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Nonstabilizerness in kinetically constrained Rydberg atom arrays

Ryan Smith, Zlatko Papić, and Andrew Hallam

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Phys. Rev. B 111, 245148 – Published 23 June, 2025

DOI: https://doi.org/10.1103/jz4d-vdhj

Abstract

Nonstabilizer states are a fundamental resource for universal quantum computation. However, despite broad significance in quantum computing, the emergence of many-body nonstabilizerness in interacting quantum systems remains poorly understood due to its analytical intractability. Here we show that Rydberg atom arrays provide a natural reservoir of nonstabilizerness that extends beyond single qubits and arises from quantum correlations generated by the Rydberg blockade. We demonstrate that this nonstabilizerness can be experimentally accessed using two complementary methods, either performing quench dynamics or via adiabatic ground state preparation. Using the analytical framework based on matrix product states, we explain the origin of Rydberg nonstabilizerness via a quantum circuit decomposition of the wave function.

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References (70)

  1. A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96, 110404 (2006).
  2. M. Levin and X.-G. Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96, 110405 (2006).
  3. H. Li and F. D. M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-Abelian fractional quantum Hall effect states, Phys. Rev. Lett. 101, 010504 (2008).
  4. F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, Symmetry protection of topological phases in one-dimensional quantum spin systems, Phys. Rev. B 85, 075125 (2012).
  5. P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. (2005) P04010.
  6. J. H. Bardarson, F. Pollmann, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett. 109, 017202 (2012).
  7. M. Serbyn, Z. Papić, and D. A. Abanin, Universal slow growth of entanglement in interacting strongly disordered systems, Phys. Rev. Lett. 110, 260601 (2013).
  8. A. Lukin, M. Rispoli, R. Schittko, M. E. Tai, A. M. Kaufman, S. Choi, V. Khemani, J. Léonard, and M. Greiner, Probing entanglement in a many-body–localized system, Science 364, 256 (2019).
  9. N. Laflorencie, Quantum entanglement in condensed matter systems, Phys. Rep. 646, 1 (2016).
  10. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  11. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011), january 2011 Special Issue.
  12. J. I. Cirac, D. Pérez-García, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys. 93, 045003 (2021).
  13. D. Gottesman, The Heisenberg representation of quantum computers, in Proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics, edited S. P. Corney, R. Delbourgo, and P. D. Jarvis (International Press, Cambridge, MA, 1999), pp. 32–43.
  14. B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Phys. Rev. Lett. 102, 110502 (2009).
  15. E. Knill, Fault-tolerant postselected quantum computation: Schemes, arXiv:quant-ph/0402171.
  16. S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
  17. E. T. Campbell and D. E. Browne, Bound states for magic state distillation in fault-tolerant quantum computation, Phys. Rev. Lett. 104, 030503 (2010).
  18. M. Howard and E. Campbell, Application of a resource theory for magic states to fault-tolerant quantum computing, Phys. Rev. Lett. 118, 090501 (2017).
  19. S. Zhou, Z.-C. Yang, A. Hamma, and C. Chamon, Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics, SciPost Phys. 9, 087 (2020).
  20. K. Goto, T. Nosaka, and M. Nozaki, Probing chaos by magic monotones, Phys. Rev. D 106, 126009 (2022).
  21. Z.-W. Liu and A. Winter, Many-body quantum magic, PRX Quantum 3, 020333 (2022).
  22. L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer Rényi entropy, Phys. Rev. Lett. 128, 050402 (2022).
  23. T. Haug and L. Piroli, Quantifying nonstabilizerness of matrix product states, Phys. Rev. B 107, 035148 (2023).
  24. P. S. Tarabunga, E. Tirrito, T. Chanda, and M. Dalmonte, Many-body magic via Pauli-Markov chains—from criticality to gauge theories, PRX Quantum 4, 040317 (2023).
  25. X. Turkeshi, M. Schirò, and P. Sierant, Measuring nonstabilizerness via multifractal flatness, Phys. Rev. A 108, 042408 (2023).
  26. M. Bejan, C. McLauchlan, and B. Béri, Dynamical magic transitions in monitored clifford+T circuits, PRX Quantum 5, 030332 (2024).
  27. P. Niroula, C. D. White, Q. Wang, S. Johri, D. Zhu, C. Monroe, C. Noel, and M. J. Gullans, Phase transition in magic with random quantum circuits, Nat. Phys. 20, 1786 (2024).
  28. P. S. Tarabunga and C. Castelnovo, Magic in generalized Rokhsar-Kivelson wavefunctions, Quantum 8, 1347 (2024).
  29. T. Haug, L. Aolita, and M. S. Kim, Probing quantum complexity via universal saturation of stabilizer entropies, arXiv:2406.04190.
  30. S. F. E. Oliviero, L. Leone, A. Hamma, and S. Lloyd, Measuring magic on a quantum processor, npj Quantum Inf. 8, 148 (2022).
  31. M. Heinrich and D. Gross, Robustness of magic and symmetries of the stabiliser polytope, Quantum 3, 132 (2019).
  32. S. Sarkar, C. Mukhopadhyay, and A. Bayat, Characterization of an operational quantum resource in a critical many-body system, New J. Phys. 22, 083077 (2020).
  33. P. S. Tarabunga, Critical behaviours of nonstabilizerness in quantum spin chains, Quantum 8, 1413 (2024).
  34. M. Frau, P. S. Tarabunga, M. Collura, M. Dalmonte, and E. Tirrito, Non-stabilizerness versus entanglement in matrix product states, Phys. Rev. B 110, 045101 (2024).
  35. G. Lami and M. Collura, Nonstabilizerness via perfect pauli sampling of matrix product states, Phys. Rev. Lett. 131, 180401 (2023).
  36. Z. Liu and B. K. Clark, Non-equilibrium quantum Monte Carlo algorithm for stabilizer Rényi entropy in spin systems, Phys. Rev. B 111, 085144 (2025).
  37. T. Haug and L. Piroli, Stabilizer entropies and nonstabilizerness monotones, Quantum 7, 1092 (2023).
  38. P. S. Tarabunga, E. Tirrito, M. C. Bañuls, and M. Dalmonte, Nonstabilizerness via matrix product states in the Pauli basis, Phys. Rev. Lett. 133, 010601 (2024).
  39. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  40. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  41. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018).
  42. W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Periodic orbits, entanglement, and quantum many-body scars in constrained models: Matrix product state approach, Phys. Rev. Lett. 122, 040603 (2019).
  43. A. A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, and M. Serbyn, Slow quantum thermalization and many-body revivals from mixed phase space, Phys. Rev. X 10, 011055 (2020).
  44. M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021).
  45. Z. Papić, Weak ergodicity breaking through the lens of quantum entanglement, in Entanglement in Spin Chains: From Theory to Quantum Technology Applications (Springer, Cham, 2022), pp. 341–395.
  46. S. Moudgalya, B. A. Bernevig, and N. Regnault, Quantum many-body scars and Hilbert space fragmentation: A review of exact results, Rep. Prog. Phys. 85, 086501 (2022).
  47. A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, Quantum many-body scars: A quasiparticle perspective, Annu. Rev. Condens. Matter Phys. 14, 443 (2023).
  48. L. Leone and L. Bittel, Stabilizer entropies are monotones for magic-state resource theory, Phys. Rev. A 110, L040403 (2024).
  49. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  50. P. Fendley, K. Sengupta, and S. Sachdev, Competing density-wave orders in a one-dimensional hard-boson model, Phys. Rev. B 69, 075106 (2004).
  51. I. Lesanovsky and H. Katsura, Interacting Fibonacci anyons in a Rydberg gas, Phys. Rev. A 86, 041601(R) (2012).
  52. C.-J. Lin and O. I. Motrunich, Exact quantum many-body scar states in the Rydberg-blockaded atom chain, Phys. Rev. Lett. 122, 173401 (2019).
  53. T. Iadecola, M. Schecter, and S. Xu, Quantum many-body scars from magnon condensation, Phys. Rev. B 100, 184312 (2019).
  54. V. Khemani, C. R. Laumann, and A. Chandran, Signatures of integrability in the dynamics of Rydberg-blockaded chains, Phys. Rev. B 99, 161101(R) (2019).
  55. S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papić, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent SU(2) dynamics and perfect quantum many-body scars, Phys. Rev. Lett. 122, 220603 (2019).
  56. K. Bull, J.-Y. Desaules, and Z. Papić, Quantum scars as embeddings of weakly broken Lie algebra representations, Phys. Rev. B 101, 165139 (2020).
  57. K. Omiya and M. Müller, Quantum many-body scars in bipartite Rydberg arrays originating from hidden projector embedding, Phys. Rev. A 107, 023318 (2023).
  58. J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Time-dependent variational principle for quantum lattices, Phys. Rev. Lett. 107, 070601 (2011).
  59. G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91, 147902 (2003).
  60. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  61. I. Lesanovsky, Many-body spin interactions and the ground state of a dense Rydberg lattice gas, Phys. Rev. Lett. 106, 025301 (2011).
  62. I. Lesanovsky, Liquid ground state, gap, and excited states of a strongly correlated spin chain, Phys. Rev. Lett. 108, 105301 (2012).
  63. Bloqade.jl: Package for the quantum computation and quantum simulation based on the neutral-atom architecture, https://github.com/QuEraComputing/Bloqade.jl/.
  64. L. Zhao, P. R. Datla, W. Tian, M. M. Aliyu, and H. Loh, Observation of quantum thermalization restricted to Hilbert space fragments, Phys. Rev. X 15, 011035 (2025).
  65. F. Verstraete and J. I. Cirac, Matrix product states represent ground states faithfully, Phys. Rev. B 73, 094423 (2006).
  66. M. B. Hastings, An area law for one-dimensional quantum systems, J. Stat. Mech. (2007) P08024.
  67. A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator, Nature (London) 568, 207 (2019).
  68. G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletić, and M. D. Lukin, Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021).
  69. M. Ahmadi, H. B. Dang, G. Gour, and B. C. Sanders, Quantification and manipulation of magic states, Phys. Rev. A 97, 062332 (2018).
  70. A. N. Ivanov and O. I. Motrunich, Volume-entangled exact eigenstates in the PXP and related models in any dimension, Phys. Rev. Lett. 134, 050403 (2025).

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Phys. Rev. B 111, 245148– Published 23 June, 2025
  • Received 21 June 2024
  • Revised 26 April 2025
  • Accepted 30 May 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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