Quantum computing
Everyone seems to be talking about quantum computing, so this semester I might try to learn a little about it, which means you might be subjected to it too. (Mathematics overcompensates those who follows trends, so why not try to benefit.) Let me try to describe the basic mathematical ideas of how quantum computing works, why it can be good, and why it can be difficult. I'm going to focus purely on the mathematics - I won't touch on any physics or engineering aspects, which add their own layers of complexity. But there's a whole world of theoretical quantum computing out there, and it connects with braids, TQFT, and lots of other parts of mathematics! Basic idea: In classical computers, we might study a bit: it takes the value 0 or 1. In quantum computers, we consider qubits (quantum bits). These can kind of be 0 and 1 at the same time. More precisely, we think of a qubit as $z \mathbf{0} + w \mathbf{1}$ where $z, w \in \mathbb{C}$ and $|z|^2 + |w|^2 = 1$. If bot