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We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods.
1901
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1904
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1904
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1973
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A. Yu. Kitaev, “Quantum measurements and the Abelian Stabilizer Problem,” (1995), arXiv:quant-ph/9511026
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Paul Glasserman, Philip Heidelberger, and Perwez Shahabuddin, “Efficient Monte Carlo Methods for Value-at-Risk,” in Mastering Risk , Vol. 2 (2000) pp. 5–18
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Thomas G Draper, “Addition on a Quantum Computer,” (2000), arXiv:quant-ph/0008033
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Ghasem Tarmast, “Multivariate Log-Normal Distribution,” International Statistical Institute Proceedings: 53rd Session, Seoul (2001)
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Gilles Brassard, Peter Hoyer, Michele Mosca, and Alain Tapp, “Quantum Amplitude Amplification and Estimation,” Contemporary Mathematics 305
2002
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Lov Grover and Terry Rudolph, “Creating superpositions that correspond to efficiently integrable probability distributions,” (2002), arXiv:quant-ph/0208112
2002
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Paul Glasserman, Monte Carlo Methods in Financial Engineering (Springer-Verlag New York, 2003) p. 596
2003
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John C. Hull, Options, futures, and other derivatives , 6th ed. (Pearson Prentice Hall, Upper Saddle River, NJ [u.a.], 2006)
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Pavel V. Shevchenko and Pierre Del Moral, “Valuation of barrier options using sequential monte carlo,” Journal of Computational Finance 20
2014
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2014
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Ashley Montanaro, “Quantum speedup of monte carlo methods,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 471
2015
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Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature 549
2017
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Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning,” Nature 549
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Thomas G Draper, Samuel A Kutin, Eric M Rains, and Krysta M Svore, “A logarithmic-depth quantum carry-lookahead adder,” Quantum Information and Computation 6
2006
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Vivek V Shende, Stephen S Bullock, and Igor L Markov, “Synthesis of quantum-logic circuits,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25
2006
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Miroslav Dobšíček, Göran Johansson, Vitaly Shumeiko, and Göran Wendin, “Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark,” Phys. Rev. A 76
2007
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M. Žnidarič, O. Giraud, and B. Georgeot, “Optimal number of controlled-not gates to generate a three-qubit state,” Physical Review A 77
2008
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Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd, “Quantum algorithm for linear systems of equations,” Phys. Rev. Lett. 103
2009
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Emmanuel Gobet, “Advanced monte carlo methods for barrier and related exotic options,” Handbook of Numerical Analysis, 15
2009
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Michael A. Nielsen and Isaac L. Chuang, Cambridge University Press (2010) p. 702
2010
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2017
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Kristan Temme, Sergey Bravyi, and Jay M. Gambetta, “Error mitigation for short-depth quantum circuits,” Phys. Rev. Lett. 119
2017
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N. Moll, P. Barkoutsos, L. S. Bishop, J. M. Chow, A. Cross, D. J. Egger, S. Filipp, A. Fuhrer, J. M. Gambetta, M. Ganzhorn, A. Kandala, A. Mezzacapo, P. Müller, W. Riess, G. Salis, J. Smolin, I. Tavernelli, and K. Temme, “Quantum optimization using variational algorithms on near-term quantum devices,” Quantum Science and Technology 3
2018
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2018
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Patrick Rebentrost, Brajesh Gupt, and Thomas R. Bromley, “Quantum computational finance: Monte carlo pricing of financial derivatives,” Phys. Rev. A 98
2018
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E. F. Dumitrescu, A. J. McCaskey, G. Hagen, G. R. Jansen, T. D. Morris, T. Papenbrock, R. C. Pooser, D. J. Dean, and P. Lougovski, “Cloud quantum computing of an atomic nucleus,” Phys. Rev. Lett. 120
2018
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Abhinav Kandala, Kristan Temme, Antonio D. Corcoles, Antonio Mezzacapo, Jerry M. Chow, and Jay M. Gambetta, “Error mitigation extends the computational reach of a noisy quantum processor,” Nature 567
2019
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M. Ganzhorn, D.J. Egger, P. Barkoutsos, P. Ollitrault, G. Salis, N. Moll, M. Roth, A. Fuhrer, P. Mueller, S. Woerner, I. Tavernelli, and S. Filipp, “Gate-efficient simulation of molecular eigenstates on a quantum computer,” Phys. Rev. Applied 11
2019
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Vojtech Havlicek, Antonio D. Corcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta, “Supervised learning with quantum-enhanced feature spaces,” Nature 567
2019
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Roman Orus, Samuel Mugel, and Enrique Lizaso, “Quantum computing for finance: Overview and prospects,” Reviews in Physics 4
2019
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Stefan Woerner and Daniel J. Egger, “Quantum risk analysis,” npj Quantum Information 5
2019
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Christa Zoufal, Aurélien Lucchi, and Stefan Woerner, “Quantum generative adversarial networks for learning and loading random distributions,” npj Quantum Information 5
2019
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Blanka Horvath, Aitor Muguruza, and Mehdi Tomas, “Deep learning volatility,” SSRN Electronic Journal (2019), 10.2139/ssrn.3322085
2019
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Yohichi Suzuki, Shumpei Uno, Rudy Raymond, Tomoki Tanaka, Tamiya Onodera, and Naoki Yamamoto, “Amplitude estimation without phase estimation,” Quantum Information Processing 19
2020
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