EE 290O. Advanced Topics in Control: Introduction to Quantum … · 2012-02-28 · EE 290O. Advanced Topics in Control: Introduction to Quantum Dynamics and Control Instructor: Alireza

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/

1

2

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

3



Physical theories, a historical/intuitive chart

4

Object Speed

Obj

ect S

ize

fasterslower

smal

ler

larg

er Newtonian Mechanics

Quantum Mechanics

Quantum Field Theory, ...

Relativity

TheoryElectromagnetic

6



Birth of Quantum Mechanics

7

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.


8

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.


9

Electron Diffraction (Thomson and Davisson-Germer 1927)

Non-classical feature: Electrons behave like a wave rather than a particle.

Wave diffraction phenomenon

10



Quantum Mechanics

11

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.

12

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

13



First Quantum Revolution

14

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



Second Quantum Revolution

16

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

17

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

18

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

19

M. Fuechsle etc, Nature Nano. 5, 502 (2010).

Quantum tunneling

Quantum Technology Tools

20

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.



Control Theory of Quantum Systems

22

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

23

Cold Water

Hot Water:

Control Theory

24

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

25

System(Plant)Input

Controller(Actuator)

Measurement(Monitor)

Output

Input-Reference



Classical Classical Control Theory

27

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

28

Modern classical control theory utilizes the time domain state-space representation.

The state of the system P is parameterized by a number of variables

1

X = {xi}.. ..!Y

!t= g (X, u)

!X

!t= f (X, u)

1

!Y

!t= g (X, u)

!X

!t= f (X, u)

1

!Y

!t= g (X, u)

!X

!t= f (X, u)

Quantum Control Theory

29

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

30

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

31

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:

32

Linear Algebra for Quantum Mechanicsor Linear algebra with Dirac Notations

Documents

EE 290O. Advanced Topics in Control: Introduction to Quantum … · 2012-02-28 · EE 290O. Advanced Topics in Control: Introduction to Quantum Dynamics and Control Instructor: Alireza