Quantum money is the idea of using quantum states as currency. The first proposal for a quantum money scheme was developed by Wiesner and in that scheme the quantum states used as bills are unforgeable due to the no-cloning theorem. However, Wiesner's scheme requires communication with the bank each time a bill is spent.
In this talk I will discuss a quantum money scheme where bills can be spent without communicating with the bank (a public key quantum money scheme). Our scheme uses the mathematical theory of knots. This talk is based on joint work with Edward Farhi, Avinatan Hassidim, Andrew Lutomirski, and Peter Shor.