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Optimizing two-qubit gates for ultracold fermions in optical lattices

Jan A. P. Reuter1,2,*, Juhi Singh1,2, Tommaso Calarco1,2,3, Felix Motzoi1,2, and Robert Zeier1,†

  • *Contact author: ja.reuter@fz-juelich.de
  • †Contact author: r.zeier@fz-juelich.de
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Phys. Rev. A 113, 052603 – Published 5 May, 2026

DOI: https://doi.org/10.1103/j6x3-hh74

Abstract

Ultracold neutral atoms in optical lattices are a promising platform for simulating the behavior of complex materials and implementing quantum gates. We optimize collision gates for fermionic Li6 atoms confined in a double-well potential, controlling the laser amplitude and keeping its relative phase constant. We obtain high-fidelity gates based on a one-dimensional confinement simulation. Our approach extends beyond earlier Fermi-Hubbard simulations by capturing a momentum dependence in the interaction energy. This leads to a higher interaction strength when atoms begin in separate subwells compared to the same subwell. This momentum dependence might limit the gate fidelity under realistic experimental conditions, but also enables tailored applications in quantum chemistry and quantum simulation by optimizing gates for each of these cases separately.

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References (60)

  1. D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. B. Ataides, N. Maskara, I. Cong, X. Gao, P. S. Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, et al., Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
  2. S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V. Vuletić, and M. D. Lukin, High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature (London) 622, 268 (2023).
  3. F. Gyger, M. Ammenwerth, R. Tao, H. Timme, S. Snigirev, I. Bloch, and J. Zeiher, Continuous operation of large-scale atom arrays in optical lattices, Phys. Rev. Res. 6, 033104 (2024).
  4. A. L. Shaw, Z. Chen, J. Choi, D. K. Mark, P. Scholl, R. Finkelstein, A. Elben, S. Choi, and M. Endres, Benchmarking highly entangled states on a 60-atom analogue quantum simulator, Nature (London) 628, 71 (2024).
  5. T. Busch, B.-G. Englert, K. Rzażewski, and M. Wilkens, Two cold atoms in a harmonic trap, Found. Phys. 28, 549 (1998).
  6. T. Calarco, E. A. Hinds, D. Jaksch, J. Schmiedmayer, J. I. Cirac, and P. Zoller, Quantum gates with neutral atoms: Controlling collisional interactions in time-dependent traps, Phys. Rev. A 61, 022304 (2000).
  7. Z. Idziaszek and T. Calarco, Two atoms in an anisotropic harmonic trap, Phys. Rev. A 71, 050701(R) (2005).
  8. J.-J. Liang and C. Zhang, Two ultracold atoms in a completely anisotropic trap, Phys. Scr. 77, 025302 (2008).
  9. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  10. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed. (Cambridge University Press, Cambridge, 2020).
  11. D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82, 1975 (1999).
  12. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, Controlled collisions for multi-particle entanglement of optically trapped atoms, Nature (London) 425, 937 (2003).
  13. T. Calarco, U. Dorner, P. S. Julienne, C. J. Williams, and P. Zoller, Quantum computations with atoms in optical lattices: Marker qubits and molecular interactions, Phys. Rev. A 70, 012306 (2004).
  14. M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, Controlled exchange interaction between pairs of neutral atoms in an optical lattice, Nature (London) 448, 452 (2007).
  15. S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A. M. Rey, A. Polkovnikov, E. A. Demler, M. D. Lukin, and I. Bloch, Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices, Science 319, 295 (2008).
  16. B. Yang, H. Sun, C.-J. Huang, H.-Y. Wang, Y. Deng, H.-N. Dai, Z.-S. Yuan, and J.-W. Pan, Cooling and entangling ultracold atoms in optical lattices, Science 369, 550 (2020).
  17. A. Impertro, S. Karch, J. F. Wienand, S. J. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Local readout and control of current and kinetic energy operators in optical lattices, Phys. Rev. Lett. 133, 063401 (2024).
  18. S. Zöllner, G. M. Bruun, and C. J. Pethick, Polarons and molecules in a two-dimensional Fermi gas, Phys. Rev. A 83, 021603(R) (2011).
  19. S. Murmann, A. Bergschneider, V. M. Klinkhamer, G. Zürn, T. Lompe, and S. Jochim, Two fermions in a double well: Exploring a fundamental building block of the Hubbard model, Phys. Rev. Lett. 114, 080402 (2015).
  20. T. Hartke, B. Oreg, N. Jia, and M. Zwierlein, Quantum register of fermion pairs, Nature (London) 601, 537 (2022).
  21. Z. Zhu, Y. Kiefer, S. Jele, M. Gächter, G. Bisson, K. Viebahn, and T. Esslinger, Splitting and connecting singlets in atomic quantum circuits, Phys. Rev. X 15, 041032 (2025).
  22. M. Xu, L. H. Kendrick, A. Kale, Y. Gang, C. Feng, S. Zhang, A. W. Young, M. Lebrat, and M. Greiner, A neutral-atom Hubbard quantum simulator in the cryogenic regime, Nature (London) 642, 909 (2025).
  23. C. Tabares, C. Kokail, P. Zoller, D. González-Cuadra, and A. González-Tudela, Programming optical-lattice Fermi-Hubbard quantum simulators, PRX Quantum 6, 030356 (2025).
  24. D. K. Mark, H.-Y. Hu, J. Kwan, C. Kokail, S. Choi, and S. F. Yelin, Efficiently measuring d-wave pairing and beyond in quantum gas microscopes, Phys. Rev. Lett. 135, 123402 (2025).
  25. Y. Kiefer, Z. Zhu, L. Fischer, S. Jele, M. Gächter, G. Bisson, K. Viebahn, and T. Esslinger, Protected quantum gates using qubit doublons in dynamical optical lattices, Nature (London) 652, 609 (2026).
  26. D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, J. Ye, and P. Zoller, Fermionic quantum processing with programmable neutral atom arrays, Proc. Natl. Acad. Sci. USA 120, e2304294120 (2023).
  27. C. Sanner, L. Sonderhouse, R. B. Hutson, L. Yan, W. R. Milner, and J. Ye, Pauli blocking of atom-light scattering, Science 374, 979 (2021).
  28. S. H. Hauck and V. M. Stojanović, Coherent atom transport via enhanced shortcuts to adiabaticity: Double-well optical lattice, Phys. Rev. Appl. 18, 014016 (2022).
  29. C. Cicali, M. Calzavara, E. Cuestas, T. Calarco, R. Zeier, and F. Motzoi, Fast neutral-atom transport and transfer between optical tweezers, Phys. Rev. Appl. 24, 024070 (2025).
  30. T. Chalopin, P. Bojović, D. Bourgund, S. Wang, T. Franz, I. Bloch, and T. Hilker, Optical superlattice for engineering Hubbard couplings in quantum simulation, Phys. Rev. Lett. 134, 053402 (2025).
  31. P. Bojović, T. Hilker, S. Wang, J. Obermeyer, M. Barendregt, D. Tell, T. Chalopin, P. M. Preiss, I. Bloch, and T. Franz, High-fidelity collisional quantum gates with fermionic atoms, Nature (London) 652, 602 (2026).
  32. J. Nemirovsky and Y. Sagi, Fast universal two-qubit gate for neutral fermionic atoms in optical tweezers, Phys. Rev. Res. 3, 013113 (2021).
  33. J. Singh, J. A. P. Reuter, T. Calarco, F. Motzoi, and R. Zeier, Optimizing two-qubit gates for ultracold atoms using Fermi-Hubbard models, Phys. Rev. Appl. 24, 034007 (2025).
  34. F. Gkritsis, D. Dux, J. Zhang, N. Jain, C. Gogolin, and P. M. Preiss, Simulating chemistry with fermionic optical superlattices, PRX Quantum 6, 010318 (2025).
  35. P. Bojović, Experimental data provided by the Max Planck Institute of Quantum Optics.
  36. G. H. Wannier, The structure of electronic excitation levels in insulating crystals, Phys. Rev. 52, 191 (1937).
  37. W. Kohn, Analytic properties of Bloch waves and Wannier functions, Phys. Rev. 115, 809 (1959).
  38. W. Kohn, Construction of Wannier functions and applications to energy bands, Phys. Rev. B 7, 4388 (1973).
  39. Z. Hadzibabic and J. Dalibard, Two-dimensional Bose fluids: An atomic physics perspective, Riv. Nuovo Cimento 34, 389 (2011).
  40. E. Haller, M. J. Mark, R. Hart, J. G. Danzl, L. Reichsöllner, V. Melezhik, P. Schmelcher, and H.-C. Nägerl, Confinement-induced resonances in low-dimensional quantum systems, Phys. Rev. Lett. 104, 153203 (2010).
  41. F. Lorenzi, A. Bardin, and L. Salasnich, On-shell approximation for the s-wave scattering theory, Phys. Rev. A 107, 033325 (2023).
  42. T. Bergeman, M. G. Moore, and M. Olshanii, Atom-atom scattering under cylindrical harmonic confinement: Numerical and analytic studies of the confinement induced resonance, Phys. Rev. Lett. 91, 163201 (2003).
  43. D. S. Petrov and G. V. Shlyapnikov, Interatomic collisions in a tightly confined Bose gas, Phys. Rev. A 64, 012706 (2001).
  44. O. V. Sinkin, R. Holzlöhner, J. Zweck, and C. R. Menyuk, Optimization of the split-step Fourier method in modeling optical-fiber communications systems, J. Lightwave Technol. 21, 61 (2003).
  45. S. Montangero, E. Montangero, and Evenson, Introduction to Tensor Network Methods (Springer, Cham, 2018).
  46. W. Bao, S. Jin, and P. A. Markowich, On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime, J. Comput. Phys. 175, 487 (2002).
  47. R. L. Speth, W. H. Green, S. MacNamara, and G. Strang, Balanced splitting and rebalanced splitting, SIAM J. Numer. Anal. 51, 3084 (2013).
  48. B. Numerov, Note on the numerical integration of d2x/dt2=f(x,t), Astron. Nachr. 230, 359 (1927).
  49. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (CRC Press, Boca Raton, FL, 2021).
  50. I. Kuprov and C. T. Rodgers, Derivatives of spin dynamics simulations, J. Chem. Phys. 131, 234108 (2009).
  51. S. Machnes, E. Assémat, D. Tannor, and F. K. Wilhelm, Tunable, flexible, and efficient optimization of control pulses for practical qubits, Phys. Rev. Lett. 120, 150401 (2018).
  52. K.-T. Tang, Mathematical Methods for Engineers and Scientists (Springer, Berlin, 2007), Vol. 3.
  53. J. Singh, R. Zeier, T. Calarco, and F. Motzoi, Compensating for nonlinear distortions in controlled quantum systems, Phys. Rev. Appl. 19, 064067 (2023).
  54. F. Motzoi, J. M. Gambetta, S. T. Merkel, and F. K. Wilhelm, Optimal control methods for rapidly time-varying Hamiltonians, Phys. Rev. A 84, 022307 (2011).
  55. S. Yang, G. Masella, V. Moeini, A. Bellahsene, C. Li, T. Bienaimé, and S. Whitlock, Compact arbitrary optical waveform modulator with digital feedback, Phys. Rev. Appl. 23, 054009 (2025).
  56. P. K. Mogensen and A. N. Riseth, Optim: A mathematical optimization package for Julia, J. Open Source Softw. 3, 615 (2018).
  57. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172, 296 (2005).
  58. P. de Fouquieres, S. Schirmer, S. Glaser, and I. Kuprov, Second order gradient ascent pulse engineering, J. Magn. Reson. 212, 412 (2011).
  59. M. Dalgaard, F. Motzoi, J. H. M. Jensen, and J. Sherson, Hessian-based optimization of constrained quantum control, Phys. Rev. A 102, 042612 (2020).
  60. J. A. P. Reuter, J. Singh, T. Calarco, F. Motzoi, and R. Zeier, Data for “optimizing two-qubit gates for ultracold fermions in optical lattices” [Data set], Zenodo (2026), https://doi.org/10.5281/zenodo.18891172.

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Phys. Rev. A 113, 052603– Published 5 May, 2026
  • Received 11 December 2025
  • Accepted 6 April 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.

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