Presented by Edward Farhi. Money, either in the form of bills or information on a computer, should be impossible to copy and also verifiable as good money when tendered to a merchant. Quantum mechanics may make this possible to achieve with far greater security than can be achieved without quantum mechanics. Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint without sending the money back to the mint. I will present a concrete quantum money scheme based on quantum superpositions of diagrams that encode knots. This scheme is hopefully secure against computationally bounded adversaries. This may be the basis of E-commerce on a future quantum internet which would not require communication with a central server such as the credit card company, PayPal or Google Checkout.