Introduction to Quantum Computing

The course can be taken as a singular course.

Quantum computing is an interdisciplinary field at the intersection of mathematics, physics, and computer science.  It is based on a fundamentally different computational paradigm, offering the potential of solving certain problems dramatically faster than is possible on conventional computers.  For example, many modern cryptographic protocols rely on the presumed difficulty of large number factorization, but Shor's quantum algorithm can perform this task in polynomial time on a sufficiently large fault-tolerant quantum computer.  This technology is rapidly developing, with governments and industry investing significantly in research and development of quantum technologies and the pursuit of quantum advantage. This course introduces the mathematical foundations of quantum computing and gives a solid basis for future study in this field.

Though beneficial for broader context, prior courses in quantum mechanics and computer science / programming are not required to take this course. The main prerequisities are trigonometry, complex numbers, a Linear Algebra course, willingness to work through mathematical formalism, and a good amount of curiosity.Topics covered in this course:

• Quantum interference, superposition, qubits, the Bloch sphere
• Hilbert spaces, Dirac bra-ket notation, unitary and Hermitian operators, spectral theorem, projectors
• Pauli matrices, SU(2), SO(3)
• Multiple-qubit systems, tensor products, entanglement
• Observables and measurement
• Quantum gates (e.g. Hadamard, C-NOT, bit-flip, phase-flip), circuits, reversible implementations of classical circuits and quantum implementations
• Dense coding, quantum key distribution for secure cryptographic communication
• EPR paradox and Bell’s theorem
• No-cloning principle, quantum teleportation
• Simple quantum algorithms, e.g. Deutsch-Jozsa, Bernstein-Vazirani
• Grover’s search algorithm and amplitude amplification
• Quantum Fourier transform
• Shor’s factoring algorithm, discrete logarithm problem
• Introduction to quantum error correction

Generell studiekompetanse og følgende spesielle opptakskrav: Matematikk R1 og i tillegg enten:

• Matematikk R2

• Fysikk 1 + 2 eller

• Kjemi 1+ 2 eller

• Biologi 1 + 2 eller

• Informasjonsteknologi 1 +2 eller

• Geofag 1 + 2 eller

• Teknologi og forskningslære 1 + 2

Recommended prerequisite for incoming exchange students is MAT-1020 Linear algebra or equal .

Application code is 9197.

After the course, the student has acquired the following:

Knowledge

• Detailed knowledge of abstract linear algebra and how it defines the formal structure underlying quantum computing - in particular, for foundational notions such as qubits and quantum gates.
• Understanding of tensor products and the unique quantum concept of entanglement, and how entanglement gives rise to the Bell inequality.
• Be familiar with some quantum algorithms such as Shor’s quantum algorithm for factorization and Grover’s quantum search algorithm.

Skills

• Having sufficient insight into abstract linear algebra to be able to apply this language to formulate and solve problems.
• Ability to construct and run simple quantum algorithms on a quantum computer simulator.

General competence

• Understand how quantum computers differ from classical computers, and how they do not.
• Be able to communicate how quantum computation is potentially much faster than classical computation for certain types of problems.

Anbefalte forkunnskaper

MAT-1004 Linear algebra, MAT-1020 Linear algebra

Language of instruction and examination

Schedule

This course is open to incoming exchange students.

Study Level: Bachelor's

Admission prerequisites: To take this course, you must first meet the requirements listed in the "Admission requirements" section above.

For details on how to apply for exchange, course selection guidelines, or to contact the Incoming Admissions Team, please visit: Admission for Student Exchange.

More info about the coursework requirements

The following work requirements must all be evaluated as approved to take the final exam:

• One in-class midterm test will take place physically at the university.

• Obligatory assignments for hand-in.

• Attendance and participation at tutorial seminars supporting the obligatory assignments.

Precise approval requirements will be discussed at the start of the semester.