  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
2019]. Our hybrid payment system uses 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.
