# Option Pricing using Quantum Computers

## TL;DR

This paper introduces a quantum computing approach for option pricing that leverages amplitude estimation for quadratic speedup, covering various option types and demonstrating implementation on real quantum hardware.

## Contribution

It develops quantum circuits for option pricing using amplitude estimation and evaluates their performance on IBM's quantum hardware with error mitigation.

## Key findings

- Quantum circuits successfully price different options.
- Amplitude estimation provides quadratic speedup over classical methods.
- Error mitigation improves results on noisy hardware.

## Abstract

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.