MAT-2400 Introduction to Quantum Computing - 10 stp

Quantum computing is a new and exciting, interdisciplinary field linking mathematics, physics, and computer science. It is based on a radically different computational paradigm, offering the possibility of solving certain problems that are exponentially hard for current conventional computers. For example, many existing security protocols rely on the difficulty of large number factorization, but Shor's quantum algorithm is able to do this quickly (in polynomial time). This technology is rapidly developing, with currently a number of industry players and governments around the world that are investing significantly in research and development, and the race for quantum supremacy. This course is intended to introduce students to quantum computing and give a solid foundation for future study in this emergent 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, discrete logarithm problem, Shor’s factoring algorithm

MAT-1004 Lineær algebra or MAT-1020 Lineær algebra

Application code 9336.

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.