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A Threshold for Quantum Advantage in Derivative Pricing

Author

Listed:
  • Shouvanik Chakrabarti
  • Rajiv Krishnakumar
  • Guglielmo Mazzola
  • Nikitas Stamatopoulos
  • Stefan Woerner
  • William J. Zeng

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.

Suggested Citation

  • Shouvanik Chakrabarti & Rajiv Krishnakumar & Guglielmo Mazzola & Nikitas Stamatopoulos & Stefan Woerner & William J. Zeng, 2020. "A Threshold for Quantum Advantage in Derivative Pricing," Papers 2012.03819, arXiv.org, revised May 2021.
    • Handle: RePEc:arx:papers:2012.03819
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    Cited by:

    1. Mark-Oliver Wolf & Tom Ewen & Ivica Turkalj, 2023. "Quantum Architecture Search for Quantum Monte Carlo Integration via Conditional Parameterized Circuits with Application to Finance," Papers 2304.08793, arXiv.org, revised Sep 2023.
    2. Jo~ao F. Doriguello & Alessandro Luongo & Jinge Bao & Patrick Rebentrost & Miklos Santha, 2021. "Quantum algorithm for stochastic optimal stopping problems with applications in finance," Papers 2111.15332, arXiv.org, revised Jul 2023.
    3. Abha Naik & Esra Yeniaras & Gerhard Hellstern & Grishma Prasad & Sanjay Kumar Lalta Prasad Vishwakarma, 2023. "From Portfolio Optimization to Quantum Blockchain and Security: A Systematic Review of Quantum Computing in Finance," Papers 2307.01155, arXiv.org.
    4. Roman Rietsche & Christian Dremel & Samuel Bosch & Léa Steinacker & Miriam Meckel & Jan-Marco Leimeister, 2022. "Quantum computing," Electronic Markets, Springer;IIM University of St. Gallen, vol. 32(4), pages 2525-2536, December.
    5. Skavysh, Vladimir & Priazhkina, Sofia & Guala, Diego & Bromley, Thomas R., 2023. "Quantum monte carlo for economics: Stress testing and macroeconomic deep learning," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    6. Francesca Cibrario & Or Samimi Golan & Giacomo Ranieri & Emanuele Dri & Mattia Ippoliti & Ron Cohen & Christian Mattia & Bartolomeo Montrucchio & Amir Naveh & Davide Corbelletto, 2024. "Quantum Amplitude Loading for Rainbow Options Pricing," Papers 2402.05574, arXiv.org, revised Feb 2024.
    7. Yen-Jui Chang & Wei-Ting Wang & Hao-Yuan Chen & Shih-Wei Liao & Ching-Ray Chang, 2023. "Preparing random state for quantum financing with quantum walks," Papers 2302.12500, arXiv.org, revised Mar 2023.
    8. Yen-Jui Chang & Wei-Ting Wang & Hao-Yuan Chen & Shih-Wei Liao & Ching-Ray Chang, 2023. "A novel approach for quantum financial simulation and quantum state preparation," Papers 2308.01844, arXiv.org.
    9. Dylan Herman & Cody Googin & Xiaoyuan Liu & Alexey Galda & Ilya Safro & Yue Sun & Marco Pistoia & Yuri Alexeev, 2022. "A Survey of Quantum Computing for Finance," Papers 2201.02773, arXiv.org, revised Jun 2022.
    10. Koichi Miyamoto & Kenji Kubo, 2021. "Pricing multi-asset derivatives by finite difference method on a quantum computer," Papers 2109.12896, arXiv.org.
    11. Yongming Li & Ariel Neufeld, 2023. "Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its proof of overcoming the curse of dimensionality," Papers 2301.09241, arXiv.org, revised Mar 2023.
    12. Vladimir Skavysh & Sofia Priazhkina & Diego Guala & Thomas Bromley, 2022. "Quantum Monte Carlo for Economics: Stress Testing and Macroeconomic Deep Learning," Staff Working Papers 22-29, Bank of Canada.

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