A Threshold for Quantum Advantage in Derivative Pricing

TL;DR

This paper establishes an upper bound on the quantum resources needed for advantage in derivative pricing, introduces a new re-parameterization method to reduce resource demands, and provides detailed estimates for practical quantum advantage scenarios.

Contribution

It presents the first complete resource estimates for quantum derivative pricing and introduces a novel re-parameterization approach to overcome existing challenges.

Findings

Benchmark derivatives require 8,000 logical qubits and a T-depth of 54 million.

Quantum advantage in derivative pricing estimated to be achievable within about one second.

Current quantum systems are far from meeting these resource requirements.

Abstract

We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing - the re-parameterization method - that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 8k logical qubits and a T-depth of 54 million. We estimate that quantum advantage would require executing this program at the order of a second. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.