Quantum computation is in the news; there is a lot of hype, and a long time promise of a technological revolution. But why should it interest mathematicians?
I will try to explain the subject from a mathematical perspective. In the first talk I will define the model of quantum gates and circuits,
and try to provide some insights into the source of quantum algorithmic advantage, using some examples of
quantum algorithms. I will also touch upon the remarkable flexibility of the model; it has several very different equivalent
definitions, connecting the topic for example to Markov chains, knot invariants, and more.
In the second talk, I will try to explain some more advanced topics related to quantum entanglement;
I have not yet decided exactly what those would include, but options involve some superposition of
Einstein's spooky action at a distance, quantum error correcting codes, and some hints about the remarkable recent resolution
of Connes' embedding conjecture, using ideas related to quantum entanglement.