A Threshold for Quantum Advantage in Derivative Pricing

Shouvanik Chakrabarti; Rajiv Krishnakumar; Guglielmo Mazzola; Nikitas Stamatopoulos; Stefan Woerner; William J. Zeng

doi:10.22331/q-2021-06-01-463

A Threshold for Quantum Advantage in Derivative Pricing

Shouvanik Chakrabarti^1,2, Rajiv Krishnakumar¹, Guglielmo Mazzola³, Nikitas Stamatopoulos¹, Stefan Woerner³, and William J. Zeng¹

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.

Popular summary

Derivative contracts are ubiquitous in finance with various uses from hedging risk to speculation, and currently have an estimated global gross market value in the tens of trillions of dollars. The goal of derivative pricing is to determine the value of entering a derivative contract today, given the uncertainty about future values of the underlying assets. In many cases, the pricing of derivative contracts uses Monte Carlo methods which consume significant computational resources for financial institutions and therefore, finding a quantum advantage for this application would be very valuable to the financial sector as a whole. This work gives the first detailed resource estimates of the required conditions for quantum advantage in derivative pricing. In doing so, it also introduces a new method for loading stochastic processes into a quantum computer, the re-parameterization method, which overcomes blocking challenges in previous approaches. We find that the benchmark use cases we examine require 8k logical qubits and a T-depth of 54 million and 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.

► BibTeX data

@article{Chakrabarti2021thresholdquantum,
  doi = {10.22331/q-2021-06-01-463},
  url = {https://doi.org/10.22331/q-2021-06-01-463},
  title = {A {T}hreshold for {Q}uantum {A}dvantage in {D}erivative {P}ricing},
  author = {Chakrabarti, Shouvanik and Krishnakumar, Rajiv and Mazzola, Guglielmo and Stamatopoulos, Nikitas and Woerner, Stefan and Zeng, William J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {463},
  month = jun,
  year = {2021}
}

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A Threshold for Quantum Advantage in Derivative Pricing

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