Projects in Previous Years

1st Semester 2015/16: Quantum Logic

Soroush Rafiee Rad
If you are interested in this project, please contact the instructor by email.
This project aims to introduce logics for reasoning about quantum theory and quantum computation. Quantum logic was started by Birkoff and von Neumann for studying the relation among physical observables in quantum physics. From the early experiments in quantum physics it became clear that the result from measurements of certain physical observables were inconsistent with classical logics. The goal of quantum logic is to formalise the reasoning about these physical observables.

The language of this logic is the same as propositional logic, with a different semantics. This logic was later extended to also include the dynamics of quantum systems under actions such as measurements and later to include probabilities. We will study some probabilistic extensions as well as the dynamic logic approach. We will study how to reason about compound systems and entangled states and how these concepts are employed in quantum computation. We will, in particular, study in details certain protocols such as quantum key distribution and quantum teleportation. We shall also point to the recent developments in areas such as game theory, decision theory and epistemology and dynamics of belief that make use of concepts from quantum theory.

The course will be a mixture of lectures and group discussion and the meetings will take place 3 times a week.
Familiarity with propositional logic will be assumed. The course will be mostly self contained and in particular knowledge of quantum physics or quantum computation is not necessary. Familiarity with Hilbert Spaces and Linear Algebra will be helpful.
Assessment is on the basis of homework, a final report and class discussions.