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Scalable platform for qudit-based quantum computing using polar molecules

Soleh Kh. Muminov1,2,*, Evgeniy O. Kiktenko1,3, Anastasiia S. Nikolaeva1,4,†, Denis A. Drozhzhin1,4, Sergey I. Matveenko1,5, Aleksey K. Fedorov1,4, and Georgy V. Shlyapnikov1,6,7

  • *Contact author: solehm@mail.ru
  • †Contact author: anastasiia.nikolaeva21@gmail.com
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Phys. Rev. Research 8, 023014 – Published 2 April, 2026

DOI: https://doi.org/10.1103/tcqw-ll6v

Abstract

We propose a scalable qudit-based quantum processor using rotational states of polar molecules. Previously, molecular internal states were used to enlarge Hilbert space, whereas our approach uses optical tweezer arrays to achieve scalable architectures with exponential state-space growth without increasing qudit dimensionality d. Entangling gates are implemented by adiabatically bringing traps together to activate dipole-dipole interactions. We develop encoding schemes mapping single qubits into qudits with 2≤d≤5 and pairs of qubits into d=4,5 qudits, enabling universal set of quantum gates. Additional levels in d=3 and d=5 qudits simplify multiqubit gate decompositions. We analyze experimental parameters for SrF and NaCs molecules. This approach provides a promising route to scalable quantum information processing with multilevel systems using existing experimental platforms.

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References (106)

  1. A. Muthukrishnan and C. R. Stroud, Jr., Multivalued logic gates for quantum computation, Phys. Rev. A 62, 052309 (2000).
  2. S. D. Bartlett, H. de Guise, and B. C. Sanders, Quantum encodings in spin systems and harmonic oscillators, Phys. Rev. A 65, 052316 (2002).
  3. Z. Zilic and K. Radecka, Scaling and better approximating quantum Fourier transform by higher radices, IEEE Trans. Comput. 56, 202 (2007).
  4. V. Parasa and M. Perkowski, Quantum phase estimation using multivalued logic, in Proceedings of the 41st IEEE International Symposium on Multiple-Valued Logic, Tuusula, Finland (IEEE, Piscataway, NJ, 2011), pp. 224–229.
  5. E. T. Campbell, H. Anwar, and D. E. Browne, Magic-state distillation in all prime dimensions using quantum Reed-Muller codes, Phys. Rev. X 2, 041021 (2012).
  6. G. Duclos-Cianci and D. Poulin, Kitaev’s Zd-code threshold estimates, Phys. Rev. A 87, 062338 (2013).
  7. E. T. Campbell, Enhanced fault-tolerant quantum computing in d-level systems, Phys. Rev. Lett. 113, 230501 (2014).
  8. H. Anwar, B. J. Brown, E. T. Campbell, and D. E. Browne, Fast decoders for qudit topological codes, New J. Phys. 16, 063038 (2014).
  9. R. S. Andrist, J. R. Wootton, and H. G. Katzgraber, Error thresholds for Abelian quantum double models: Increasing the bit-flip stability of topological quantum memory, Phys. Rev. A 91, 042331 (2015).
  10. F. H. Watson, E. T. Campbell, H. Anwar, and D. E. Browne, Qudit color codes and gauge color codes in all spatial dimensions, Phys. Rev. A 92, 022312 (2015).
  11. A. Krishna and J.-P. Tillich, Towards low overhead magic state distillation, Phys. Rev. Lett. 123, 070507 (2019).
  12. E. O. Kiktenko, A. S. Nikolaeva, and A. K. Fedorov, Colloquium: Qudits for decomposing multiqubit gates and realizing quantum algorithms, Rev. Mod. Phys. 97, 021003 (2025).
  13. A. D. Greentree, S. G. Schirmer, F. Green, L. C. L. Hollenberg, A. R. Hamilton, and R. G. Clark, Maximizing the Hilbert space for a finite number of distinguishable quantum states, Phys. Rev. Lett. 92, 097901 (2004).
  14. E. O. Kiktenko, A. K. Fedorov, O. V. Man’ko, and V. I. Man’ko, Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities, Phys. Rev. A 91, 042312 (2015).
  15. E. O. Kiktenko, A. K. Fedorov, A. A. Strakhov, and V. I. Man'ko, Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits, Phys. Lett. A 379, 1409 (2015).
  16. T. C. Ralph, K. J. Resch, and A. Gilchrist, Efficient Toffoli gates using qudits, Phys. Rev. A 75, 022313 (2007).
  17. A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature (London) 481, 170 (2012).
  18. L. B. Nguyen, N. Goss, K. Siva, Y. Kim, E. Younis, B. Qing, A. Hashim, D. I. Santiago, and I. Siddiqi, Empowering a qudit-based quantum processor by traversing the dual bosonic ladder, Nat. Commun. 15, 7117 (2024).
  19. E. O. Kiktenko, A. S. Nikolaeva, P. Xu, G. V. Shlyapnikov, and A. K. Fedorov, Scalable quantum computing with qudits on a graph, Phys. Rev. A 101, 022304 (2020).
  20. A. S. Nikolaeva, I. V. Zalivako, A. S. Borisenko, N. V. Semenin, K. P. Galstyan, A. E. Korolkov, E. O. Kiktenko, K. Y. Khabarova, I. A. Semerikov, A. K. Fedorov, and N. N. Kolachevsky, Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits, Phys. Rev. Lett. 135, 060601 (2025).
  21. K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru-Guzik, Noisy intermediate-scale quantum algorithms, Rev. Mod. Phys. 94, 015004 (2022).
  22. A. Morvan, V. V. Ramasesh, M. S. Blok, J. M. Kreikebaum, K. O’Brien, L. Chen, B. K. Mitchell, R. K. Naik, D. I. Santiago, and I. Siddiqi, Qutrit randomized benchmarking, Phys. Rev. Lett. 126, 210504 (2021).
  23. N. Goss, A. Morvan, B. Marinelli, B. K. Mitchell, L. B. Nguyen, R. K. Naik, L. Chen, C. Jünger, J. M. Kreikebaum, D. I. Santiago, et al., High-fidelity qutrit entangling gates for superconducting circuits, Nat. Commun. 13, 7481 (2022).
  24. Y. Sung, A. Vepsäläinen, J. Braumüller, F. Yan, J. I.-J. Wang, M. Kjaergaard, R. Winik, P. Krantz, A. Bengtsson, A. J. Melville, et al., Multi-level quantum noise spectroscopy, Nat. Commun. 12, 967 (2021).
  25. M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, A universal qudit quantum processor with trapped ions, Nat. Phys. 18, 1053 (2022).
  26. I. V. Zalivako, A. S. Nikolaeva, A. S. Borisenko, A. E. Korolkov, P. L. Sidorov, K. P. Galstyan, N. V. Semenin, V. N. Smirnov, M. A. Aksenov, K. M. Makushin, et al., Towards a multiqudit quantum processor based on a 171Yb+ ion string: Realizing basic quantum algorithms, Quantum Rep. 7, 19 (2025).
  27. Y. Fu, W. Liu, X. Ye, Y. Wang, C. Zhang, C.-K. Duan, X. Rong, and J. Du, Experimental investigation of quantum correlations in a two-qutrit spin system, Phys. Rev. Lett. 129, 100501 (2022).
  28. H. Zhou, H. Gao, N. T. Leitao, O. Makarova, I. Cong, A. M. Douglas, L. S. Martin, and M. D. Lukin, Robust Hamiltonian engineering for interacting qudit systems, Phys. Rev. X 14, 031017 (2024).
  29. I. F. de Fuentes, T. Botzem, M. A. Johnson, A. Vaartjes, S. Asaad, V. Mourik, F. E. Hudson, K. M. Itoh, B. C. Johnson, A. M. Jakob, et al., Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields, Nat. Commun. 15, 1380 (2024).
  30. D. González-Cuadra, T. V. Zache, J. Carrasco, B. Kraus, and P. Zoller, Hardware efficient quantum simulation of non-Abelian gauge theories with qudits on Rydberg platforms, Phys. Rev. Lett. 129, 160501 (2022).
  31. R. Sawant, J. A. Blackmore, P. D. Gregory, J. Mur-Petit, D. Jaksch, J. Aldegunde, J. M. Hutson, M. R. Tarbutt, and S. L. Cornish, Ultracold polar molecules as qudits, New J. Phys. 22, 013027 (2020).
  32. K.-K. Ni, S. Ospelkaus, M. De Miranda, A. Pe’Er, B. Neyenhuis, J. Zirbel, S. Kotochigova, P. Julienne, D. Jin, and J. Ye, A high phase-space-density gas of polar molecules, Science 322, 231 (2008).
  33. S. A. Moses, J. P. Covey, M. T. Miecnikowski, B. Yan, B. Gadway, J. Ye, and D. S. Jin, Creation of a low-entropy quantum gas of polar molecules in an optical lattice, Science 350, 659 (2015).
  34. M. Wall, K. Maeda, and L. D. Carr, Realizing unconventional quantum magnetism with symmetric top molecules, New J. Phys. 17, 025001 (2015).
  35. S. R. Manmana, E. Stoudenmire, K. R. Hazzard, A. M. Rey, and A. V. Gorshkov, Topological phases in ultracold polar-molecule quantum magnets, Phys. Rev. B 87, 081106 (2013).
  36. L. Anderegg, B. L. Augenbraun, Y. Bao, S. Burchesky, L. W. Cheuk, W. Ketterle, and J. M. Doyle, Laser cooling of optically trapped molecules, Nat. Phys. 14, 890 (2018).
  37. J. Deiglmayr, A. Grochola, M. Repp, K. Mörtlbauer, C. Glück, J. Lange, O. Dulieu, R. Wester, and M. Weidemüller, Formation of ultracold polar molecules in the rovibrational ground state, Phys. Rev. Lett. 101, 133004 (2008).
  38. S. Ospelkaus, K.-K. Ni, D. Wang, M. De Miranda, B. Neyenhuis, G. Quéméner, P. Julienne, J. Bohn, D. Jin, and J. Ye, Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules, Science 327, 853 (2010).
  39. K.-K. Ni, S. Ospelkaus, D. Wang, G. Quéméner, B. Neyenhuis, M. De Miranda, J. Bohn, J. Ye, and D. Jin, Dipolar collisions of polar molecules in the quantum regime, Nature (London) 464, 1324 (2010).
  40. M. De Miranda, A. Chotia, B. Neyenhuis, D. Wang, G. Quéméner, S. Ospelkaus, J. Bohn, J. Ye, and D. Jin, Controlling the quantum stereodynamics of ultracold bimolecular reactions, Nat. Phys. 7, 502 (2011).
  41. B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, Observation of dipolar spin-exchange interactions with lattice-confined polar molecules, Nature (London) 501, 521 (2013).
  42. K. R. Hazzard, B. Gadway, M. Foss-Feig, B. Yan, S. A. Moses, J. P. Covey, N. Y. Yao, M. D. Lukin, J. Ye, D. S. Jin, et al., Many-body dynamics of dipolar molecules in an optical lattice, Phys. Rev. Lett. 113, 195302 (2014).
  43. L. D. Carr, D. DeMille, R. V. Krems, and J. Ye, Cold and ultracold molecules: Science, technology and applications, New J. Phys. 11, 055049 (2009).
  44. A. André, D. DeMille, J. M. Doyle, M. D. Lukin, S. E. Maxwell, P. Rabl, R. J. Schoelkopf, and P. Zoller, A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators, Nat. Phys. 2, 636 (2006).
  45. A. M. Kaufman and K.-K. Ni, Quantum science with optical tweezer arrays of ultracold atoms and molecules, Nat. Phys. 17, 1324 (2021).
  46. D. DeMille, Quantum computation with trapped polar molecules, Phys. Rev. Lett. 88, 067901 (2002).
  47. P. D. Gregory, J. A. Blackmore, S. L. Bromley, J. M. Hutson, and S. L. Cornish, Robust storage qubits in ultracold polar molecules, Nat. Phys. 17, 1149 (2021).
  48. L. R. Picard, A. J. Park, G. E. Patenotte, S. Gebretsadkan, D. Wellnitz, A. M. Rey, and K.-K. Ni, Entanglement and iSWAP gate between molecular qubits, Nature (London) 637, 821 (2025).
  49. K.-K. Ni, T. Rosenband, and D. D. Grimes, Dipolar exchange quantum logic gate with polar molecules, Chem. Sci. 9, 6830 (2018).
  50. Y. Bao, S. S. Yu, L. Anderegg, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, Dipolar spin-exchange and entanglement between molecules in an optical tweezer array, Science 382, 1138 (2023).
  51. L. Caldwell, H. J. Williams, N. J. Fitch, J. Aldegunde, J. M. Hutson, B. E. Sauer, and M. R. Tarbutt, Long rotational coherence times of molecules in a magnetic trap, Phys. Rev. Lett. 124, 063001 (2020).
  52. D. K. Ruttley, T. R. Hepworth, A. Guttridge, and S. L. Cornish, Long-lived entanglement of molecules in magic-wavelength optical tweezers, Nature (London) 637, 827 (2025).
  53. D. Mitra, K. H. Leung, and T. Zelevinsky, Quantum control of molecules for fundamental physics, Phys. Rev. A 105, 040101 (2022).
  54. E. R. Hudson, H. Lewandowski, B. C. Sawyer, and J. Ye, Cold molecule spectroscopy for constraining the evolution of the fine structure constant, Phys. Rev. Lett. 96, 143004 (2006).
  55. T. Zelevinsky, S. Kotochigova, and J. Ye, Precision test of mass-ratio variations with lattice-confined ultracold molecules, Phys. Rev. Lett. 100, 043201 (2008).
  56. D. DeMille, S. Sainis, J. Sage, T. Bergeman, S. Kotochigova, and E. Tiesinga, Enhanced sensitivity to variation of me/mp in molecular spectra, Phys. Rev. Lett. 100, 043202 (2008).
  57. B. E. Sauer, H. T. Ashworth, J. J. Hudson, M. R. Tarbutt, and E. A. Hinds, Probing the electron EDM with cold molecules, AIP Conf. Proc. 869, 44 (2006).
  58. A. C. Vutha, W. C. Campbell, Y. V. Gurevich, N. R. Hutzler, M. Parsons, D. Patterson, E. Petrik, B. Spaun, J. M. Doyle, G. Gabrielse, and D. DeMille, Search for the electric dipole moment of the electron with thorium monoxide, Phys. B: At. Mol. Opt. Phys. 44, 079803 (2011).
  59. M. Hughes, M. D. Frye, R. Sawant, G. Bhole, J. A. Jones, S. L. Cornish, M. Tarbutt, J. M. Hutson, D. Jaksch, and J. Mur-Petit, Robust entangling gate for polar molecules using magnetic and microwave fields, Phys. Rev. A 101, 062308 (2020).
  60. F. Herrera, Y. Cao, S. Kais, and K. B. Whaley, Infrared-dressed entanglement of cold open-shell polar molecules for universal matchgate quantum computing, New J. Phys. 16, 075001 (2014).
  61. E. S. Shuman, J. F. Barry, and D. DeMille, Laser cooling of a diatomic molecule, Nature (London) 467, 820 (2010).
  62. L. Anderegg, L. W. Cheuk, Y. Bao, S. Burchesky, W. Ketterle, K.-K. Ni, and J. M. Doyle, An optical tweezer array of ultracold molecules, Science 365, 1156 (2019).
  63. D. K. Ruttley, A. Guttridge, S. Spence, R. C. Bird, C. R. Le Sueur, J. M. Hutson, and S. L. Cornish, Formation of ultracold molecules by merging optical tweezers, Phys. Rev. Lett. 130, 223401 (2023).
  64. S. F. Yelin, K. Kirby, and R. Côté, Schemes for robust quantum computation with polar molecules, Phys. Rev. A 74, 050301 (2006).
  65. A. Micheli, G. K. Brennen, and P. Zoller, A toolbox for lattice-spin models with polar molecules, Nat. Phys. 2, 341 (2006).
  66. A. V. Gorshkov, S. R. Manmana, G. Chen, J. Ye, E. Demler, M. D. Lukin, and A. M. Rey, Tunable superfluidity and quantum magnetism with ultracold polar molecules, Phys. Rev. Lett. 107, 115301 (2011).
  67. J. W. Park, Z. Z. Yan, H. Loh, S. A. Will, and M. W. Zwierlein, Second-scale nuclear spin coherence time of ultracold 23Na40K molecules, Science 357, 372 (2017).
  68. P. D. Gregory, L. M. Fernley, A. L. Tao, S. L. Bromley, J. Stepp, Z. Zhang, S. Kotochigova, K. R. Hazzard, and S. L. Cornish, Second-scale rotational coherence and dipolar interactions in a gas of ultracold polar molecules, Nat. Phys. 20, 415 (2024).
  69. S. Ospelkaus, K.-K. Ni, G. Quéméner, B. Neyenhuis, D. Wang, M. De Miranda, J. Bohn, J. Ye, and D. Jin, Controlling the hyperfine state of rovibronic ground-state polar molecules, Phys. Rev. Lett. 104, 030402 (2010).
  70. J. A. Blackmore, L. Caldwell, P. D. Gregory, E. M. Bridge, R. Sawant, J. Aldegunde, J. Mur-Petit, D. Jaksch, J. M. Hutson, B. Sauer, et al., Ultracold molecules for quantum simulation: Rotational coherences in CaF and RbCs, Quantum Sci. Technol. 4, 014010 (2018).
  71. S. A. Will, J. W. Park, Z. Z. Yan, H. Loh, and M. W. Zwierlein, Coherent microwave control of ultracold Na23 K40 molecules, Phys. Rev. Lett. 116, 225306 (2016).
  72. Z. Ji, T. Gong, Y. He, J. M. Hutson, Y. Zhao, L. Xiao, and S. Jia, Microwave coherent control of ultracold ground-state molecules formed by short-range photoassociation, Phys. Chem. Chem. Phys. 22, 13002 (2020).
  73. T. R. Hepworth, D. K. Ruttley, F. von Gierke, P. D. Gregory, A. Guttridge, and S. L. Cornish, Long-lived multilevel coherences and spin-1 dynamics encoded in the rotational states of ultracold molecules, Nat. Commun. 16, 7131 (2025).
  74. Q. Wei, S. Kais, B. Friedrich, and D. Herschbach, Entanglement of polar symmetric top molecules as candidate qubits, J. Chem. Phys. 135, 154102 (2011).
  75. Z.-Y. Zhang and J.-M. Liu, Creation of high-dimensional entanglement of polar molecules via optimal control fields, Phys. Rev. A 105, 023113 (2022).
  76. F. Luis, P. J. Alonso, O. Roubeau, V. Velasco, D. Zueco, D. Aguilà, J. I. Martínez, L. A. Barrios, and G. Aromí, A dissymmetric [Gd2] coordination molecular dimer hosting six addressable spin qubits, Commun. Chem. 3, 176 (2020).
  77. A. Hernández-Antón, F. Luis, and A. Castro, Optimal control of spin qudits subject to decoherence using amplitude-and-frequency-constrained pulses, Quantum Sci. Technol. 10, 025042 (2025).
  78. J. T. Zhang, L. R. Picard, W. B. Cairncross, K. Wang, Y. Yu, F. Fang, and K.-K. Ni, An optical tweezer array of ground-state polar molecules, Quantum Sci. Technol. 7, 035006 (2022).
  79. D. K. Ruttley, A. Guttridge, T. R. Hepworth, and S. L. Cornish, Enhanced quantum control of individual ultracold molecules using optical tweezer arrays, PRX Quantum 5, 020333 (2024).
  80. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory), Course on Theoretical Physics, Vol. 3 (Elsevier Butterworth-Heinemann, Oxford, 2013).
  81. G. Brennen, D. O’Leary, and S. Bullock, Criteria for exact qudit universality, Phys. Rev. A 71, 052318 (2005).
  82. D. A. Drozhzhin, E. O. Kiktenko, A. K. Fedorov, and A. S. Nikolaeva, Transition-aware decomposition of single-qudit gates, Entropy 28, 56 (2025).
  83. A. S. Nikolaeva, E. O. Kiktenko, and A. K. Fedorov, Efficient realization of quantum algorithms with qudits, EPJ Quantum Technol. 11, 43 (2024).
  84. W. E. Ernst, J. Kändler, S. Kindt, and T. Törring, Electric dipole moment of SrF X2Σ+ from high-precision Stark effect measurements, Chem. Phys. Lett. 113, 351 (1985).
  85. Y. Hao, L. F. Pašteka, L. Visscher, P. Aggarwal, H. L. Bethlem, A. Boeschoten, A. Borschevsky, M. Denis, K. Esajas, S. Hoekstra, et al., High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling, J. Chem. Phys. 151, 034302 (2019).
  86. C. Haimberger, J. Kleinert, P. Zabawa, A. Wakim, and N. P. Bigelow, Formation of ultracold, highly polar X1Σ+ NaCs molecules, New J. Phys. 11, 055042 (2009).
  87. Y. Florshaim, E. Zohar, D. Z. Koplovich, I. Meltzer, R. Weill, J. Nemirovsky, A. Stern, and Y. Sagi, Spatial adiabatic passage of ultracold atoms in optical tweezers, Sci. Adv. 10, eadl1220 (2024).
  88. L. Caldwell and M. R. Tarbutt, Enhancing dipolar interactions between molecules using state-dependent optical tweezer traps, Phys. Rev. Lett. 125, 243201 (2020).
  89. L. Caldwell and M. R. Tarbutt, General approach to state-dependent optical-tweezer traps for polar molecules, Phys. Rev. Res. 3, 013291 (2021).
  90. S. Will (private communication).
  91. S. Burchesky, L. Anderegg, Y. Bao, S. S. Yu, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, Rotational coherence times of polar molecules in optical tweezers, Phys. Rev. Lett. 127, 123202 (2021).
  92. R. Bause, M. Li, A. Schindewolf, X.-Y. Chen, M. Duda, S. Kotochigova, I. Bloch, and X.-Y. Luo, Tune-out and magic wavelengths for ground-state Na23 K40 molecules, Phys. Rev. Lett. 125, 023201 (2020).
  93. J. A. Blackmore, R. Sawant, P. D. Gregory, S. L. Bromley, J. Aldegunde, J. M. Hutson, and S. L. Cornish, Controlling the ac Stark effect of RbCs with dc electric and magnetic fields, Phys. Rev. A 102, 053316 (2020).
  94. C. P. Williams, Quantum gates, in Explorations in Quantum Computing, Texts in Computer Science (Springer, London, 2011), pp. 51–122.
  95. A. S. Nikolaeva, E. O. Kiktenko, and A. K. Fedorov, Decomposing the generalized Toffoli gate with qutrits, Phys. Rev. A 105, 032621 (2022).
  96. R. Grimm, M. Weidemüller, and Y. B. Ovchinnikov, Optical dipole traps for neutral atoms, Adv. At. Mol. Opt. Phys. 42, 95 (2000).
  97. R. A. Cline, J. D. Miller, M. R. Matthews, and D. J. Heinzen, Spin relaxation of optically trapped atoms by light scattering, Opt. Lett. 19, 207 (1994).
  98. L. Caldwell and M. R. Tarbutt, Sideband cooling of molecules in optical traps, Phys. Rev. Res. 2, 013251 (2020).
  99. S. Kotochigova, Q. Guan, E. Tiesinga, V. Scarola, B. DeMarco, and B. Gadway, Rotational magic conditions for ultracold molecules in the presence of Raman and Rayleigh scattering, New J. Phys. 26, 063025 (2024).
  100. M. Bergonzoni, S. Jandura, and G. Pupillo, iSWAP gate with polar molecules: Robustness criteria for entangling operations, Phys. Rev. A 112, 032621 (2025).
  101. See Supplemental Material at http://link.aps.org/supplemental/10.1103/tcqw-ll6v for detailed derivations and numerical analysis, which includes Refs. [51, 67, 102, 103, 104, 105, 106].
  102. J. Aldegunde and J. M. Hutson, Hyperfine structure of alkali-metal diatomic molecules, Phys. Rev. A 96, 042506 (2017).
  103. P. A. Bonczyk and V. W. Hughes, Hyperfine structure of the v = 0, J = 1 state in Rb85F, Rb87F, K39F, and K41F by the molecular-beam electric-resonance method, Phys. Rev. 161, 15 (1967).
  104. J. Aldegunde and J. M. Hutson, Hyperfine structure of 2Σ molecules containing alkaline-earth-metal atoms, Phys. Rev. A 97, 042505 (2018).
  105. W. J. Childs, L. S. Goodman, and I. Renhorn, Radio-frequency optical double-resonance spectrum of SrF: The X2Σ+ state, J. Mol. Spectrosc. 87, 522 (1981).
  106. J. Lin, J. He, M. Jin, G. Chen, and D. Wang, Seconds-scale coherence on nuclear spin transitions of ultracold polar molecules in 3D optical lattices, Phys. Rev. Lett. 128, 223201 (2022).

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Phys. Rev. Research 8, 023014– Published 2 April, 2026
  • Received 22 August 2025
  • Accepted 2 March 2026
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