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Quantum unary approach to option pricing

Sergi Ramos-Calderer, Adrián Pérez-Salinas, Diego García-Martín, Carlos Bravo-Prieto, Jorge Cortada, Jordi Planagumà, and José I. Latorre
Phys. Rev. A 103, 032414 – Published 15 March 2021

Abstract

We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude distribution corresponding to the asset value at maturity is generated using a low-depth circuit; second, the computation of the expected return is computed with simple controlled gates; and third, standard amplitude estimation is used to gain quantum advantage. On the positive side, unary representation remarkably simplifies the structure and depth of the quantum circuit. Amplitude distributions use quantum superposition to bypass the role of classical Monte Carlo simulation. The unary representation also provides a postselection consistency check that allows for a substantial mitigation in the error of the computation. On the negative side, unary representation requires linearly many qubits to represent a target probability distribution, as compared to the logarithmic scaling of binary algorithms. We compare the performance of both unary vs binary option pricing algorithms using error maps, and find that unary representation may bring a relevant advantage in practice for near-term devices.

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  • Received 24 September 2020
  • Accepted 18 February 2021

DOI:https://doi.org/10.1103/PhysRevA.103.032414

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Sergi Ramos-Calderer1,2,*, Adrián Pérez-Salinas1,3, Diego García-Martín1,3,4, Carlos Bravo-Prieto1,3, Jorge Cortada5, Jordi Planagumà5, and José I. Latorre1,2,6

  • 1Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
  • 2Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
  • 3Barcelona Supercomputing Center (BSC), 08034 Barcelona, Spain
  • 4Instituto de Física Teórica, UAM-CSIC, Madrid, Spain
  • 5Caixabank, Barcelona, Spain
  • 6Center for Quantum Technologies, National University of Singapore, Singapore

  • *sergi.ramos@tii.ae

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Issue

Vol. 103, Iss. 3 — March 2021

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