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Parametrized multiqubit gates for neutral-atom quantum platforms

Madhav Mohan1,*, Julius de Hond2, and Servaas Kokkelmans1

  • *Contact author: m.mohan@tue.nl

Phys. Rev. Applied 23, 054074 – Published 27 May, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.054074

Abstract

A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral-atom platform has the capability to implement native N-qubit gates (for N2). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls—laser pulses to excite an atom to Rydberg states—that implement phase gates with one and two controls, the C1P and C2P gates, respectively, on neutral-atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. In addition, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral-atom hardware.

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References (73)

  1. H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, A tweezer array with 6100 highly coherent atomic qubits, arXiv:2403.12021.
  2. D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner et al., A quantum processor based on coherent transport of entangled atom arrays, Nature 604, 451 (2022).
  3. R. B.-S. Tsai, X. Sun, A. L. Shaw, R. Finkelstein, and M. Endres, Benchmarking and fidelity response theory of high-fidelity Rydberg entangling gates, PRX Quantum 6, 010331 (2025).
  4. A. G. Radnaev, W. C. Chung, D. C. Cole, D. Mason, T. G. Ballance, M. J. Bedalov, D. A. Belknap, M. R. Berman, M. Blakely, I. L. Bloomfield et al., A universal neutral-atom quantum computer with individual optical addressing and non-destructive readout, arXiv:2408.08288.
  5. D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2023).
  6. S. E. Rasmussen, K. Groenland, R. Gerritsma, K. Schoutens, and N. T. Zinner, Single-step implementation of high-fidelity n-bit Toffoli gates, Phys. Rev. A 101, 022308 (2020).
  7. D. Crow, R. Joynt, and M. Saffman, Improved error thresholds for measurement-free error correction, Phys. Rev. Lett. 117, 130503 (2016).
  8. M. A. Perlin, V. N. Premakumar, J. Wang, M. Saffman, and R. Joynt, Fault-tolerant measurement-free quantum error correction with multiqubit gates, Phys. Rev. A 108, 062426 (2023).
  9. K. Mølmer, L. Isenhower, and M. Saffman, Efficient Grover search with Rydberg blockade, J. Phys. B 44, 184016 (2011).
  10. R. J. P. T. de Keijzer, V. E. Colussi, B. Škorić, and S. J. J. M. F. Kokkelmans, Optimization of the variational quantum eigensolver for quantum chemistry applications, AVS Quantum Sci. 4, 010501 (2022).
  11. T. Patel, D. Silver, and D. Tiwari, Geyser: A compilation framework for quantum computing with neutral atoms, in Proc. 49th Annu. Int. Symp. Comput. Arch. (ACM, New York, 2022), pp. 383–395.
  12. K. Staudacher, L. Schmid, J. Zeiher, R. Wille, and D. Kranzlmüller, Multi-controlled phase gate synthesis with ZX-calculus applied to neutral atom hardware, Electron. Proc. Theor. Comput. Sci. 406, 96 (2024).
  13. S. Jandura and G. Pupillo, Time-optimal two- and three-qubit gates for Rydberg atoms, Quantum 6, 712 (2022).
  14. M. Khazali and K. Mølmer, Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits, Phys. Rev. X 10, 021054 (2020).
  15. S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara et al., High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature 622, 268 (2023).
  16. L. Isenhower, M. Saffman, and K. Mølmer, Multibit CkNOT quantum gates via Rydberg blockade, Quantum Inf. Process. 10, 755 (2011).
  17. D. Yu, H. Wang, J.-M. Liu, S.-L. Su, J. Qian, and W. Zhang, Multiqubit Toffoli gates and optimal geometry with Rydberg atoms, Phys. Rev. Appl. 18, 034072 (2022).
  18. J.-L. Wu, Y. Wang, J.-X. Han, Y.-K. Feng, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, One-step implementation of Rydberg-antiblockade SWAP and controlled-SWAP gates with modified robustness, Photonics Res. 9, 814 (2021).
  19. Y. Xiao, Y.-H. Kang, R.-H. Zheng, J. Song, Y.-H. Chen, and Y. Xia, Effective nonadiabatic holonomic SWAP gate with Rydberg atoms using invariant-based reverse engineering, Phys. Rev. A 109, 062610 (2024).
  20. P.-Y. Song, J.-F. Wei, P. Xu, L.-L. Yan, M. Feng, S.-L. Su, and G. Chen, Fast realization of high-fidelity nonadiabatic holonomic quantum gates with a time-optimal-control technique in Rydberg atoms, Phys. Rev. A 109, 022613 (2024).
  21. A. Cao, W. J. Eckner, T. Lukin Yelin, A. W. Young, S. Jandura, L. Yan, K. Kim, G. Pupillo, J. Ye, N. D. Oppong, and A. M. Kaufman, Multi-qubit gates and Schrödinger cat states in an optical clock, Nature 634, 315 (2024).
  22. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, Parallel implementation of high-fidelity multiqubit gates with neutral atoms, Phys. Rev. Lett. 123, 170503 (2019).
  23. F. Sauvage and F. Mintert, Optimal control of families of quantum gates, Phys. Rev. Lett. 129, 050507 (2022).
  24. C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, and F. K. Wilhelm, Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol. 9, 19 (2022).
  25. Z. An, H.-J. Song, Q.-K. He, and D. L. Zhou, Quantum optimal control of multilevel dissipative quantum systems with reinforcement learning, Phys. Rev. A 103, 012404 (2021).
  26. T. Fösel, P. Tighineanu, T. Weiss, and F. Marquardt, Reinforcement learning with neural networks for quantum feedback, Phys. Rev. X 8, 031084 (2018).
  27. M. Y. Niu, S. Boixo, V. N. Smelyanskiy, and H. Neven, Universal quantum control through deep reinforcement learning, Npj Quantum Inf. 5, 33 (2019).
  28. M. Dalgaard, F. Motzoi, J. J. Sørensen, and J. Sherson, Global optimization of quantum dynamics with AlphaZero deep exploration, Npj Quantum Inf. 6, 6 (2020).
  29. I. Khait, J. Carrasquilla, and D. Segal, Optimal control of quantum thermal machines using machine learning, Phys. Rev. Res. 4, L012029 (2022).
  30. K. Hornik, Approximation capabilities of multilayer feedforward networks, Neural Netw. 4, 251 (1991).
  31. C. C. Margossian, A review of automatic differentiation and its efficient implementation, Wiley Interdiscip. Rev.: Data Min. Knowl. Discov. 9, e1305 (2019).
  32. M. Kalinowski, N. Maskara, and M. D. Lukin, Non-Abelian Floquet spin liquids in a digital Rydberg simulator, Phys. Rev. X 13, 031008 (2023).
  33. C. Dlaska, K. Ender, G. B. Mbeng, A. Kruckenhauser, W. Lechner, and R. van Bijnen, Quantum optimization via four-body Rydberg gates, Phys. Rev. Lett. 128, 120503 (2022).
  34. C. Fromonteil, R. Tricarico, F. Cesa, and H. Pichler, Hamilton-Jacobi-Bellman equations for Rydberg-blockade processes, Phys. Rev. Res. 6, 033333 (2024).
  35. I. N. Ashkarin, S. Lepoutre, P. Pillet, I. I. Beterov, I. I. Ryabtsev, and P. Cheinet, Long-range CCΦ gates via radio-frequency-induced Förster resonances, Phys. Rev. Res. 7, 013034 (2025).
  36. M. Morgado and S. Whitlock, Quantum simulation and computing with Rydberg-interacting qubits, AVS Quantum Sci. 3, 023501 (2021).
  37. I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, High-fidelity entanglement and detection of alkaline-earth Rydberg atoms, Nat. Phys. 16, 857 (2020).
  38. M. Peper, Y. Li, D. Y. Knapp, M. Bileska, S. Ma, G. Liu, P. Peng, B. Zhang, S. P. Horvath, A. P. Burgers, and J. D. Thompson, Spectroscopy and modeling of 171Yb Rydberg states for high-fidelity two-qubit gates, Phys. Rev. X 15, 011009 (2025).
  39. A. B. Magann, C. Arenz, M. D. Grace, T.-S. Ho, R. L. Kosut, J. R. McClean, H. A. Rabitz, and M. Sarovar, from pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms, PRX Quantum 2, 010101 (2021).
  40. A. Pagano, S. Weber, D. Jaschke, T. Pfau, F. Meinert, S. Montangero, and H. P. Büchler, Error budgeting for a controlled-phase gate with strontium-88 Rydberg atoms, Phys. Rev. Res. 4, 033019 (2022).
  41. M. Mohan, R. de Keijzer, and S. Kokkelmans, Robust control and optimal Rydberg states for neutral atom two-qubit gates, Phys. Rev. Res. 5, 033052 (2023).
  42. G. Giudici, S. Veroni, G. Giudice, H. Pichler, and J. Zeiher, Fast entangling gates for Rydberg atoms via resonant dipole-dipole interaction, arXiv:2411.05073 [quant-ph].
  43. M. Saffman, I. I. Beterov, A. Dalal, E. J. Páez, and B. C. Sanders, Symmetric Rydberg controlled-Z gates with adiabatic pulses, Phys. Rev. A 101, 062309 (2020).
  44. D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Fast quantum gates for neutral atoms, Phys. Rev. Lett. 85, 2208 (2000).
  45. M. Saffman and T. G. Walker, Analysis of a quantum logic device based on dipole-dipole interactions of optically trapped Rydberg atoms, Phys. Rev. A 72, 022347 (2005).
  46. I. S. Madjarov, Entangling, controlling, and detecting individual strontium atoms in optical tweezer arrays, Ph.D. thesis, California Institute of Technology, 2021.
  47. 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).
  48. J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson, The variational quantum eigensolver: A review of methods and best practices, Phys. Rep. 986, 1 (2022).
  49. L. H. Pedersen, N. M. Møller, and K. Mølmer, Fidelity of quantum operations, Phys. Lett. A 367, 47 (2007).
  50. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, in Proc. 3rd Int. Conf. Learn. Represent. 2015 (San Diego, 2015).
  51. R. T. Q. Chen, Y. Rubanova, J. Bettencourt, and D. K. Duvenaud, Neural ordinary differential equations, in Adv. Neural. Inf. Process. Syst. (Curran Associates, Inc., Montreal, 2018), Vol. 31.
  52. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Learning representations by back-propagating errors, Nature 323, 533 (1986).
  53. A. G. Baydin, B. A. Pearlmutter, A. A. Radul, and J. M. Siskind, Automatic differentiation in machine learning: A survey, J. Mach. Learn. Res. 18, 1 (2018).
  54. N. Lacroix, C. Hellings, C. K. Andersen, A. Di Paolo, A. Remm, S. Lazar, S. Krinner, G. J. Norris, M. Gabureac, J. Heinsoo et al., Improving the performance of deep quantum optimization algorithms with continuous gate sets, PRX Quantum 1, 020304 (2020).
  55. R. De Keijzer, J. Snijders, A. Carvalho, and S. Kokkelmans, Pulse family optimization for parametrized quantum gates using spectral clustering, Acad. Quantum 1, 1 (2024).
  56. M. Mohan, J. de Hond, and S. Kokkelmans, Additional data for publication (2024).
  57. M. A. Nielsen, A simple formula for the average gate fidelity of a quantum dynamical operation, Phys. Lett. A 303, 249 (2002).
  58. L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses, Phys. Rev. A 94, 032306 (2016).
  59. C. Fromonteil, D. Bluvstein, and H. Pichler, Protocols for Rydberg entangling gates featuring robustness against quasistatic errors, PRX Quantum 4, 020335 (2023).
  60. N. Bjorck, C. P. Gomes, B. Selman, and K. Q. Weinberger, Understanding batch normalization, in Adv. Neural. Inf. Process. Syst. (Curran Associates, Inc., Montreal, 2018), Vol. 31.
  61. F. N. Iandola, M. W. Moskewicz, K. Ashraf, and K. Keutzer, FireCaffe: Near-linear acceleration of deep neural network training on compute clusters, in Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. (Curran Associates, Inc., Las Vegas, 2016).
  62. P. Doria, T. Calarco, and S. Montangero, Optimal control technique for many-body quantum dynamics, Phys. Rev. Lett. 106, 190501 (2011).
  63. H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Differentiable programming tensor networks, Phys. Rev. X 9, 031041 (2019).
  64. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga et al., PyTorch: An imperative style, high-performance deep learning library, in Adv. Neural. Inf. Process. Syst. (Curran Associates, Inc., Vancouver, 2019), Vol. 32.
  65. R. T. Q. Chen, PyTorch implementation of differentiable ODE solvers, GitHub repository (2018), https://github.com/rtqichen/torchdiffeq.
  66. B. Hanin, Which neural net architectures give rise to exploding and vanishing gradients?, in Adv. Neural. Inf. Process. Syst. (Curran Associates, Inc., Montreal, 2018), Vol. 31.
  67. C. Sheng, X. He, P. Xu, R. Guo, K. Wang, Z. Xiong, M. Liu, J. Wang, and M. Zhan, High-fidelity single-qubit gates on neutral atoms in a two-dimensional magic-intensity optical dipole trap array, Phys. Rev. Lett. 121, 240501 (2018).
  68. A. D. Hill, M. J. Hodson, N. Didier, and M. J. Reagor, Realization of arbitrary doubly-controlled quantum phase gates, arXiv:2108.01652 [quant-ph].
  69. J. D. Arias Espinoza, K. Groenland, M. Mazzanti, K. Schoutens, and R. Gerritsma, High-fidelity method for a single-step N-bit Toffoli gate in trapped ions, Phys. Rev. A 103, 052437 (2021).
  70. K. Mølmer and A. Sørensen, Multiparticle entanglement of hot trapped ions, Phys. Rev. Lett. 82, 1835 (1999).
  71. N. J. Glaser, F. Roy, and S. Filipp, Controlled-controlled-phase gates for superconducting qubits mediated by a shared tunable coupler, Phys. Rev. Appl. 19, 044001 (2023).
  72. C. Cao, Y.-H. Han, L. Zhang, L. Fan, Y.-W. Duan, and R. Zhang, High-fidelity universal quantum controlled gates on electron-spin qubits in quantum dots inside single-sided optical microcavities, Adv. Quantum Technol. 2, 1900081 (2019).
  73. Y. Wang, Y. Chen, H. T. Bui, C. Wolf, M. Haze, C. Mier, J. Kim, D.-J. Choi, C. P. Lutz, Y. Bae et al., An atomic-scale multi-qubit platform, Science 382, 87 (2023).

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