Quantum finance

Quantum finance is an interdisciplinary research field, applying theories and methods developed by quantum physicists and economists in order to solve problems in finance. It is a branch of econophysics. Finance theory is heavily based on financial instrument pricing such as stock option pricing. Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as computational finance. Many computational finance problems have a high degree of computational complexity and are slow to converge to a solution on classical computers. In particular, when it comes to option pricing, there is additional complexity resulting from the need to respond to quickly changing markets. For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change in the almost continuously changing stock market. As a result, the finance community is always looking for ways to overcome the resulting performance issues that arise when pricing options. This has led to research that applies alternative computing techniques to finance. One of these alternatives is quantum computing. Just as physics models have evolved from classical to quantum, so has computing. Quantum computers have been shown to outperform classical computers when it comes to simulating quantum mechanics as well as for several other algorithms such as Shor's algorithm for factorization and Grover's algorithm for quantum search, making them an attractive area to research for solving computational finance problems. Most quantum option pricing research typically focuses on the quantization of the classical Black–Scholes–Merton equation from the perspective of continuous equations like the Schrödinger equation. Haven builds on the work of Chen and others, but considers the market from the perspective of the Schrödinger equation.