A Threshold for Quantum Advantage in Derivative Pricing
1Goldman, Sachs & Co., New York, NY
2University of Maryland, College Park, MD
3IBM Quantum, IBM Research – Zurich
Published: | 2021-06-01, volume 5, page 463 |
Eprint: | arXiv:2012.03819v3 |
Doi: | https://doi.org/10.22331/q-2021-06-01-463 |
Citation: | Quantum 5, 463 (2021). |
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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 $\textit{re-parameterization method}$ – 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.

Featured image: Loading the probability distribution for derivative pricing with the re-parameterization method takes variationally-trained standard normal gaussians and distributes the probability mass appropriately by re-parameterizing the basis states corresponding to asset prices.
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