Introduction to Quantum Computing

Course manual 2019/2020

Course content

The goal of this course is to introduce students to the quantum model of computation and some of the most important quantum algorithms and quantum information processing protocols.

1. Bits and qubits. Deterministic and probabilistic bits. Complex numbers, quantum bits, and the Bloch sphere. Quantum measurements, global and relative phases.
2. Linear algebra. Review of linear algebra: vectors and matrices, inner product and matrix multiplication, Dirac bra-ket notation, eigenvalues and eigenvectors, unitary matrices, tensor product.
3. Quantum mechanics. Postulates of quantum mechanics: quantum states, their evolution and measurement, product and entangled states.
4. Quantum computation. The model of quantum computation. Quantum gates and circuits. Deutsch’s algorithm.
5. Elementary quantum algorithms. Quantum oracles, phase kick-back. Deutsch's algorithm. Quantum programming with Cirq.
6. Algorithms based on the Hadamard transform. Deutsch-Jozsa, Bernstein-Vazirani, Simon's algorithms.
7. Quantum information. Basic protocols: quantum key distribution, superdense coding, quantum teleportation, entanglement swapping.
8. Quantum non-locality and entanglement. Bell's inequality, non-local games.
9. Quantum search. Grover’s search algorithm: reflections, Grover rotation, geometric analysis of the algorithm.
10. Quantum Fourier transform and phase estimation. Fourier transform, its implementation, application to phase estimation.
11. Order finding and factoring. Shor’s algorithm for factoring: order finding and factoring.
12. Mixed states, quantum operations, graphical notation. Mixed states, superoperators, tensor networks.
13. Quantum error correction. Stabilizer formalism, basic quantum error correcting codes.
14. Classical and quantum complexity. Turing machine, basic classical and quantum complexity classes and their relationships.

Study materials

Literature

• Kaye P., Laflamme R., Mosca M. (2007). An Introduction to Quantum Computing. Oxford University Press.

• Mermin N.D. (2007). Quantum Computer Science: An Introduction. Cambridge University Press.

• Lipton R.J., Regan K.W. (2014). Quantum Algorithms via Linear Algebra: A Primer. MIT Press.

• Nielsen M.A., Chuang I.L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.

Syllabus

• Lecture notes on Canvas

Software

• Cirq

Objectives

• Students should be able to describe the mathematical model of quantum computers
• Students should be able to compare it to probabilistic and deterministic classical computers
• Students should be able to state basic quantum algorithms
• Students should be able to analyze them step by step
• Students should be able to manipulate quantum states and quantum gates
• Students should be able to create a program in Cirq that implements a given quantum algorithm
• Students should be able to state basic quantum information protocols
• Students should be able to analyze them step by step
• Students should be able to explain the tasks they achieve
• Students should be able to explain classical correlations and quantum entanglement
• Students should be able to explain the advantage of entanglement over classical correlations
• Students should be able to explain the power and limitations of quantum computers

Teaching methods

• Lecture
• Computer lab session/practical training
• Self-study

New material will be introduced to the students during the lectures. They will deepen their understanding during the exercises classes by solving problems with the help of teaching assistants, and by independently solving the homework problems afterwards.

Learning activities

Attendance

Programme's requirements concerning attendance (OER-B):

• Each student is expected to actively participate in the course for which he/she is registered.
• If a student can not be present due to personal circumstances with a compulsory part of the programme, he / she must report this as quickly as possible in writing to the relevant lecturer and study advisor.
• It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are stated in advance in the course manual and on Canvas.
• In the first and second year, a student should be present in at least 80% of the seminars and tutor groups. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. In case of personal circumstances, as described in OER-A Article A-6.4, an other arrangement will be proposed in consultation with the study advisor.

Assessment

To pass the course, the exam grade has to be at least 5.

Inspection of assessed work

Via Canvas.

Assignments

There will be 3 assignments (one every two weeks) that are graded and contribute towards the final grade. Every week there will be a quiz on Canvas that is graded automatically and also contributes towards the final grade.

Exercises done during the exercise classes will not be graded.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• dr. M. Ozols

Teaching assistants:

• Arjan Cornelissen (arjan@cwi.nl)
• Subhasree Patro (subhasree.patro@cwi.nl)
• Emiel Koridon (emiel.koridon@student.uva.nl)