Description
In every day life we experience the determinism of the classical world. If you flip a coin the result may be unknown to you but it will be completely deterministic, either head or tail, i.e. the state of this system will take one of two values. A quantum mechanical coin is way more complicated! If you had a quantum coin in your pocket you would discover that its state is not necessarily head or tail, it can actually be described geometrically by a two-dimensional sphere called the Bloch sphere. Same thing with dead/alive cats and boxes! The geometry of quantum states is one of the properties that makes them so interesting and so much more complex than classical, deterministic mechanics. When you put many quantum coins together you start encountering even more surprising phenomena, one example above them all: quantum entanglement, or how Einstein defined it: "a spooky action at a distance". With a bunch of quantum coins you can also assemble a quantum computer. Although it seems that we are just sticking the word "quantum" in front of everything, quantum computers have actually been constructed in the real world and they can achieve otherwise classically (i.e. your pc) impossible (at least with running time < universe life) tasks. In this project we want to discuss various mathematical properties of quantum systems: their geometrical description, the information they contain, how they can be used to construct new and powerful algorithms. Between the possible topics:
Pre-requisites2H Mathematical Physics or equivalently Theoretical Physics II. (Lagrangian formulation and intro to Quantum mechanics) Useful but not mandatory Co-requisites3H Quantum Mechanics or equivalently Foundations of Physics 2A. 3H Quantum Computing. ResourcesFor some background:
Reading material.
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