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  • Letter
  • Open Access

Experimental measurement of quantum first-passage time distributions

Joseph M. Ryan*, Simon Gorbaty, Thomas J. Kessler, Mitchell G. Peaks, Stephen W. Teitsworth, and Crystal Noel

  • Duke Quantum Center, Department of Electrical and Computer Engineering and Department of Physics, Duke University, Durham, North Carolina 27708, USA

  • *Contact author: joseph.ryan@duke.edu
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Phys. Rev. Research 8, L022025 – Published 7 May, 2026

DOI: https://doi.org/10.1103/p3pl-1m6n

Abstract

Classical first-passage time distributions have been extensively studied both theoretically and experimentally. Their quantum counterparts—quantum first-passage time distributions (QFPTDs)—remain largely unexplored and have deep implications for both fundamental physics and the development of emerging quantum technologies. We measure the first QFPTDs using a motional mode of a single trapped ion. We develop a composite-phase laser pulse sequence to perform tunable stroboscopic single-shot projective measurements of the motional state of a trapped ion. We measure QFPTDs of the ion energy when coupled to electric-field noise. The measurement protocol developed here is broadly applicable to other quantum systems and provides a powerful method for exploring a broad range of QFPTD phenomena. With these results, we open a field of experimental investigations of QFPT processes with potential future relevance to quantum search algorithms, unraveling connections between classical and quantum dynamics, and study of the quantum measurement problem.

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References (80)

  1. C. Zunke, J. Bewerunge, F. Platten, S. U. Egelhaaf, and A. Godec, First-passage statistics of colloids on fractals: Theory and experimental realization, Sci. Adv. 8, eabk0627 (2022).
  2. A. L. Thorneywork, J. Gladrow, Y. Qing, M. Rico-Pasto, F. Ritort, H. Bayley, A. B. Kolomeisky, and U. F. Keyser, Direct detection of molecular intermediates from first-passage times, Sci. Adv. 6, eaaz4642 (2020).
  3. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, 2001).
  4. E. Schrödinger, Zur theorie der fall-und steigversuche an teilchen mit brownscher bewegung, Phys. Z. 16, 289 (1915).
  5. P. Hänggi, P. Talkner, and M. Borkovec, Reaction-rate theory: Fifty years after Kramers, Rev. Mod. Phys. 62, 251 (1990).
  6. O. Bénichou, M. Moreau, and G. Oshanin, Kinetics of stochastically gated diffusion-limited reactions and geometry of random walk trajectories, Phys. Rev. E 61, 3388 (2000).
  7. W. Dai, A. M. Sengupta, and R. M. Levy, First passage times, lifetimes, and relaxation times of unfolded proteins, Phys. Rev. Lett. 115, 048101 (2015).
  8. M. A. Micheelsen, C. Rischel, J. Ferkinghoff-Borg, R. Guerois, and L. Serrano, Mean first-passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding, Europhys. Lett. 61, 561 (2003).
  9. Y. Bomze, R. Hey, H. T. Grahn, and S. W. Teitsworth, Noise-induced current switching in semiconductor superlattices: Observation of nonexponential kinetics in a high-dimensional system, Phys. Rev. Lett. 109, 026801 (2012).
  10. S. W. Teitsworth, M. E. Olson, and Y. Bomze, Scaling properties of noise-induced switching in a bistable tunnel diode circuit, Eur. Phys. J. B 92, 74 (2019).
  11. N. Sazuka, J. ichi Inoue, and E. Scalas, The distribution of first-passage times and durations in forex and future markets, Phys. A: Stat. Mech. Appl. 388, 2839 (2009).
  12. J. Perelló, M. Gutiérrez-Roig, and J. Masoliver, Scaling properties and universality of first-passage-time probabilities in financial markets, Phys. Rev. E 84, 066110 (2011).
  13. R. Metzler, G. Oshanin, and S. Redner, First-Passage Phenomena and Their Applications (World Scientific, Singapore, 2014).
  14. C. Yin, Y. Wen, Z. Zong, and Y. Shen, The first passage time problem for mixed-exponential jump processes with applications in insurance and finance, Abstr. Appl. Anal. 2014, 571724 (2014).
  15. S. N. Stechmann and J. D. Neelin, First-passage-time prototypes for precipitation statistics, J. Atmos. Sci. 71, 3269 (2014).
  16. D. Lucente, C. Herbert, and F. Bouchet, Committor functions for climate phenomena at the predictability margin: The example of El Niño–southern oscillation in the Jin and Timmermann model, J. Atmos. Sci. 79, 2387 (2022).
  17. D. Tesfay, L. Serdukova, Y. Zheng, P. Wei, J. Duan, and J. Kurths, Influence of extreme events modeled by Lévy flight on atlantic meridional overturning circulation stability, Phys. D: Nonlinear Phenom. 481, 134849 (2025).
  18. K. Mølmer, Y. Castin, and J. Dalibard, Monte Carlo wave-function method in quantum optics, J. Opt. Soc. Am. B 10, 524 (1993).
  19. S. Maniscalco, J. Piilo, and K.-A. Suominen, Zeno and anti-Zeno effects for quantum Brownian motion, Phys. Rev. Lett. 97, 130402 (2006).
  20. P. Hanggi and P. Talkner, First-passage time problems for non-Markovian processes, Phys. Rev. A 32, 1934 (1985).
  21. F. Thiel, E. Barkai, and D. A. Kessler, First detected arrival of a quantum walker on an infinite line, Phys. Rev. Lett. 120, 040502 (2018).
  22. D. A. Kessler, E. Barkai, and K. Ziegler, First-detection time of a quantum state under random probing, Phys. Rev. A 103, 022222 (2021).
  23. M. J. Kewming, A. Kiely, S. Campbell, and G. T. Landi, First passage times for continuous quantum measurement currents, Phys. Rev. A 109, L050202 (2024).
  24. H. Friedman, D. A. Kessler, and E. Barkai, Quantum walks: The first detected passage time problem, Phys. Rev. E 95, 032141 (2017).
  25. E. H. Hauge and J. A. Støvneng, Tunneling times: A critical review, Rev. Mod. Phys. 61, 917 (1989).
  26. J. Muga and C. Leavens, Arrival time in quantum mechanics, Phys. Rep. 338, 353 (2000).
  27. S. Das and D. Dürr, Arrival time distributions of spin-1/2 particles, Sci. Rep. 9, 2242 (2019).
  28. S. Das, M. Nöth, and D. Dürr, Exotic Bohmian arrival times of spin-1/2 particles: An analytical treatment, Phys. Rev. A 99, 052124 (2019).
  29. S. Das and W. Struyve, Questioning the adequacy of certain quantum arrival-time distributions, Phys. Rev. A 104, 042214 (2021).
  30. S. E. Venegas-Andraca, Quantum walks: A comprehensive review, Quantum Info. Proc. 11, 1015 (2012).
  31. N. Shenvi, J. Kempe, and K. B. Whaley, Quantum random-walk search algorithm, Phys. Rev. A 67, 052307 (2003).
  32. A. M. Childs and J. Goldstone, Spatial search by quantum walk, Phys. Rev. A 70, 022314 (2004).
  33. D. Lewis, A. Benhemou, N. Feinstein, L. Banchi, and S. Bose, Optimal quantum spatial search with one-dimensional long-range interactions, Phys. Rev. Lett. 126, 240502 (2021).
  34. D. Qu, S. Marsh, K. Wang, L. Xiao, J. Wang, and P. Xue, Deterministic search on star graphs via quantum walks, Phys. Rev. Lett. 128, 050501 (2022).
  35. T. Yamasaki, H. Kobayashi, and H. Imai, Analysis of absorbing times of quantum walks, Phys. Rev. A 68, 012302 (2003).
  36. J. Kempe, Discrete quantum walks hit exponentially faster, Probab. Theory Relat. Fields 133, 215 (2005).
  37. R. Yin and E. Barkai, Restart expedites quantum walk hitting times, Phys. Rev. Lett. 130, 050802 (2023).
  38. F. Thiel, I. Mualem, D. Meidan, E. Barkai, and D. A. Kessler, Dark states of quantum search cause imperfect detection, Phys. Rev. Res. 2, 043107 (2020).
  39. Q. Liu, K. Ziegler, D. A. Kessler, and E. Barkai, Driving quantum systems with periodic conditional measurements, Phys. Rev. Res. 4, 023129 (2022).
  40. S. Dhar, S. Dasgupta, A. Dhar, and D. Sen, Detection of a quantum particle on a lattice under repeated projective measurements, Phys. Rev. A 91, 062115 (2015).
  41. S. Dhar, S. Dasgupta, and A. Dhar, Quantum time of arrival distribution in a simple lattice model, J. Phys. A: Math. Theor. 48, 115304 (2015).
  42. H. Krovi and T. A. Brun, Quantum walks with infinite hitting times, Phys. Rev. A 74, 042334 (2006).
  43. N. S. Williams and A. N. Jordan, Entanglement genesis under continuous parity measurement, Phys. Rev. A 78, 062322 (2008).
  44. S. Tornow and K. Ziegler, Measurement-induced quantum walks on an IBM quantum computer, Phys. Rev. Res. 5, 033089 (2023).
  45. B. Walter, G. Perfetto, and A. Gambassi, Thermodynamic phases in first detected return times of quantum many-body systems, Phys. Rev. A 111, L040202 (2025).
  46. Q. Wang, S. Ren, R. Yin, K. Ziegler, E. Barkai, and S. Tornow, First hitting times on a quantum computer: Tracking vs. local monitoring, topological effects, and dark states, Entropy 26, 869 (2024).
  47. R. Yin, Q. Wang, S. Tornow, and E. Barkai, Restart uncertainty relation for monitored quantum dynamics, Proc. Natl. Acad. Sci. USA 122, e2402912121 (2025).
  48. S. Gammelmark, B. Julsgaard, and K. Mølmer, Past quantum states of a monitored system, Phys. Rev. Lett. 111, 160401 (2013).
  49. D. Tan, S. J. Weber, I. Siddiqi, K. Mølmer, and K. W. Murch, Prediction and retrodiction for a continuously monitored superconducting qubit, Phys. Rev. Lett. 114, 090403 (2015).
  50. M. Tsang, Time-symmetric quantum theory of smoothing, Phys. Rev. Lett. 102, 250403 (2009).
  51. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).
  52. Q. A. Turchette, C. J. Myatt, B. E. King, C. A. Sackett, D. Kielpinski, W. M. Itano, C. Monroe, and D. J. Wineland, Decoherence and decay of motional quantum states of a trapped atom coupled to engineered reservoirs, Phys. Rev. A 62, 053807 (2000).
  53. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  54. K. R. Brown, A. W. Harrow, and I. L. Chuang, Arbitrarily accurate composite pulse sequences, Phys. Rev. A 70, 052318 (2004).
  55. S. Wimperis, Iterative schemes for phase-distortionless composite 180° pulses, J. Magn. Reson. 93, 199 (1991).
  56. S. Wimperis, Broadband, narrowband, and passband composite pulses for use in advanced NMR experiments, J. Magn. Reson. Ser. A 109, 221 (1994).
  57. M. Mallweger, M. Guevara-Bertsch, B. T. Torosov, R. Thomm, N. Kuk, H. Parke, C. F. Roos, G. Higgins, M. Hennrich, and N. V. Vitanov, Motional-state analysis of a trapped ion by ultranarrowband composite pulses, Phys. Rev. A 110, 053103 (2024).
  58. See Supplemental Material at http://link.aps.org/supplemental/10.1103/p3pl-1m6n for details on the experimental setup, composite-phase step pulse sequence, laser intensity noise models, sampling error bars, and the qualitative difference between QFPTDs with NB=1 and NB≥2, which includes Refs. [51, 79, 80].
  59. D. F. V. James, Theory of heating of the quantum ground state of trapped ions, Phys. Rev. Lett. 81, 317 (1998).
  60. A. J. Rasmusson, I. Jung, F. Schroer, A. Kyprianidis, and P. Richerme, Measurement-induced heating of trapped ions, J. Phys. B: At. Mol. Opt. Phys. 57, 225002 (2024).
  61. C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta, and J. P. Home, Encoding a qubit in a trapped-ion mechanical oscillator, Nature (London) 566, 513 (2019).
  62. M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, Ion-trap measurements of electric-field noise near surfaces, Rev. Mod. Phys. 87, 1419 (2015).
  63. C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, 3rd ed., Springer Series in Synergetics (Springer, Berlin, Heidelberg, 2004).
  64. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007).
  65. T. P. Harty, High-fidelity microwave-driven quantum logic in intermediate-field Ca+43, Ph.D. thesis, University of Oxford, 2013.
  66. J. M. Ryan, S. W. Teitsworth, and C. Noel (unpublished).
  67. W. Vassen, C. Cohen-Tannoudji, M. Leduc, D. Boiron, C. I. Westbrook, A. Truscott, K. Baldwin, G. Birkl, P. Cancio, and M. Trippenbach, Cold and trapped metastable noble gases, Rev. Mod. Phys. 84, 175 (2012).
  68. A. Kreuter, C. Becher, G. P. T. Lancaster, A. B. Mundt, C. Russo, H. Häffner, C. Roos, J. Eschner, F. Schmidt-Kaler, and R. Blatt, Spontaneous emission lifetime of a single trapped Ca+ ion in a high finesse cavity, Phys. Rev. Lett. 92, 203002 (2004).
  69. A. A. Madej and J. D. Sankey, Quantum jumps and the single trapped barium ion: Determination of collisional quenching rates for the 5d2D5/2 level, Phys. Rev. A 41, 2621 (1990).
  70. M. Kang, W. C. Campbell, and K. R. Brown, Quantum error correction with metastable states of trapped ions using erasure conversion, PRX Quantum 4, 020358 (2023).
  71. O. Katz and C. Monroe, Programmable quantum simulations of bosonic systems with trapped ions, Phys. Rev. Lett. 131, 033604 (2023).
  72. K. Sun, M. Kang, H. Nuomin, G. Schwartz, D. N. Beratan, K. R. Brown, and J. Kim, Quantum simulation of spin-boson models with structured bath, Nat. Commun. 16, 4042 (2025).
  73. M. Štefaňák, I. Jex, and T. Kiss, Recurrence and Pólya number of quantum walks, Phys. Rev. Lett. 100, 020501 (2008).
  74. Y.-J. Wang, R.-Y. Yin, L.-Y. Dou, A.-N. Zhang, and X.-B. Song, Quantum first detection of a quantum walker on a perturbed ring, Phys. Rev. Res. 5, 013202 (2023).
  75. X.-Y. Xu, Q.-Q. Wang, W.-W. Pan, K. Sun, J.-S. Xu, G. Chen, J.-S. Tang, M. Gong, Y.-J. Han, C.-F. Li, and G.-C. Guo, Measuring the winding number in a large-scale chiral quantum walk, Phys. Rev. Lett. 120, 260501 (2018).
  76. C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Programmable quantum simulations of spin systems with trapped ions, Rev. Mod. Phys. 93, 025001 (2021).
  77. Y. Lu, W. Chen, S. Zhang, K. Zhang, J. Zhang, J.-N. Zhang, and K. Kim, Implementing arbitrary ising models with a trapped-ion quantum processor, Phys. Rev. Lett. 134, 050602 (2025).
  78. J. M. Ryan, S. Gorbaty, T. J. Kessler, M. G. Peaks, S. W. Teitsworth, and C. Noel, Data from “Experimental measurement of quantum first-passage time distributions” [Dataset], Duke Research Data Repository (2025), https://doi.org/10.7924/R4HT2X079.
  79. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, et al., SciPy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
  80. G. Pagano, P. W. Hess, H. B. Kaplan, W. L. Tan, P. Richerme, P. Becker, A. Kyprianidis, J. Zhang, E. Birckelbaw, M. R. Hernandez, Y. Wu, and C. Monroe, Cryogenic trapped-ion system for large scale quantum simulation, Quantum Sci. Technol. 4, 014004 (2018).

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Phys. Rev. Research 8, L022025– Published 7 May, 2026
  • Received 8 September 2025
  • Revised 13 January 2026
  • Accepted 1 April 2026
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