  We put forward the idea that classical blockchains and smart contracts are
potentially useful primitives not only for classical cryptography, but for
quantum cryptography as well. Abstractly, a smart contract is a functionality
that allows parties to deposit funds, and release them upon fulfillment of
algorithmically checkable conditions, and can thus be employed as a formal tool
to enforce monetary incentives.
  In this work, we give the first example of the use of smart contracts in a
quantum setting. We describe a simple hybrid classical-quantum payment system
whose main ingredients are a classical blockchain capable of handling stateful
smart contracts, and quantum lightning, a strengthening of public-key quantum
money introduced by Zhandry (Eurocrypt'19). Our hybrid payment system employs
quantum states as banknotes and a classical blockchain to settle disputes and
to keep track of the valid serial numbers. It has several desirable properties:
it is decentralized, requiring no trust in any single entity; payments are as
quick as quantum communication, regardless of the total number of users; when a
quantum banknote is damaged or lost, the rightful owner can recover the lost
value.
