Research on quantum technology spans multiple disciplines: physics, computer
science, engineering, and mathematics. The objective of this manuscript is to
provide an accessible introduction to this emerging field for economists that
is centered around quantum computing and quantum money. We proceed in three
steps. First, we discuss basic concepts in quantum computing and quantum
communication, assuming knowledge of linear algebra and statistics, but not of
computer science or physics. This covers fundamental topics, such as qubits,
superposition, entanglement, quantum circuits, oracles, and the no-cloning
theorem. Second, we provide an overview of quantum money, an early invention of
the quantum communication literature that has recently been partially
implemented in an experimental setting. One form of quantum money offers the
privacy and anonymity of physical cash, the option to transact without the
involvement of a third party, and the efficiency and convenience of a debit
card payment. Such features cannot be achieved in combination with any other
form of money. Finally, we review all existing quantum speedups that have been
identified for algorithms used to solve and estimate economic models. This
includes function approximation, linear systems analysis, Monte Carlo
simulation, matrix inversion, principal component analysis, linear regression,
interpolation, numerical differentiation, and true random number generation. We
also discuss the difficulty of achieving quantum speedups and comment on common
misconceptions about what is achievable with quantum computing.

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