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A Geometric Logic for Classical and Quantum Computation

### Jamie Vicary

I will describe a new kind of 2-dimensional type theory, with a
geometrical syntax built from points, lines and surfaces. This allow
computational tasks, such as encryption and decryption, to be
represented as equations between topological structures, with a
classical semantics giving back the standard notion of one-time-pad
encrypted communication. Under an alternative quantum semantics, the
same syntax gives rise to quantum teleportation, giving a strong new
mathematical connection between classical and quantum computing.

Everything will be presented in a straightforward way, with lots of
pictures. No knowledge of quantum computing is necessary to understand
this talk!