Introduction to quantum computation
Summary
The course introduces the paradigm of quantum computation in an axiomatic way. We introduce the notion of quantum bit, gates, circuits and we treat the most important quantum algorithms. We also touch upon error correcting codes. This course is independent of COM-309.
Content
Introduction to quantum computation
- Classical circuit model, reversible computation.
- Quantum bits, Hilbert space of N qubits, unitary transformations, measurement postulate.
- Quantum circuit model, universal sets of gates.
- Deutsch and Josza's problem and algorithm.
Basic algorithms
- Hidden sub-group problem and Simon's algorithm
- Mathematical parenthesis: factoring integers and period of arithmetic functions. Notions on continued fraction expansions.
- Quantum Fourier transform and the period finding algorithm
- Shor's factoring algorithm.
- Grover's search algorithm.
Error correcting codes
- Models of noise and errors.
- Shor and Steane error correcting codes.
- Stabilizer codes.
- Calderbank-Shor-Steane construction.
Keywords
Quantum computation, quantum circuits, universal gates, quantum Fourier transform, Deutsch-Josza's algorithm. Simon algorithm, Shor's algorithm, Grover's algorithm, entanglement, quantum error correction.
Learning Prerequisites
Required courses
Linear algebra course, basic probability course
Important concepts to start the course
Matrices, unitary matrices, eigenvectors, eigenvalues, inner product, algebra of complex numbers
Learning Outcomes
By the end of the course, the student must be able to:
- Explain the concept of quantum algorithm on the circuit model
- Describe universal gates
- Describe basic quantum algorithms
- Compute the evolution of a state through a circuit
- Apply the measurement postulate
- Manipulate algebraic expressions involving the Dirac notation
- Carry out implementation on public NISQ devices
- Give an example of an error correcting code
Teaching methods
Ex cathedra classes. Exercices. Use of IBM Q NISQ devices
Expected student activities
Participation in class, exercise sessions, use of IBM Q NISQ devices
Assessment methods
- Mini project on IBM Q experience
- Graded homeworks
- Written final exam
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
| Others | Assistants answer questions during exercise sessions |
Resources
Bibliography
N. David Mermin. Quantum Computer Science. An Introduction. Cambridge University Press.
Nielsen and Chuang. Quantum Computation and Information. Cambridge University Press.
Ressources en bibliothèque
Moodle Link
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Introduction to quantum computation
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Introduction to quantum computation
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Introduction to quantum computation
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Introduction to quantum computation
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Introduction to quantum computation
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel