Option Pricing using Quantum Computers

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.

Fixed a typo. This article has been accepted in Quantum

References in corpus (27)

• Quantum Machine Learning
• Elementary gates for quantum computation
• Quantum algorithm for solving linear systems of equations
• Surface codes: Towards practical large-scale quantum computation
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Quantum Amplitude Amplification and Estimation
• Quantum principal component analysis
• Error mitigation for short-depth quantum circuits
• Quantum Algorithms Revisited
• Extending the computational reach of a noisy superconducting quantum processor
• Quantum Networks for Elementary Arithmetic Operations
• Synthesis of Quantum Logic Circuits
• Quantum computing for finance: overview and prospects
• Quantum optimization using variational algorithms on near-term quantum devices
• Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
• Cloud Quantum Computing of an Atomic Nucleus
• Quantum-state preparation with universal gate decompositions
• Quantum speedup of Monte Carlo methods
• Quantum Risk Analysis
• Quantum computational finance: Monte Carlo pricing of financial derivatives
• Amplitude estimation without phase estimation
• Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark
• Gate-efficient simulation of molecular eigenstates on a quantum computer
• Characterization of a two-transmon processor with individual single-shot qubit readout
• How many CNOT gates does it take to generate a three-qubit state ?
• Iterative phase estimation

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