# Applications of Quantum Computing to Economics

I have recently been interested in the field of 'Econophysics' which as I understand it is the practice of basically applying results of physics in areas such as non-linear dynamics and stochastic physics to already known facts of economics (i.e. it is not a field of new discoveries but just a different perspective on economics).

I am also a lover of all things Quantum.

I was wondering if there have been any attempts to use QC to simulate economic models, which tend to be really difficult on classical computers. The field of "Quantum Finance" (how much more buzzword-y can a field get...), is able to describe many phenomena in finance and monetary supply management using quantum concepts like Hilbert Spaces and state collapses (this has nothing to do with quantum mechanics, it just uses the same formalism). Maybe in the same way that Hamiltonian simulation can be done easily on a quantum computer, because it just naturally lends itself to the medium, these Quantum Finance models can also be done easily?

## 1 Answer

There is a lot of proposition how to use quantum computers in finance, see this question.

Your are right that you can simulate Hamiltonians on a quantum computer easier than on classical computer. However, in some cases it is difficult to construct respective quantum circuit. On the other hand, circuits for so-called Ising Hamiltonians used for solution of quadratic binary problems can be easily prepared. See for example this article: Ising formulations of many NP problems. As you can see in the article, for example Travelling salesman problem can be described by Ising Hamiltonian. Since many task from economics and finance can be converted to TSP (e.g. currency arbitrage or production schedulling), you can see possibilities of Ising Hamiltonians simulation on QC for business applications.

Generally speaking, if you are able to prepare a quantum circuit for a Hamitonian describing some economic problem efficiently, you receive an advantage in the simulation performance in comparison with classical computers.

Just one note, Hilbert space is not quantum concept, but rather mathematical one as Hilbert spaces are used also outside quantum mechanics.

• Thanks! ~ you are totally right, i should have said 'A Mathematical Framework Adjacent to Quantum Mechanics' Jan 22, 2021 at 19:12