IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v17y2026i1p1-37.html

Dynamic programming in economics on a quantum annealer

Author

Listed:
  • Jesús Fernández‐Villaverde
  • Isaiah Hull

Abstract

We introduce novel algorithms for solving dynamic programming problems in economics on a quantum annealer, a specialized quantum computer used for combinatorial optimization. Quantum annealers begin in a superposition of all states and generate candidate global solutions in milliseconds, regardless of problem size. In contrast to existing methods, those developed in this paper (1) recover value and policy functions, (2) avoid fundamental scaling bottlenecks, and (3) are already implementable for small (but non‐trivial) problems on current hardware. We demonstrate the method by solving the real business cycle model on a quantum annealer.

Suggested Citation

  • Jesús Fernández‐Villaverde & Isaiah Hull, 2026. "Dynamic programming in economics on a quantum annealer," Quantitative Economics, Econometric Society, vol. 17(1), pages 1-37, January.
    • Handle: RePEc:wly:quante:v:17:y:2026:i:1:p:1-37
    DOI: 10.3982/QE2555
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/QE2555
    Download Restriction: no
    File URL: https://libkey.io/10.3982/QE2555?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Eric Ghysels & Jack Morgan & Hamed Mohammadbagherpoor, 2023. "Quantum Computational Algorithms for Derivative Pricing and Credit Risk in a Regime Switching Economy," Papers 2311.00825, arXiv.org.
    2. Jesús Fernández‐Villaverde & Samuel Hurtado & Galo Nuño, 2025. "Corrigendum: Financial Frictions and the Wealth Distribution," Econometrica, Econometric Society, vol. 93(4), pages 1491-1496, July.
    3. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    4. Andrew Sweeting, 2013. "Dynamic Product Positioning in Differentiated Product Markets: The Effect of Fees for Musical Performance Rights on the Commercial Radio Industry," Econometrica, Econometric Society, vol. 81(5), pages 1763-1803, September.
    5. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    6. Sergio Boixo & Vadim N. Smelyanskiy & Alireza Shabani & Sergei V. Isakov & Mark Dykman & Vasil S. Denchev & Mohammad H. Amin & Anatoly Yu Smirnov & Masoud Mohseni & Hartmut Neven, 2016. "Computational multiqubit tunnelling in programmable quantum annealers," Nature Communications, Nature, vol. 7(1), pages 1-7, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. is not listed on IDEAS
    2. Sofia Priazhkina & Samuel Palmer & Pablo Martín-Ramiro & Román Orús & Samuel Mugel & Vladimir Skavysh, 2024. "Digital Payments in Firm Networks: Theory of Adoption and Quantum Algorithm," Staff Working Papers 24-17, Bank of Canada.
    3. David Staines, 2026. "Statistical and Numerical Convergence in Stochastic Equilibrium," Papers 2606.07469, arXiv.org, revised Jun 2026.
    4. Raphael Auer & Angela Dupont & Leonardo Gambacorta & Joon Suk Park & Koji Takahashi & Andras Valko, 2024. "Quantum computing and the financial system: opportunities and risks," BIS Papers, Bank for International Settlements, number 149.
    5. Andreas Ferrara, 2026. "A Practitioner's Guide to Using Large Language Models and Generative AI in Economic History," NBER Working Papers 35374, National Bureau of Economic Research, Inc.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fernández-Villaverde, Jesús & Hull, Isaiah, 2023. "Dynamic Programming on a Quantum Annealer: Solving the RBC Model," CEPR Discussion Papers 18190, Centre for Economic Policy Research.
    2. S. Sirakaya & Stephen Turnovsky & M. Alemdar, 2006. "Feedback Approximation of the Stochastic Growth Model by Genetic Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 185-206, May.
    3. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    4. Tapan Mitra & Santanu Roy, 2023. "Stochastic growth, conservation of capital and convergence to a positive steady state," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 311-351, July.
    5. Uhlig, H.F.H.V.S., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Other publications TiSEM cc1b2469-9d2f-445a-a2b3-1, Tilburg University, School of Economics and Management.
    6. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    7. Marlon Azinovic-Yang & Jan v{Z}emliv{c}ka, 2025. "Deep Learning in the Sequence Space," Papers 2509.13623, arXiv.org, revised Mar 2026.
    8. Francisco J. Ruge-Murcia, 2013. "Generalized Method of Moments estimation of DSGE models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 20, pages 464-485, Edward Elgar Publishing.
    9. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    10. Akdeniz, Levent & Dechert, W. Davis, 1997. "Do CAPM results hold in a dynamic economy? A numerical analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 981-1003, June.
    11. Lars Grüne & Willi Semmler, 2007. "Asset pricing with dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 233-265, May.
    12. Coleman, Wilbur John, II, 1993. "Solving Nonlinear Dynamic Models on Parallel Computers," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 325-330, July.
    13. Peter Woehrmann & Willi Semmler & Martin Lettau, "undated". "Nonparametric Estimation of the Time-varying Sharpe Ratio in Dynamic Asset Pricing Models," IEW - Working Papers 225, Institute for Empirical Research in Economics - University of Zurich.
    14. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    15. Willi Semmler & Lars Grüne, 2004. "Asset Pricing with Delayed Consumption Decisions," Computing in Economics and Finance 2004 59, Society for Computational Economics.
    16. Isaiah Hull & Or Sattath & Eleni Diamanti & Göran Wendin, 2024. "Quantum Algorithms," Contributions to Economics, in: Quantum Technology for Economists, chapter 0, pages 37-103, Springer.
    17. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    18. Pascal, Julien, 2024. "Artificial neural networks to solve dynamic programming problems: A bias-corrected Monte Carlo operator," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    19. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
    20. Marlon Azinovic-Yang & Jan Zemlicka, 2025. "Deep Learning in the Sequence Space," CERGE-EI Working Papers wp802, The Center for Economic Research and Graduate Education - Economics Institute, Prague.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:quante:v:17:y:2026:i:1:p:1-37. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.