Quantum Technology for Economists

Abstract

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.

Dynamic Programming on a Quantum Annealer: Solving the RBC Model

“…Subsection 5.2 proposes a new quantum-classical hybrid algorithm, Algorithm 3, where we run one part of the PPI on a classical computer and the rest on a QA. Using these hybrid algorithms has become popular in the literature (Hull et al, 2020).…”

“…UQCs offer theoretical reductions in time and space complexity for various algorithms used in computational economics and econometrics (Hull et al, 2020). For instance, Ambainis et al (2019) and Glos et al (2021) prove theoretical quantum speed-ups for several classes of dynamic programming problem, including the traveling salesperson and vertex ordering problems.…”