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  • Open Access

Universal Quantum Computer from Relativistic Motion

Philip A. LeMaitre1,*, T. Rick Perche2,3,4,†, Marius Krumm1, and Hans J. Briegel1

  • *Contact author: philip.lemaitre@uibk.ac.at
  • †Contact author: trickperche@perimeterinstitute.ca
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Phys. Rev. Lett. 134, 190601 – Published 14 May, 2025

DOI: https://doi.org/10.1103/PhysRevLett.134.190601

Abstract

We present an explicit construction of a relativistic quantum computing architecture using a variational quantum circuit approach that is shown to allow for universal quantum computing. The variational quantum circuit consists of tunable single-qubit rotations and entangling gates that are implemented successively. The single-qubit rotations are parameterized by the proper time intervals of the qubits’ trajectories and can be tuned by varying their relativistic motion in spacetime. The entangling layer is mediated by a relativistic quantum field instead of through direct coupling between the qubits. Within this setting, we give a prescription for how to use quantum field-mediated entanglement and manipulation of the relativistic motion of qubits to obtain a universal gate set, for which compact nonperturbative expressions that are valid for general spacetimes are also obtained. We also derive a lower bound on the channel fidelity that shows the existence of parameter regimes in which all entangling operations are effectively unitary, despite the noise generated from the presence of a mediating quantum field. Finally, we consider an explicit implementation of the quantum Fourier transform with relativistic qubits.

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References (53)

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2010).
  2. M. Caleffi, M. Amoretti, D. Ferrari, J. Illiano, A. Manzalini, and A. S. Cacciapuoti, Distributed quantum computing: A survey, Comput. Netw. 254, 110672 (2024).
  3. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li et al., Satellite-to-ground quantum key distribution, Nature (London) 549, 43 (2017).
  4. A. Valentini, Non-local correlations in quantum electrodynamics, Phys. Lett. A 153, 321 (1991).
  5. B. Reznik, Entanglement from the vacuum, Found. Phys. 33, 167 (2003).
  6. A. Pozas-Kerstjens and E. Martín-Martínez, Harvesting correlations from the quantum vacuum, Phys. Rev. D 92, 064042 (2015).
  7. A. Pozas-Kerstjens and E. Martín-Martínez, Entanglement harvesting from the electromagnetic vacuum with hydrogenlike atoms, Phys. Rev. D 94, 064074 (2016).
  8. D. Mendez-Avalos, L. J. Henderson, K. Gallock-Yoshimura, and R. B. Mann, Entanglement harvesting of three Unruh-DeWitt detectors, Gen. Relativ. Gravit. 54, 87 (2022).
  9. T. R. Perche, J. Polo-Gómez, B. d. S. L. Torres, and E. Martín-Martínez, Fully relativistic entanglement harvesting, Phys. Rev. D 109, 045018 (2024).
  10. M. Hotta, Quantum measurement information as a key to energy extraction from local vacuums, Phys. Rev. D 78, 045006 (2008).
  11. M. Hotta, Energy entanglement relation for quantum energy teleportation, Phys. Lett. A 374, 3416 (2010).
  12. M. Hotta, J. Matsumoto, and G. Yusa, Quantum energy teleportation without a limit of distance, Phys. Rev. A 89, 012311 (2014).
  13. N. A. Rodríguez-Briones, H. Katiyar, E. Martín-Martínez, and R. Laflamme, Experimental activation of strong local passive states with quantum information, Phys. Rev. Lett. 130, 110801 (2023).
  14. E. Martin-Martinez, D. Aasen, and A. Kempf, Processing quantum information with relativistic motion of atoms, Phys. Rev. Lett. 110, 160501 (2013).
  15. D. E. Bruschi, A. Dragan, A. R. Lee, I. Fuentes, and J. Louko, Relativistic motion generates quantum gates and entanglement resonances, Phys. Rev. Lett. 111, 090504 (2013).
  16. E. Martín-Martínez and C. Sutherland, Quantum gates via relativistic remote control, Phys. Lett. B 739, 74 (2014).
  17. D. E. Bruschi, C. Sabín, P. Kok, G. Johansson, P. Delsing, and I. Fuentes, Towards universal quantum computation through relativistic motion, Sci. Rep. 6, 18349 (2016).
  18. D. Layden, E. Martin-Martinez, and A. Kempf, Universal scheme for indirect quantum control, Phys. Rev. A 93, 040301(R) (2016).
  19. E. Aspling and M. Lawler, Universal quantum computing with field-mediated Unruh–DeWitt qubits, arXiv:2402.10173.
  20. W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976).
  21. B. DeWitt, General Relativity: An Einstein Centenary Survey (Cambridge University Press, Cambridge, England, 1979).
  22. J. Louko and A. Satz, Transition rate of the Unruh–DeWitt detector in curved spacetime, Classical Quantum Gravity 25, 055012 (2008).
  23. J. Biamonte, Universal variational quantum computation, Phys. Rev. A 103, L030401 (2021).
  24. M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational quantum algorithms, Nat. Rev. Phys. 3, 625 (2021).
  25. L. Leone, S. F. E. Oliviero, L. Cincio, and M. Cerezo, On the practical usefulness of the hardware efficient ansatz, Quantum 8, 1395 (2024).

  26. Notice that in this model we are neglecting any local noise experienced by the qubits in our implementation of the local unitaries. This effect could be incorporated by considering the typical T1 and T2 decoherence processes [27] and by making sure that the time of implementation of the local unitaries is sufficiently smaller than the T1 and T2 relaxation times.

  27. F. Bloch, Nuclear induction, Phys. Rev. 70, 460 (1946).
  28. E. Martín-Martínez, T. R. Perche, and B. de S. L. Torres, General relativistic quantum optics: Finite-size particle detector models in curved spacetimes, Phys. Rev. D 101, 045017 (2020).
  29. E. Martín-Martínez, T. R. Perche, and B. d. S. L. Torres, Broken covariance of particle detector models in relativistic quantum information, Phys. Rev. D 103, 025007 (2021).
  30. A. G. S. Landulfo, Nonperturbative approach to relativistic quantum communication channels, Phys. Rev. D 93, 104019 (2016).
  31. T. R. Perche, Closed-form expressions for smeared bidistributions of a massless scalar field: Nonperturbative and asymptotic results in relativistic quantum information, Phys. Rev. D 110, 025013 (2024).

  32. A quasi-free state is a zero mean Gaussian state. Typical states that satisfy this condition are thermal states and most choices of vacua [33].

  33. R. Haag, Local Quantum Physics: Fields, Particles, Algebras, 1st ed. (Springer Publishing Company, Incorporated, 2012).

  34. This would not be the case if the field was in a highly excited state or if the qubits were in extreme states of motion while interacting with the field (such as accelerations high enough so that Unruh-like effects would take place [35, 36, 37]).

  35. W. G. Unruh and R. M. Wald, What happens when an accelerating observer detects a Rindler particle, Phys. Rev. D 29, 1047 (1984).
  36. S. Takagi, Vacuum Noise and Stress Induced by Uniform Acceleration: Hawking-Unruh effect in Rindler manifold of arbitrary dimension, Prog. Theor. Phys. Suppl. 88, 1 (1986).
  37. C. J. Fewster, B. A. Juárez-Aubry, and J. Louko, Waiting for Unruh, Classical Quantum Gravity 33, 165003 (2016).

  38. Notice that having N2≪λ−2 does not prevent us from having meaningful entanglement generated by the unitary U^C, provided that |λ2Δij|∼1. This is a reasonable assumption provided that T∼λ−2L, where T is the time duration of the interaction with the field and L is the minimal separation between qubits in the setup.

  39. D. Deutsch, A. Barenco, and A. Ekert, Universality in quantum computation, Proc. R. Soc. A 449, 669 (1995).

  40. This assumption corresponds to the statement that the effective coupling range of the qubits is much smaller than their separation and that their separation is much smaller than the distance traversed by light in a time interval T.

  41. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.134.190601 for calculation details, further details on the noise lower bounds and the quantum Fourier transform example, and the proof of universality, which includes Refs. [1,42–45].
  42. Z. P. Yang and X. X. Feng, A note on the trace inequality for products of Hermitian matrix power, J. Inequal. Pure Appl. Math. 3, 78 (2002).
  43. E. R. Anschuetz and B. T. Kiani, Quantum variational algorithms are swamped with traps, Nat. Commun. 13, 7760 (2022).
  44. E. R. Anschuetz, A unified theory of quantum neural network loss landscapes, arXiv:2408.11901.
  45. S. Blanes, F. Casas, J. A. Oteo, and J. Ros, The magnus expansion and some of its applications, Phys. Rep. 470, 151 (2009).
  46. P. A. LeMaitre, T. R. Perche, and M. Krumm, https://github.com/AntiPhoton47/RVQC/.
  47. M. Cerezo, A. Sone, T. Volkoff, L. Cincio, and P. J. Coles, Cost function dependent barren plateaus in shallow parametrized quantum circuits, Nat. Commun. 12, 1791 (2021).
  48. Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Connecting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum 3, 010313 (2022).
  49. A. Deshpande, M. Hinsche, S. Najafi, K. Sharma, R. Sweke, and C. Zoufal, Dynamic parameterized quantum circuits: Expressive and barren-plateau free, arXiv:2411.05760.
  50. A. Skolik, J. R. McClean, M. Mohseni, P. Van Der Smagt, and M. Leib, Layerwise learning for quantum neural networks, Quantum Mach. Intell. 3, 5 (2021).
  51. E. Grant, L. Wossnig, M. Ostaszewski, and M. Benedetti, An initialization strategy for addressing barren plateaus in parametrized quantum circuits, Quantum 3, 214 (2019).
  52. E. Tjoa and E. Martín-Martínez, When entanglement harvesting is not really harvesting, Phys. Rev. D 104, 125005 (2021).
  53. T. R. Perche and E. Martín-Martínez, Role of quantum degrees of freedom of relativistic fields in quantum information protocols, Phys. Rev. A 107, 042612 (2023).

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Phys. Rev. Lett. 134, 190601– Published 14 May, 2025
  • Received 22 November 2024
  • Revised 11 March 2025
  • Accepted 8 April 2025
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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.

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