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:

- 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

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

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.

Due date : Thursday April 21st, 1:35pm

Lectures April 26th & 28th:

- Entropy and Information

Reading: Nielsen Chuang
Chapters 11 pp. 500-527

Final Exam: first week of May

- 3 hours, on all Chapters treated during the course.