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Preparing a thermofield double state with feedback quantum algorithms

Guilherme E. L. Pexe1,*, Lucas A. M. Rattighieri2, Felipe F. Fanchini3,4, Dario Rosa5, and Amilson R. Fritsch1

  • *Contact author: guilherme.pexe@ifsc.usp.br
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Phys. Rev. D 114, 076018 – Published 13 October, 2026

DOI: https://doi.org/10.1103/nwjw-vkty

Abstract

The efficient preparation of correlated thermal states, such as the thermofield double state, is a fundamental prerequisite for simulating quantum gravity models and many-body thermodynamics on quantum processors. In this work, we investigate the ground-state preparation of the two coupled Sachdev-Ye-Kitaev model, known as the Maldacena-Qi model, which is dual to a traversable wormhole in anti–de Sitter space in two dimensions, utilizing feedback-based quantum algorithms. We demonstrate that the standard feedback-based quantum algorithm (FALQON) and its time-rescaled variant (TR-FALQON) face severe kinetic limitations in this system, failing to converge to the highly entangled ground state when initialized in trivial product states. To overcome these barriers, we propose the hybrid ITE-TR-FALQON protocol, which integrates the imaginary-time evolution present in imaginary-time-enhanced FALQON with the time-rescaling mechanism. Our ideal state-vector simulations show that imaginary-time filtering overcomes the stagnation observed for the unitary protocols with the chosen driver and initial state, while time rescaling reduces the number of algorithmic layers. The hybrid protocol achieves fidelities close to unity with the exact-diagonalization ground state and reproduces its von Neumann and Rényi entropies with high precision. These results constitute a numerical proof of principle: implementing the nonunitary updates, repeated feedback measurements, and the resulting compiled circuits remains a substantial obstacle, and the protocol in its present form is not a practical state-preparation method for current noisy intermediate-scale quantum devices.

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References (30)

  1. S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70, 3339 (1993).
  2. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94, 106002 (2016).
  3. S. Sachdev, Bekenstein-Hawking entropy and strange metals, Phys. Rev. X 5, 041025 (2015).
  4. J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, J. High Energy Phys. 04 (2016) 001.
  5. J. Maldacena, D. Stanford, and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de Sitter space, Prog. Theor. Exp. Phys. 2016, 12C104 (2016).
  6. A. Kitaev and S. J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, J. High Energy Phys. 05 (2018) 183.
  7. Y. Gu, A. Lucas, and X.-L. Qi, Spread of entanglement in a Sachdev-Ye-Kitaev chain, J. High Energy Phys. 09 (2017) 120.
  8. V. Rosenhaus, An introduction to the SYK model, J. Phys. A 52, 323001 (2019).
  9. J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 08 (2016) 106.
  10. D. Chowdhury, A. Georges, O. Parcollet, and S. Sachdev, Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids, Rev. Mod. Phys. 94, 035004 (2022).
  11. J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491.
  12. A. M. García-García, T. Nosaka, D. Rosa, and J. J. M. Verbaarschot, Quantum chaos transition in a two-site Sachdev-Ye-Kitaev model dual to an eternal traversable wormhole, Phys. Rev. D 100, 026002 (2019).
  13. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  14. L. Susskind, Computational complexity and black hole horizons, Fortschr. Phys. 64, 24 (2016).
  15. J. Liu, Z. Lin, and L. Jiang, Laziness, barren plateau, and noises in machine learning, Mach. Learn. Sci. Technol. 5, 015058 (2024).
  16. A. B. Magann, K. M. Rudinger, M. D. Grace, and M. Sarovar, Lyapunov-control-inspired strategies for quantum combinatorial optimization, Phys. Rev. A 106, 062414 (2022).
  17. G. E. L. Pexe, L. A. M. Rattighieri, A. L. Malvezzi, and F. F. Fanchini, Using a feedback-based quantum algorithm to analyze the critical properties of the ANNNI model without classical optimization, Phys. Rev. B 110, 224422 (2024).
  18. L. A. M. Rattighieri, G. E. L. Pexe, B. L. Bernardo, and F. F. Fanchini, Accelerating feedback-based quantum algorithms through time rescaling, Phys. Rev. A 112, 042607 (2025).
  19. T. N. V. Long, L. N. Tran, and L. B. Ho, Imaginary-time-enhanced feedback-based quantum algorithms for universal ground-state preparation, arXiv:2512.13044.
  20. A. B. Magann, K. M. Rudinger, M. D. Grace, and M. Sarovar, Feedback-based quantum optimization, Phys. Rev. Lett. 129, 250502 (2022).
  21. B. d. L. Bernardo, Time-rescaled quantum dynamics as a shortcut to adiabaticity, Phys. Rev. Res. 2, 013133 (2020).
  22. J. L. M. Ferreira, Ângelo F. da Silva França, A. Rosas, and B. de Lima Bernardo, Shortcuts to adiabaticity designed via time-rescaling follow the same transitionless route, J. Phys. B 59, 025501 (2026).
  23. S. McArdle, T. Jones, S. Endo, Y. Li, S. C. Benjamin, and X. Yuan, Variational ansatz-based quantum simulation of imaginary time evolution, npj Quantum Inf. 5, 75 (2019).
  24. M. Motta, C. Sun, A. T. K. Tan, M. J. O’Rourke, E. Ye, A. J. Minnich, F. G. S. L. Brandão, and G. K.-L. Chan, Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution, Nat. Phys. 16, 205 (2020).
  25. N. Gomes, A. Mukherjee, F. Zhang, T. Iadecola, C. Wang, K. Ho, P. P. Orth, and Y. Yao, Adaptive variational quantum imaginary time evolution approach for ground state preparation, Adv. Quantum Technol. 4, 2100114 (2021).
  26. S.-N. Sun, M. Motta, R. N. Tazhigulov, A. T. Tan, G. K.-L. Chan, and A. J. Minnich, Quantum computation of finite-temperature static and dynamical properties of spin systems using quantum imaginary time evolution, PRX Quantum 2, 010317 (2021).
  27. K. Yeter-Aydeniz, R. C. Pooser, and G. Siopsis, Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms, npj Quantum Inf. 6, 63 (2020).
  28. H. Kamakari, S.-N. Sun, M. Motta, and A. J. Minnich, Digital quantum simulation of open quantum systems using quantum imaginary–time evolution, PRX Quantum 3, 010320 (2022).
  29. S. B. Bravyi and A. Y. Kitaev, Fermionic quantum computation, Ann. Phys. (Amsterdam) 298, 210 (2002).
  30. L. García-Álvarez, I. L. Egusquiza, L. Lamata, A. del Campo, J. Sonner, and E. Solano, Digital quantum simulation of minimal AdS/CFT, Phys. Rev. Lett. 119, 040501 (2017).

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Phys. Rev. D 114, 076018– Published 13 October, 2026
  • Received 8 July 2026
  • Accepted 17 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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