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  • Open Access

Temperature change can solve the Deutsch-Jozsa problem: An exploration of thermodynamic query complexity

Jake Xuereb*

  • Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria

  • *Contact author: jake.xuereb@tuwien.ac.at
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Phys. Rev. A 113, 012420 – Published 9 January, 2026

DOI: https://doi.org/10.1103/qky6-2bfs

Abstract

We demonstrate how a single heat exchange between a probe thermal qubit and multiqubit thermal machine encoding a Boolean function can determine whether the function is balanced or constant, thus providing a thermodynamic solution to the Deutsch-Jozsa problem. We introduce a thermodynamic model of quantum query complexity, showing how qubit thermal machines can act as oracles, queried via heat exchange with a probe. While the Deutsch-Jozsa problem requires an exponential encoding in the number of oracle bits, we also explore a restricted Bernstein-Vazirani problem, which admits a linear thermal oracle and a single thermal query solution. We establish bounds on the number of samples needed to determine the probe temperature encoding the solution for the Deutsch-Jozsa problem, showing that it remains constant with problem size. Additionally, we propose a proof-of-principle experimental implementation to solve the three-bit Bernstein-Vazirani problem via thermal kickback. This work bridges thermodynamics and complexity theory, suggesting that quantum thermodynamics could provide an unconventional route to computing beyond classical computation.

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References (40)

  1. D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proc. R. Soc. London, Ser. A 439, 553 (1992).
  2. A. Berthiaume and G. Brassard, The quantum challenge to structural complexity theory, in Proceedings of the 7th IEEE Conference on Structure in Complexity Theory (IEEE, Boston, MA, USA, 1992), pp. 132–137.
  3. A. Berthiaume and G. Brassard, Oracle quantum computing, J. Mod. Opt. 41, 2521 (1994).
  4. E. Bernstein and U. Vazirani, Quantum complexity theory, SIAM J. Comput. 26, 1411 (1997).
  5. J. Watrous, Quantum computational complexity, in Encyclopedia of Complexity and Systems Science, edited by R. A. Meyers (Springer, New York, 2009), pp. 7174–7201.
  6. S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemp. Phys. 57, 545 (2016).
  7. J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics—A topical review, J. Phys. A 49, 143001 (2016).
  8. Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Fundamental Theories of Physics Vol. 195 (Springer, Cham, 2018).
  9. P. Taranto, F. Bakhshinezhad, A. Bluhm, R. Silva, N. Friis, M. P. E. Lock, G. Vitagliano, F. C. Binder, T. Debarba, E. Schwarzhans, F. Clivaz, and M. Huber, Landauer versus Nernst: What is the true cost of cooling a quantum system? PRX Quantum 4, 010332 (2023).
  10. K. V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. Acín, Entanglement generation is not necessary for optimal work extraction, Phys. Rev. Lett. 111, 240401 (2013).
  11. E. Knill and R. Laflamme, Power of one bit of quantum information, Phys. Rev. Lett. 81, 5672 (1998).
  12. A. Ambainis, L. J. Schulman, and U. Vazirani, Computing with highly mixed states, J. ACM 53, 507 (2006).
  13. R. Laflamme, E. Knill, D. Cory, E. Fortunato, T. Havel, C. Miquel, R. Martinez, C. Negrevergne, G. Ortiz, M. Pravia, et al., Introduction to NMR quantum information processing, arXiv:quant-ph/0207172.
  14. T. Morimae, K. Fujii, and H. Nishimura, Power of one nonclean qubit, Phys. Rev. A 95, 042336 (2017).
  15. D. Poulin, R. Laflamme, G. J. Milburn, and J. P. Paz, Testing integrability with a single bit of quantum information, Phys. Rev. A 68, 022302 (2003).
  16. D. Poulin, R. Blume-Kohout, R. Laflamme, and H. Ollivier, Exponential speedup with a single bit of quantum information: Measuring the average fidelity decay, Phys. Rev. Lett. 92, 177906 (2004).
  17. D. Shepherd, Computation with unitaries and one pure qubit, arXiv:quant-ph/0608132.
  18. P. Shor and S. Jordan, Estimating Jones polynomials is a complete problem for one clean qubit, Quantum Inf. Comput. 8, 681 (2008).
  19. M. Aifer, K. Donatella, M. H. Gordon, S. Duffield, T. Ahle, D. Simpson, G. E. Crooks, and P. J. Coles, Thermodynamic linear algebra, npj Unconv. Comput. 1, 13 (2024).
  20. P. Lipka-Bartosik, K. Donatella, M. Aifer, D. Melanson, M. Perarnau-Llobet, N. Brunner, and P. J. Coles, Thermodynamic algorithms for quadratic programming, in 2024 IEEE International Conference on Rebooting Computing (ICRC) (IEEE, San Diego, CA, USA, 2024), pp. 1–13.
  21. N. Linden, S. Popescu, and P. Skrzypczyk, How small can thermal machines be? The smallest possible refrigerator, Phys. Rev. Lett. 105, 130401 (2010).
  22. A. Levy and R. Kosloff, Quantum absorption refrigerator, Phys. Rev. Lett. 108, 070604 (2012).
  23. R. Silva, G. Manzano, P. Skrzypczyk, and N. Brunner, Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource, Phys. Rev. E 94, 032120 (2016).
  24. M. T. Mitchison, Quantum thermal absorption machines: Refrigerators, engines and clocks, Contemp. Phys. 60, 164 (2019).
  25. We will examine the number of samples in Sec. 6.
  26. N. Brunner, N. Linden, S. Popescu, and P. Skrzypczyk, Virtual qubits, virtual temperatures, and the foundations of thermodynamics, Phys. Rev. E 85, 051117 (2012).
  27. F. Clivaz, R. Silva, G. Haack, J. B. Brask, N. Brunner, and M. Huber, Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling, Phys. Rev. Lett. 123, 170605 (2019).
  28. P. Erker, M. T. Mitchison, R. Silva, M. P. Woods, N. Brunner, and M. Huber, Autonomous quantum clocks: Does thermodynamics limit our ability to measure time? Phys. Rev. X 7, 031022 (2017).
  29. P. P. Hofer, J. B. Brask, M. Perarnau-Llobet, and N. Brunner, Quantum thermal machine as a thermometer, Phys. Rev. Lett. 119, 090603 (2017).
  30. M. Mehboudi, A. Sanpera, and L. A. Correa, Thermometry in the quantum regime: Recent theoretical progress, J. Phys. A 52, 303001 (2019).
  31. T. M. Cover and J. A. Thomas, Information theory and statistics, in Elements of Information Theory (Wiley, 2005), Chap. 11, pp. 347–408.
  32. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th anniversary ed. (Cambridge University Press, Cambridge, 2010).
  33. J. A. Almanza-Marrero and G. Manzano, Certifying quantum enhancements in thermal machines beyond the thermodynamic uncertainty relation, Quantum 9, 1878 (2025).
  34. J. Xuereb, Github (2025), https://github.com/jqed-xuereb/A-Temperature-Change-can-Solve-the-Deutsch---Josza-Problem.
  35. J. Pekola, Towards quantum thermodynamics in electronic circuits, Nat. Phys. 11, 118 (2015).
  36. W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha, and L. P. Kouwenhoven, Electron transport through double quantum dots, Rev. Mod. Phys. 75, 1 (2002).
  37. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quantum dots, Rev. Mod. Phys. 79, 1217 (2007).
  38. F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Silicon quantum electronics, Rev. Mod. Phys. 85, 961 (2013).
  39. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  40. M. A. Aamir, P. J. Suria, J. A. Marín Guzmán, C. Castillo-Moreno, J. M. Epstein, N. Y. Halpern, and S. Gasparinetti, Thermally driven quantum refrigerator autonomously resets a superconducting qubit, Nat. Phys. 21, 318 (2025).

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Phys. Rev. A 113, 012420– Published 9 January, 2026
  • Received 6 June 2025
  • Revised 6 August 2025
  • Accepted 4 December 2025
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