilizes the time domain state-space representation.
The state of the system P is parameterized by a number of variables
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X = {xi}.. ..!Y
!t= g (X, u)
!X
!t= f (X, u)
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!Y
!t= g (X, u)
!X
!t= f (X, u)
1
!Y
!t= g (X, u)
!X
!t= f (X, u)
Quantum Control Theory
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Classical approach:
Open loop (coherent control)
Measurement-based feedback control (real-time)
Quantum approach:
Coherent feedback control (not-covered in this course)
Open-Loop Control
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Quantum control theory is base on the modern classical theory.
Open loop quantum problems are among the bilinear control problems: 1
!X
!t= AX + uFX
!X
!t= FX + Gu
Population control: 1
dP
dt= (rbirth ! rdeath)P
Feedback Control
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Better control necessitates deeper understanding of natural laws, so quantum control can help us to better understand quantum physics.
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
!t= AX + uFX + G(X)"
Next Session:
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Linear Algebra for Quantum Mechanicsor Linear algebra with Dirac Notations