4803-Homework (Spring 2005)

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Calendar (to be updated periodically)

Lectures January 11th & 13th:
   - An introduction: various concepts of information, classical and quantum coding,
      Reading: Shannon and his contribution
    - Overview on Quantum computing Reading: Preskill Chapter 1
    - Notion of qubits, mathematical formalism: Hilbert spaces, states and operators,
      Reading: Nielsen Chuang Chapter 2.1 pp 61-79

Homework 1 (not graded): Nielsen Chuang, All exercises of Chapter 2.1,
Due date : Thursday January 20th, 1:35pm

Lectures January 18th & 20th:
   - 1-qubit, Pauli matrices, density matrices, Bloch sphere
    - N-qubit representation and tensor product, tensor product of 1-qubit states
    - Quantum gates: 1-qubit gates, the CNOT-gate, other gates.
      Reading: Nielsen Chuang Chapter 4.1-4.4 pp 171-188

Homework 2 (graded) : Nielsen Chuang, Chapter 4.2&4.3 exercises 4.5, 4.7, 4.9, 4.13, 4.14, 4.18, 4.19, 4.21, 4.24
Due date : Thursday January 27th, 1:35pm

Lectures January 25th & 27th:

    - Teleportation
   - Postulate of Quantum Mechanics (without Quantum Measurement Theory)
    - Density matrix (without partial trace)
    - The Bell inequalities
      Reading: Nielsen Chuang Chapter 2.2-2.6 (except 2.2.3-2.2.6 and 2.4.3) pp 78-111

Homework 3 (not graded) : Nielsen Chuang, As many exercises of Chapters 2.2.2, 2.2.3,2.2.7, 2.3, 2.4.2 as possible
Due date : Thursday February 3rd, 1:35pm

Lectures February 1st & 3rd:
   - Universality of quantum gates
    - Quantum circuits,
    - Quantum simulations
      Reading: Nielsen Chuang Chapter 4 pp 188-211

Homework 4 (graded) : Nielsen Chuang, Chapter 4.4-4.7 exercises 4.36, 4.37, 4.39, 4.41, 4.42, 4.43, 4.44, 4.47, 4.49
Due date : Thursday February 10th, 1:35pm

Lectures February 8th & 10th:
   - Algorithms: the quantum Fourier transform; phase estimation.
      Reading: Nielsen Chuang Chapter 5 pp 216-242

Homework 5 (not graded): Nielsen Chuang, All exercises of Chapter 5.1 & 5.2
Due date : Thursday February 17th, 1:35pm

Lectures February 15th & 17th:
   - Algorithms: phase estimation and performances, order finding. Factoring: elements of arithmetic
      Reading: prime factor decomposition (pdf) (ps) problem, correction and appendix

Homework 6 (graded): Fast Fourier Transform (pdf) (ps)
Due date : Thursday February 24th, 1:35pm

Lectures February 22nd & 24th:
   - Algorithms: factoring, arithmetic and quantum algorithm for prime number decomposition.
      Reading: Nielsen Chuang Chapter 5 pp 216-242

Homework 7 (not graded): Nielsen Chuang, All exercises of Chapter 5.3
Due date : Thursday March 3rd, 1:35pm

Lectures March 1st & 3rd:
   - Quantum operations: (i) Introduction: noise, measurement, dissipation, loss of information.
       (ii) Axiomatic approach
      Reading: Nielsen Chuang Chapter 8.1 & 8.2 pp 353-373

Homework 8 (graded): (i) Nielsen Chuang, Exercises 5.20, 5.21, 5.22, 5.23, and
                                    (ii) continued fraction expansion (pdf) (ps) exercises 1 to 5
Due date : Thursday March 10th, 1:35pm

Lectures March 8th & 10th:
   - Quantum operations: (iii) examples, (iii) applications: Master equation, wave packet reduction
      Reading: Nielsen Chuang Chapter 8.3 & 8.4 pp 373-398
Progress report: due on March 8th, .pdf file by e-mail to the instructor.

Homework 9 (not graded): Nielsen Chuang, All exercises Chap 8.1 & 8.2 pp. 353-373.
Due date : Thursday March 17th, 1:35pm

Lectures March 15th & 17th:
   - Physical Realization of Quantum Computers (the lectures will be delivered by a physicist)
      Reading: Nielsen Chuang Chapter 7.5 & 7.6 pp 297-324

Homework 10 (graded): Nielsen Chuang, Exercises: 8.5, 8.6, 8.20, 8.22, 8.26, 8.29, 8.35 Problems: 8.1, 8.2,
Due date : Thursday March 24th, 1:35pm

March 22th & 24th: Spring break

Lectures March 29th & 31st:
   - (i) definition of the von Neumann entropy, wave packet reduction, random evolutions
     (ii) Distances, Fidelity
     Reading: Nielsen Chuang Chapters 11.3 pp. 510-519 & 9 pp 399-424

Homework 11 (graded): Nielsen Chuang, Exercises: 9.8, 9.10, 9.12, 9.13, 9.15, 9.19, 9.21, 9.22,
Due date : Thursday April 7th, 1:35pm

Lectures April 5th & 7th:
- Quantum coding and error corrections: the Shor code, theory
Reading: Nielsen Chuang Chapters 10.1-10.3 pp. 425-445

Homework 12 (not graded): Nielsen Chuang, Exercises of Chapters 10.1-10.3
Due date : Thursday April 14th, 1:35pm

Lectures April 12th & 14th:
- Quantum coding and error corrections: construction of codes, CSS codes
Reading: Nielsen Chuang Chapters 10.4-10.5 pp. 445-474

Homework 13 (graded): Nielsen Chuang, Exercises 10.14, 10.19, 10.25, 10.27, 10.28, 10.47, 10.48
Due date : Thursday April 21st, 1:35pm

Lectures April 19th & 21st:
- Quantum coding and error corrections: fault-tolerant codes, topological codes
Reading: Nielsen Chuang Chapters 10.6 pp. 474- 499
Final report: due on March 21st, .pdf file by e-mail to the instructor.

Homework 14 (not graded): Nielsen Chuang, Exercises Chapter 10.5 & 10.6
Due date : Thursday April 21st, 1:35pm

Lectures April 26th & 28th:
- Entropy and Information
Reading: Nielsen Chuang Chapters 11 pp. 500-527

Homework: no homework this week

Final Exam: first week of May
- 3 hours, on all Chapters treated during the course.