Derivative Pricing using Quantum Signal Processing

Nikitas Stamatopoulos and William J. Zeng

Goldman Sachs, New York, NY

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Pricing financial derivatives on quantum computers typically includes quantum arithmetic components which contribute heavily to the quantum resources required by the corresponding circuits. In this manuscript, we introduce a method based on Quantum Signal Processing (QSP) to encode financial derivative payoffs directly into quantum amplitudes, alleviating the quantum circuits from the burden of costly quantum arithmetic. Compared to current state-of-the-art approaches in the literature, we find that for derivative contracts of practical interest, the application of QSP significantly reduces the required resources across all metrics considered, most notably the total number of T-gates by $\sim 16$x and the number of logical qubits by $\sim 4$x. Additionally, we estimate that the logical clock rate needed for quantum advantage is also reduced by a factor of $\sim 5$x. Overall, we find that quantum advantage will require $4.7$k logical qubits, and quantum devices that can execute $10^9$ T-gates at a rate of $45$MHz. While in this work we focus specifically on the payoff component of the derivative pricing process where the method we present is most readily applicable, similar techniques can be employed to further reduce the resources in other applications, such as state preparation.

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Cited by

[1] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, "Quantum algorithms: A survey of applications and end-to-end complexities", arXiv:2310.03011, (2023).

[2] Titos Matsakos and Stuart Nield, "Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors", Quantum 8, 1306 (2024).

[3] Travis L. Scholten, Carl J. Williams, Dustin Moody, Michele Mosca, William Hurley, William J. Zeng, Matthias Troyer, and Jay M. Gambetta, "Assessing the Benefits and Risks of Quantum Computers", arXiv:2401.16317, (2024).

[4] Guoming Wang and Angus Kan, "Option pricing under stochastic volatility on a quantum computer", arXiv:2312.15871, (2023).

[5] Nikitas Stamatopoulos, B. David Clader, Stefan Woerner, and William J. Zeng, "Quantum Risk Analysis of Financial Derivatives", arXiv:2404.10088, (2024).

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