FE8100 Quantum computation and quantum information, 2009
Code: FE8100 (PhD course).
Instructors: Johannes Skaar (johannes skaar krøllalfa iet ntnu no), Øystein Marøy (oystein maroy krøllalfa iet ntnu no).
Weekly hours: 4
Lecture time: Monday 12-14 in B333 OR Wednesday 12-14 in G138, Elektrobygget. (See detailed plan below)
Qualifications: Basic knowledge of linear algebra. We will try to adjust the course to varying knowledge of quantum mechanics
Date of exam: 11.December
Type of examination: Written
Material: M. A. Nielsen og I. L. Chuang: Quantum computation and quantum information. List of errors here.
Quantum mechanical description of linear optics (Sections I, II, III, V, VI).
Content:
Introduction to quantum mechanics: Linear algebra, postulates, evolution, measurements, density operators. The Einstein-Podolsky-Rosen paradox, teleportation and Bell's inequality. Classical and quantum circuits. Quantum algorithms. Quantum information theory: Schmidt decomposition and purification, fitelity, quantum operations, entropy, Holevo’s bound. Error-correcting codes, measurements of entanglement and distillation of entanglement. Quantum cryptography. Physical realizations of quantum circuits with focus on photonic realizations.
Tentative plan:
Tuesday Aug. 25: First meeting.
Wednesday Sept. 9: Measurements, composite systems, no-cloning (Chapter 2).
Wednesday Sept. 16: Superdense coding, density operators (Chapter 2).
Wednesday Sept. 23: Density operators and partial trace, teleportation (Chapter 2).
Wednesday Sept. 30: Bell's inequality (Chapter 2), quantum circuits (Chapter 4)
Monday Oct. 5: Quantum circuits.
Wednesday Oct. 14: Quantum circuits (Chapter 4), Deutsch-Jozsa algorithm (Chapter 1).
Monday Oct. 19: Quantum operations.
Wednesday Oct. 28: Quantum operations, error-correcting codes.
Monday Nov. 2: Physical implementation of quantum computers, linear optics.
Wednesday Nov. 11: Entropy.
Monday Nov. 16: Linear optics.
Wednesday Nov. 25: Quantum key distribution.
Reading list / syllabus:
Nielsen&Chuang:
Ch. 1: 13-36
Ch. 2: 60-117
Ch. 3: 129-142
Ch. 4: 171-194
Ch. 6: 248-255
Ch. 7: 277-283, 287-297
Ch. 8: 353-366, 375-379, 383-387
Ch. 9: 399-400, 403-406, 409-410
Ch. 10: 425-434
Ch. 11: 500-508, 510-511, 513-514
Ch. 12: 532, 582-583, 586-591
Quantum mechanical description of linear optics (Sections I, II, III, V, VI).
Exercises
with solutions:
Exercise
1, Linear Algebra: 2.2, 2.5, 2.7, 2.9, 2.11, 2.17, 2.18,
2.24
Solution
1
Exercise
2, Tensor products and Trace: 2.26-2.33, 2.37-2.39
Solution
2
Exercise 3, Quantum Mechanics: 2.51-2.54, 2.57, 2.59, 2.63
and 2.66. A hint for 2.63, use singular value decomposition, p.73
inN&C
Exercise 4, Quantum Circuits: 4.1, 4.2, 4.7, 4.13,
4.16-4.18, 4.32, 4.39
Exercise 5, Grover’s Algorithm: 6.1-6.3,
6.6
Exercise 6, Quantum Computers: 7.1-7.7, 7.9
Exercise 7,
Density operators: 2.71-2.72, 2.74, 2.79, 2.82
Exercise 8, Quantum
Operations: 8.4, 8.5, 8.15, 8.18, 8.26
Exercise 9, Distance
Measures: 9.2, 9.6, 9.7, 9.14 (also prove that the Trace distance is
invariant under unitary transformations), Show that F(rho,sigma)=1
<=> rho=sigma and that F(rho,sigma)=0
<=> rho and sigma has support on orthogonal subspaces.
Exercise
10, Error correcting codes: 10.1, 10.3, 10.6
Exercise 11, Entropy:
11.1, 11.3, 11.5, 11.11, 11.12, 11.13
Old exercises with some solutions (Norwegian)
Previous exams:
Eksamen med løsning, høsten 2002
Eksamen med løsning, høsten 2003 (med noen små endringer).
Eksamen med løsning, høsten 2004
Eksamen med løsning, høsten 2005
Eksamen med løsning, høsten 2006