Time-Optimal Two- and Three-Qubit Gates for Rydberg Atoms

Sven Jandura; Guido Pupillo

doi:10.22331/q-2022-05-13-712

Time-Optimal Two- and Three-Qubit Gates for Rydberg Atoms

Sven Jandura and Guido Pupillo

University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, 67000 Strasbourg, France

Published:	2022-05-13, volume 6, page 712
Eprint:	arXiv:2202.00903v2
Doi:	https://doi.org/10.22331/q-2022-05-13-712
Citation:	Quantum 6, 712 (2022).

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Abstract

We identify time-optimal laser pulses to implement the controlled-Z gate and its three qubit generalization, the C$_2$Z gate, for Rydberg atoms in the blockade regime. Pulses are optimized using a combination of numerical and semi-analytical quantum optimal control techniques that result in smooth Ansätze with just a few variational parameters. For the CZ gate, the time-optimal implementation corresponds to a global laser pulse that does not require single site addressability of the atoms, simplifying experimental implementation of the gate. We employ quantum optimal control techniques to mitigate errors arising due to the finite lifetime of Rydberg states and finite blockade strengths, while several other types of errors affecting the gates are directly mitigated by the short gate duration. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction using reasonable experimental parameters for CZ and C$_2$Z gates.

Featured image: Laser phase as a function of time for the time-optimal pulse implementing a CZ gate.

Popular summary

In this work we apply quantum optimal control techniques to optimize quantum gates on Rydberg atoms. We find the shortest possible global laser pulse to implement at CZ and a C$_2$Z gate in the blockade regime. We show how to adapt the pulses to compensate for a finite Rydberg blockade strength and how to minimize the time spent in the Rydberg state instead of the pulse duration.

► BibTeX data

@article{Jandura2022timeoptimaltwothree,
  doi = {10.22331/q-2022-05-13-712},
  url = {https://doi.org/10.22331/q-2022-05-13-712},
  title = {Time-{O}ptimal {T}wo- and {T}hree-{Q}ubit {G}ates for {R}ydberg {A}toms},
  author = {Jandura, Sven and Pupillo, Guido},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {712},
  month = may,
  year = {2022}
}

► References

[1] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2: 79, 2018. 10.22331/q-2018-08-06-79.
https://doi.org/10.22331/q-2018-08-06-79

[2] K.M. Svore, D.P. DiVincenzo, and B.M. Terhal. Noise threshold for a fault-tolerant two-dimensional lattice architecture. QIC, 7: 297–318, 2007. 10.26421/QIC7.4-2.
https://doi.org/10.26421/QIC7.4-2

[3] Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A, 86: 032324, 2012. 10.1103/PhysRevA.86.032324.
https://doi.org/10.1103/PhysRevA.86.032324

[4] Federico M. Spedalieri and Vwani P. Roychowdhury. Latency in local, two-dimensional, fault-tolerant quantum computing. QIC, 9: 666–682, 2009. 10.26421/QIC9.7-8-9.
https://doi.org/10.26421/QIC9.7-8-9

[5] Ching-Yi Lai, Gerardo Paz, Martin Suchara, and Todd A. Brun. Performance and error analysis of Knill's postselection scheme in a two-dimensional architecture. QIC, 14: 807–822, 2014. 10.26421/QIC14.9-10-7.
https://doi.org/10.26421/QIC14.9-10-7

[6] Jonathan M. Baker, Andrew Litteken, Casey Duckering, Henry Hoffmann, Hannes Bernien, and Frederic T. Chong. Exploiting Long-Distance Interactions and Tolerating Atom Loss in Neutral Atom Quantum Architectures. In 2021 ACM/IEEE 48th Annual International Symposium on Computer Architecture (ISCA), pages 818–831, Valencia, Spain, 2021. IEEE. ISBN 978-1-66543-333-4. 10.1109/ISCA52012.2021.00069.
https://doi.org/10.1109/ISCA52012.2021.00069

[7] Iris Cong, Sheng-Tao Wang, Harry Levine, Alexander Keesling, and Mikhail D. Lukin. Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms. arXiv:2105.13501, 2021. 10.48550/arXiv.2105.13501.
https://doi.org/10.48550/arXiv.2105.13501
arXiv:2105.13501

[8] Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger. Many-body physics with ultracold gases. Rev. Mod. Phys., 80: 885–964, 2008. 10.1103/RevModPhys.80.885.
https://doi.org/10.1103/RevModPhys.80.885

[9] M. Saffman, T. G. Walker, and K. Mølmer. Quantum information with Rydberg atoms. Rev. Mod. Phys., 82: 2313–2363, 2010. 10.1103/RevModPhys.82.2313.
https://doi.org/10.1103/RevModPhys.82.2313

[10] Antoine Browaeys and Thierry Lahaye. Many-body physics with individually controlled Rydberg atoms. Nat. Phys., 16: 132–142, 2020. 10.1038/s41567-019-0733-z.
https://doi.org/10.1038/s41567-019-0733-z

[11] Loïc Henriet, Lucas Beguin, Adrien Signoles, Thierry Lahaye, Antoine Browaeys, Georges-Olivier Reymond, and Christophe Jurczak. Quantum computing with neutral atoms. Quantum, 4: 327, 2020. 10.22331/q-2020-09-21-327.
https://doi.org/10.22331/q-2020-09-21-327

[12] M. Morgado and S. Whitlock. Quantum simulation and computing with Rydberg-interacting qubits. AVS Quantum Sci., 3: 023501, 2021. 10.1116/5.0036562.
https://doi.org/10.1116/5.0036562

[13] Manuel Endres, Hannes Bernien, Alexander Keesling, Harry Levine, Eric R. Anschuetz, Alexandre Krajenbrink, Crystal Senko, Vladan Vuletic, Markus Greiner, and Mikhail D. Lukin. Atom-by-atom assembly of defect-free one-dimensional cold atom arrays. Science, 354: 1024–1027, 2016. 10.1126/science.aah3752.
https://doi.org/10.1126/science.aah3752

[14] Daniel Barredo, Sylvain de Léséleuc, Vincent Lienhard, Thierry Lahaye, and Antoine Browaeys. An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays. Science, 354: 1021–1023, 2016. 10.1126/science.aah3778.
https://doi.org/10.1126/science.aah3778

[15] Daniel Ohl de Mello, Dominik Schäffner, Jan Werkmann, Tilman Preuschoff, Lars Kohfahl, Malte Schlosser, and Gerhard Birkl. Defect-Free Assembly of 2D Clusters of More Than 100 Single-Atom Quantum Systems. Phys. Rev. Lett., 122: 203601, 2019. 10.1103/PhysRevLett.122.203601.
https://doi.org/10.1103/PhysRevLett.122.203601

[16] Daniel Barredo, Vincent Lienhard, Sylvain de Léséleuc, Thierry Lahaye, and Antoine Browaeys. Synthetic three-dimensional atomic structures assembled atom by atom. Nature, 561: 79–82, 2018. 10.1038/s41586-018-0450-2.
https://doi.org/10.1038/s41586-018-0450-2

[17] Malte Schlosser, Sascha Tichelmann, Dominik Schäffner, Daniel Ohl de Mello, Moritz Hambach, and Gerhard Birkl. Large-scale multilayer architecture of single-atom arrays with individual addressability. arXiv:1902.05424, 2019. 10.48550/arXiv.1902.05424.
https://doi.org/10.48550/arXiv.1902.05424
arXiv:1902.05424

[18] 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: 2208–2211, 2000. 10.1103/PhysRevLett.85.2208.
https://doi.org/10.1103/PhysRevLett.85.2208

[19] M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller. Mesoscopic Rydberg Gate Based on Electromagnetically Induced Transparency. Phys. Rev. Lett., 102: 170502, 2009. 10.1103/PhysRevLett.102.170502.
https://doi.org/10.1103/PhysRevLett.102.170502

[20] L. Isenhower, M. Saffman, and K. Mølmer. Multibit C k NOT quantum gates via Rydberg blockade. Quantum Inf Process, 10: 755–770, 2011. 10.1007/s11128-011-0292-4.
https://doi.org/10.1007/s11128-011-0292-4

[21] Harry Levine, Alexander Keesling, Giulia Semeghini, Ahmed Omran, Tout T. Wang, Sepehr Ebadi, Hannes Bernien, Markus Greiner, Vladan Vuletić, Hannes Pichler, and Mikhail D. Lukin. Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms. Phys. Rev. Lett., 123: 170503, 2019. 10.1103/PhysRevLett.123.170503.
https://doi.org/10.1103/PhysRevLett.123.170503

[22] T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman. Rydberg-Mediated Entanglement in a Two-Dimensional Neutral Atom Qubit Array. Phys. Rev. Lett., 123: 230501, 2019. 10.1103/PhysRevLett.123.230501.
https://doi.org/10.1103/PhysRevLett.123.230501

[23] C J Picken, R Legaie, K McDonnell, and J D Pritchard. Entanglement of neutral-atom qubits with long ground-Rydberg coherence times. Quantum Sci. Technol., 4: 015011, 2018. 10.1088/2058-9565/aaf019.
https://doi.org/10.1088/2058-9565/aaf019

[24] Zhuo Fu, Peng Xu, Yuan Sun, Yang-Yang Liu, Xiao-Dong He, Xiao Li, Min Liu, Run-Bing Li, Jin Wang, Liang Liu, and Ming-Sheng Zhan. High-fidelity entanglement of neutral atoms via a Rydberg-mediated single-modulated-pulse controlled-phase gate. Phys. Rev. A, 105: 042430, 2022. 10.1103/PhysRevA.105.042430.
https://doi.org/10.1103/PhysRevA.105.042430

[25] Michael J. Martin, Yuan-Yu Jau, Jongmin Lee, Anupam Mitra, Ivan H. Deutsch, and Grant W. Biedermann. A Mølmer-Sørensen Gate with Rydberg-Dressed Atoms. arXiv:2111.14677, 2021. 10.48550/arXiv.2111.14677.
https://doi.org/10.48550/arXiv.2111.14677
arXiv:2111.14677

[26] Ivaylo S. Madjarov, Jacob P. Covey, Adam L. Shaw, Joonhee Choi, Anant Kale, Alexandre Cooper, Hannes Pichler, Vladimir Schkolnik, Jason R. Williams, and Manuel Endres. High-Fidelity Entanglement and Detection of Alkaline-Earth Rydberg Atoms. Nat. Phys., 16: 857–861, 2020. 10.1038/s41567-020-0903-z.
https://doi.org/10.1038/s41567-020-0903-z

[27] Sylvain de Léséleuc, Daniel Barredo, Vincent Lienhard, Antoine Browaeys, and Thierry Lahaye. Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states. Phys. Rev. A, 97: 053803, 2018. 10.1103/PhysRevA.97.053803.
https://doi.org/10.1103/PhysRevA.97.053803

[28] X. L. Zhang, A. T. Gill, L. Isenhower, T. G. Walker, and M. Saffman. Fidelity of a Rydberg-blockade quantum gate from simulated quantum process tomography. Phys. Rev. A, 85: 042310, 2012. 10.1103/PhysRevA.85.042310.
https://doi.org/10.1103/PhysRevA.85.042310

[29] D. D. Bhaktavatsala Rao and Klaus Mølmer. Robust Rydberg-interaction gates with adiabatic passage. Phys. Rev. A, 89: 030301, 2014. 10.1103/PhysRevA.89.030301.
https://doi.org/10.1103/PhysRevA.89.030301

[30] I. I. Beterov, M. Saffman, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, S. Bergamini, E. A. Kuznetsova, and I. I. Ryabtsev. Two-qubit gates using adiabatic passage of the Stark-tuned Förster resonances in Rydberg atoms. Phys. Rev. A, 94: 062307, 2016. 10.1103/PhysRevA.94.062307.
https://doi.org/10.1103/PhysRevA.94.062307

[31] Anupam Mitra, Michael J. Martin, Grant W. Biedermann, Alberto M. Marino, Pablo M. Poggi, and Ivan H. Deutsch. Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing. Phys. Rev. A, 101: 030301, 2020. 10.1103/PhysRevA.101.030301.
https://doi.org/10.1103/PhysRevA.101.030301

[32] M. Saffman, I. I. Beterov, A. Dalal, E. J. Paez, and B. C. Sanders. Symmetric Rydberg controlled-Z gates with adiabatic pulses. Phys. Rev. A, 101: 062309, 2020. 10.1103/PhysRevA.101.062309.
https://doi.org/10.1103/PhysRevA.101.062309

[33] I. I. Beterov, D. B. Tretyakov, V. M. Entin, E. A. Yakshina, I. I. Ryabtsev, M. Saffman, and S. Bergamini. Application of adiabatic passage in Rydberg atomic ensembles for quantum information processing. J. Phys. B: At. Mol. Opt. Phys., 53: 182001, 2020. 10.1088/1361-6455/ab8719.
https://doi.org/10.1088/1361-6455/ab8719

[34] Yucheng He, Jing-Xin Liu, F.-Q. Guo, Lei-Lei Yan, Ronghui Luo, Erjun Liang, Shi-Lei Su, and M. Feng. Multiple-qubit Rydberg quantum logic gate via dressed-states scheme. arXiv:2010.14704, 2021. 10.48550/arXiv.2010.14704.
https://doi.org/10.48550/arXiv.2010.14704
arXiv:2010.14704

[35] David Petrosyan, Felix Motzoi, Mark Saffman, and Klaus Mølmer. High-fidelity Rydberg quantum gate via a two-atom dark state. Phys. Rev. A, 96: 042306, 2017. 10.1103/PhysRevA.96.042306.
https://doi.org/10.1103/PhysRevA.96.042306

[36] Jin-Lei Wu, Yan Wang, Jin-Xuan Han, Shi-Lei Su, Yan Xia, Yongyuan Jiang, and Jie Song. Unselective ground-state blockade of Rydberg atoms for implementing quantum gates. arXiv:2107.09975, 2021a. 10.1007/s11467-021-1104-7.
https://doi.org/10.1007/s11467-021-1104-7
arXiv:2107.09975

[37] Jin-Lei Wu, Yan Wang, Jin-Xuan Han, Shi-Lei Su, Yan Xia, Yongyuan Jiang, and Jie Song. Resilient quantum gates on periodically driven Rydberg atoms. Phys. Rev. A, 103: 012601, 2021b. 10.1103/PhysRevA.103.012601.
https://doi.org/10.1103/PhysRevA.103.012601

[38] 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. 10.1103/PhysRevA.94.032306.
https://doi.org/10.1103/PhysRevA.94.032306

[39] Shuai Liu, Jun-Hui Shen, Ri-Hua Zheng, Yi-Hao Kang, Zhi-Cheng Shi, Jie Song, and Yan Xia. Optimized nonadiabatic holonomic quantum computation based on Förster resonance in Rydberg atoms. Front. Phys., 17: 21502, 2022. 10.1007/s11467-021-1108-3.
https://doi.org/10.1007/s11467-021-1108-3

[40] Cai-Peng Shen, Jin-Lei Wu, Shi-Lei Su, and Erjun Liang. Construction of robust Rydberg controlled-phase gates. Opt. Lett., 44: 2036, 2019. 10.1364/OL.44.002036.
https://doi.org/10.1364/OL.44.002036

[41] Chen-Yue Guo, L.-L. Yan, Shou Zhang, Shi-Lei Su, and Weibin Li. Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms. Phys. Rev. A, 102: 042607, 2020. 10.1103/PhysRevA.102.042607.
https://doi.org/10.1103/PhysRevA.102.042607

[42] Steffen J. Glaser, Ugo Boscain, Tommaso Calarco, Christiane P. Koch, Walter Köckenberger, Ronnie Kosloff, Ilya Kuprov, Burkhard Luy, Sophie Schirmer, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm. Training Schrödinger's cat: Quantum optimal control: Strategic report on current status, visions and goals for research in Europe. Eur. Phys. J. D, 69: 279, 2015. 10.1140/epjd/e2015-60464-1.
https://doi.org/10.1140/epjd/e2015-60464-1

[43] D. J. Egger and F. K. Wilhelm. Optimized controlled Z gates for two superconducting qubits coupled through a resonator. Supercond. Sci. Technol., 27: 014001, 2014. 10.1088/0953-2048/27/1/014001.
https://doi.org/10.1088/0953-2048/27/1/014001

[44] J. Kelly, R. Barends, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, I.-C. Hoi, E. Jeffrey, A. Megrant, J. Mutus, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Cleland, and John M. Martinis. Optimal Quantum Control Using Randomized Benchmarking. Phys. Rev. Lett., 112: 240504, 2014. 10.1103/PhysRevLett.112.240504.
https://doi.org/10.1103/PhysRevLett.112.240504

[45] Shang-Yu Huang and Hsi-Sheng Goan. Optimal control for fast and high-fidelity quantum gates in coupled superconducting flux qubits. Phys. Rev. A, 90: 012318, 2014. 10.1103/PhysRevA.90.012318.
https://doi.org/10.1103/PhysRevA.90.012318

[46] M. Werninghaus, D. J. Egger, F. Roy, S. Machnes, F. K. Wilhelm, and S. Filipp. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Inf, 7: 14, 2021. 10.1038/s41534-020-00346-2.
https://doi.org/10.1038/s41534-020-00346-2

[47] V. Nebendahl, H. Haffner, and C. F. Roos. Optimal control of entangling operations for trapped ion quantum computing. Phys. Rev. A, 79: 012312, 2009. 10.1103/PhysRevA.79.012312.
https://doi.org/10.1103/PhysRevA.79.012312

[48] T. Choi, S. Debnath, T. A. Manning, C. Figgatt, Z.-X. Gong, L.-M. Duan, and C. Monroe. Optimal Quantum Control of Multimode Couplings between Trapped Ion Qubits for Scalable Entanglement. Phys. Rev. Lett., 112: 190502, 2014. 10.1103/PhysRevLett.112.190502.
https://doi.org/10.1103/PhysRevLett.112.190502

[49] Michael H Goerz, Tommaso Calarco, and Christiane P Koch. The quantum speed limit of optimal controlled phasegates for trapped neutral atoms. J. Phys. B: At. Mol. Opt. Phys., 44: 154011, 2011. 10.1088/0953-4075/44/15/154011.
https://doi.org/10.1088/0953-4075/44/15/154011

[50] M. M. Müller, D. M. Reich, M. Murphy, H. Yuan, J. Vala, K. B. Whaley, T. Calarco, and C. P. Koch. Optimizing entangling quantum gates for physical systems. Phys. Rev. A, 84: 042315, 2011. 10.1103/PhysRevA.84.042315.
https://doi.org/10.1103/PhysRevA.84.042315

[51] Michael H. Goerz, Eli J. Halperin, Jon M. Aytac, Christiane P. Koch, and K. Birgitta Whaley. Robustness of high-fidelity Rydberg gates with single-site addressability. Phys. Rev. A, 90: 032329, 2014. 10.1103/PhysRevA.90.032329.
https://doi.org/10.1103/PhysRevA.90.032329

[52] A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science, 365: 570–574, 2019. 10.1126/science.aax9743.
https://doi.org/10.1126/science.aax9743

[53] Jian Cui, Rick van Bijnen, Thomas Pohl, Simone Montangero, and Tommaso Calarco. Optimal control of Rydberg lattice gases. Quantum Sci. Technol., 2: 035006, 2017. 10.1088/2058-9565/aa7daf.
https://doi.org/10.1088/2058-9565/aa7daf

[54] A. Smith, B. E. Anderson, H. Sosa-Martinez, C. A. Riofrío, Ivan H. Deutsch, and Poul S. Jessen. Quantum Control in the Cs 6 S 1 / 2 Ground Manifold Using Radio-Frequency and Microwave Magnetic Fields. Phys. Rev. Lett., 111: 170502, 2013. 10.1103/PhysRevLett.111.170502.
https://doi.org/10.1103/PhysRevLett.111.170502

[55] B. E. Anderson, H. Sosa-Martinez, C. A. Riofrío, Ivan H. Deutsch, and Poul S. Jessen. Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System. Phys. Rev. Lett., 114: 240401, 2015. 10.1103/PhysRevLett.114.240401.
https://doi.org/10.1103/PhysRevLett.114.240401

[56] Nathan K. Lysne, Kevin W. Kuper, Pablo M. Poggi, Ivan H. Deutsch, and Poul S. Jessen. Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations. Phys. Rev. Lett., 124: 230501, 2020. 10.1103/PhysRevLett.124.230501.
https://doi.org/10.1103/PhysRevLett.124.230501

[57] Sven Jandura and Guido Pupillo. Figshare data repository, 2022. URL https://doi.org/10.6084/m9.figshare.19658427.
https://doi.org/10.6084/m9.figshare.19658427

[58] F. Robicheaux, T. M. Graham, and M. Saffman. Photon-recoil and laser-focusing limits to Rydberg gate fidelity. Phys. Rev. A, 103: 022424, 2021. 10.1103/PhysRevA.103.022424.
https://doi.org/10.1103/PhysRevA.103.022424

[59] Line Hjortshøj Pedersen, Niels Martin Møller, and Klaus Mølmer. Fidelity of quantum operations. Physics Letters A, 367: 47–51, 2007. 10.1016/j.physleta.2007.02.069.
https://doi.org/10.1016/j.physleta.2007.02.069

[60] Navin Khaneja, Timo Reiss, Cindie Kehlet, Thomas Schulte-Herbrüggen, and Steffen J. Glaser. Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms. Journal of Magnetic Resonance, 172: 296–305, 2005. 10.1016/j.jmr.2004.11.004.
https://doi.org/10.1016/j.jmr.2004.11.004

[61] A. Garon, S. J. Glaser, and D. Sugny. Time-optimal control of SU(2) quantum operations. Phys. Rev. A, 88: 043422, 2013. 10.1103/PhysRevA.88.043422.
https://doi.org/10.1103/PhysRevA.88.043422

[62] Bilal Riaz, Cong Shuang, and Shahid Qamar. Optimal control methods for quantum gate preparation: A comparative study. Quantum Inf Process, 18: 100, 2019. 10.1007/s11128-019-2190-0.
https://doi.org/10.1007/s11128-019-2190-0

[63] Frank K. Wilhelm, Susanna Kirchhoff, Shai Machnes, Nicolas Wittler, and Dominique Sugny. An introduction into optimal control for quantum technologies. arXiv:2003.10132, 2020. 10.48550/arXiv.2003.10132.
https://doi.org/10.48550/arXiv.2003.10132
arXiv:2003.10132

[64] Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer Series in Operation Research and Financial Engineering. Springer, New York, NY, 2. ed edition, 2006. ISBN 978-1-4939-3711-0 978-0-387-30303-1.

[65] Eric Jones, Travis Oliphant, Pearu Peterson, and others. SciPy: Open source scientific tools for Python, 2001.

[66] L. S. Pontryagin and Lucien W. Neustadt. The Mathematical Theory of Optimal Processes. Classics of Soviet Mathematics. Gordon and Breach Science Publishers, New York, english ed edition, 1986. ISBN 978-2-88124-077-5.

[67] E. B. Lee and L. Markus. Foundations of Optimal Control Theory. R.E. Krieger Pub. Co, Malabar, Fla, 1986. ISBN 978-0-89874-807-9.

[68] U. Boscain, M. Sigalotti, and D. Sugny. Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control. PRX Quantum, 2: 030203, 2021. 10.1103/PRXQuantum.2.030203.
https://doi.org/10.1103/PRXQuantum.2.030203

[69] Seraph Bao, Silken Kleer, Ruoyu Wang, and Armin Rahmani. Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: Preparing a maximally entangled state with singular bang-bang protocols. Phys. Rev. A, 97: 062343, 2018. 10.1103/PhysRevA.97.062343.
https://doi.org/10.1103/PhysRevA.97.062343

[70] Chungwei Lin, Yebin Wang, Grigory Kolesov, and Uroš Kalabić. Application of Pontryagin's minimum principle to Grover's quantum search problem. Phys. Rev. A, 100: 022327, 2019. 10.1103/PhysRevA.100.022327.
https://doi.org/10.1103/PhysRevA.100.022327

[71] Chungwei Lin, Dries Sels, and Yebin Wang. Time-optimal control of a dissipative qubit. Phys. Rev. A, 101: 022320, 2020. 10.1103/PhysRevA.101.022320.
https://doi.org/10.1103/PhysRevA.101.022320

[72] L. Van Damme, Q. Ansel, S. J. Glaser, and D. Sugny. Robust optimal control of two-level quantum systems. Phys. Rev. A, 95: 063403, 2017. 10.1103/PhysRevA.95.063403.
https://doi.org/10.1103/PhysRevA.95.063403

[73] Zhi-Cheng Yang, Armin Rahmani, Alireza Shabani, Hartmut Neven, and Claudio Chamon. Optimizing Variational Quantum Algorithms Using Pontryagin's Minimum Principle. Phys. Rev. X, 7: 021027, 2017. 10.1103/PhysRevX.7.021027.
https://doi.org/10.1103/PhysRevX.7.021027

[74] Dong Eui Chang. A simple proof of the Pontryagin maximum principle on manifolds. Automatica, 47: 630–633, 2011. 10.1016/j.automatica.2011.01.037.
https://doi.org/10.1016/j.automatica.2011.01.037

[75] D. Barredo, S. Ravets, H. Labuhn, L. Béguin, A. Vernier, F. Nogrette, T. Lahaye, and A. Browaeys. Demonstration of a Strong Rydberg Blockade in Three-Atom Systems with Anisotropic Interactions. Phys. Rev. Lett., 112: 183002, 2014. 10.1103/PhysRevLett.112.183002.
https://doi.org/10.1103/PhysRevLett.112.183002

[76] C. Ates, T. Pohl, T. Pattard, and J. M. Rost. Antiblockade in Rydberg Excitation of an Ultracold Lattice Gas. Phys. Rev. Lett., 98: 023002, 2007. 10.1103/PhysRevLett.98.023002.
https://doi.org/10.1103/PhysRevLett.98.023002

[77] L. S. Theis and F. K. Wilhelm. Nonadiabatic corrections to fast dispersive multiqubit gates involving Z control. Phys. Rev. A, 95: 022314, 2017. 10.1103/PhysRevA.95.022314.
https://doi.org/10.1103/PhysRevA.95.022314

[78] Mohammadsadegh Khazali and Klaus Mølmer. Fast Multiqubit Gates by Adiabatic Evolution in Interacting Excited-State Manifolds of Rydberg Atoms and Superconducting Circuits. Phys. Rev. X, 10: 021054, 2020. 10.1103/PhysRevX.10.021054.
https://doi.org/10.1103/PhysRevX.10.021054

[79] Yeelai Chew, Takafumi Tomita, Tirumalasetty Panduranga Mahesh, Seiji Sugawa, Sylvain de Léséleuc, and Kenji Ohmori. Ultrafast energy exchange between two single Rydberg atoms on the nanosecond timescale. arXiv:2111.12314, 2021. 10.48550/arXiv.2111.12314.
https://doi.org/10.48550/arXiv.2111.12314
arXiv:2111.12314

[80] N. Šibalić, J.D. Pritchard, C.S. Adams, and K.J. Weatherill. ARC: An open-source library for calculating properties of alkali Rydberg atoms. Computer Physics Communications, 220: 319–331, 2017. 10.1016/j.cpc.2017.06.015.
https://doi.org/10.1016/j.cpc.2017.06.015

[81] Thad G. Walker and M. Saffman. Consequences of Zeeman degeneracy for the van der Waals blockade between Rydberg atoms. Phys. Rev. A, 77: 032723, 2008. 10.1103/PhysRevA.77.032723.
https://doi.org/10.1103/PhysRevA.77.032723

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[1] Sascha Heußen, David F. Locher, and Markus Müller, "Measurement-Free Fault-Tolerant Quantum Error Correction in Near-Term Devices", PRX Quantum 5 1, 010333 (2024).

[2] Daniel J. Egger, Chiara Capecci, Bibek Pokharel, Panagiotis Kl. Barkoutsos, Laurin E. Fischer, Leonardo Guidoni, and Ivano Tavernelli, "Pulse variational quantum eigensolver on cross-resonance-based hardware", Physical Review Research 5 3, 033159 (2023).

[3] Charles Fromonteil, Dolev Bluvstein, and Hannes Pichler, "Protocols for Rydberg Entangling Gates Featuring Robustness against Quasistatic Errors", PRX Quantum 4 2, 020335 (2023).

[4] Shannon Whitlock, "Robust phase-controlled gates for scalable atomic quantum processors using optical standing waves", Quantum 7, 941 (2023).

[5] Ludwig Schmid, David F Locher, Manuel Rispler, Sebastian Blatt, Johannes Zeiher, Markus Müller, and Robert Wille, "Computational capabilities and compiler development for neutral atom quantum processors—connecting tool developers and hardware experts", Quantum Science and Technology 9 3, 033001 (2024).

[6] Wan-Xia Li, Jin-Lei Wu, Shi-Lei Su, and Jing Qian, "High-tolerance antiblockade SWAP gates using optimal pulse drivings", Physical Review A 109 1, 012608 (2024).

[7] Richard Bing-Shiun Tsai, Henrique Silvério, and Loc Henriet, "Pulse-Level Scheduling of Quantum Circuits for Neutral-Atom Devices", Physical Review Applied 18 6, 064035 (2022).

[8] Dolev Bluvstein, Simon J. Evered, Alexandra A. Geim, Sophie H. Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, J. Pablo Bonilla Ataides, Nishad Maskara, Iris Cong, Xun Gao, Pedro Sales Rodriguez, Thomas Karolyshyn, Giulia Semeghini, Michael J. Gullans, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin, "Logical quantum processor based on reconfigurable atom arrays", Nature 626 7997, 58 (2024).

[9] Christiane P. Koch, Ugo Boscain, Tommaso Calarco, Gunther Dirr, Stefan Filipp, Steffen J. Glaser, Ronnie Kosloff, Simone Montangero, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm, "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", EPJ Quantum Technology 9 1, 19 (2022).

[10] X. X. Li, D. X. Li, and X. Q. Shao, "Generation of complete graph states in a spin-1/2 Heisenberg chain with a globally optimized magnetic field", Physical Review A 109 4, 042604 (2024).

[11] Luis S. Yagüe Bosch, Tim Ehret, Francesco Petiziol, Ennio Arimondo, and Sandro Wimberger, "Shortcut‐to‐Adiabatic Controlled‐Phase Gate in Rydberg Atoms", Annalen der Physik 535 12, 2300275 (2023).

[12] Daniel Basilewitsch, Clemens Dlaska, and Wolfgang Lechner, "Comparing planar quantum computing platforms at the quantum speed limit", Physical Review Research 6 2, 023026 (2024).

[13] Marcin Kalinowski, Nishad Maskara, and Mikhail D. Lukin, "Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator", Physical Review X 13 3, 031008 (2023).

[14] Sven Jandura, Jeff D. Thompson, and Guido Pupillo, "Optimizing Rydberg Gates for Logical-Qubit Performance", PRX Quantum 4 2, 020336 (2023).

[15] Robert de Keijzer, Oliver Tse, and Servaas Kokkelmans, "Pulse based Variational Quantum Optimal Control for hybrid quantum computing", Quantum 7, 908 (2023).

[16] Tam’si Ley, Anna Ouskova Leonteva, Johannes Schachenmayer, and Pierre Collet, Lecture Notes in Computer Science 13927, 64 (2023) ISBN:978-3-031-44354-1.

[17] Dominik S. Wild, Sabina Drăgoi, Corbin McElhanney, Jonathan Wurtz, and Sheng-Tao Wang, "Quantum dynamics of a fully blockaded Rydberg atom ensemble", Physical Review A 109 4, 043111 (2024).

[18] Yuan Sun, "Suppression of high-frequency components in off-resonant modulated driving protocols for Rydberg-blockade gates", Physical Review Applied 20 6, L061002 (2023).

[19] K. McDonnell, L. F. Keary, and J. D. Pritchard, "Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency", Physical Review Letters 129 20, 200501 (2022).

[20] Madhav Mohan, Robert de Keijzer, and Servaas Kokkelmans, "Robust control and optimal Rydberg states for neutral atom two-qubit gates", Physical Review Research 5 3, 033052 (2023).

[21] Rui Li, Jing Qian, and Weiping Zhang, "Proposal for practical Rydberg quantum gates using a native two-photon excitation", Quantum Science and Technology 8 3, 035032 (2023).

[22] Francesco Cesa and Hannes Pichler, "Universal Quantum Computation in Globally Driven Rydberg Atom Arrays", Physical Review Letters 131 17, 170601 (2023).

[23] Shuo Ma, Genyue Liu, Pai Peng, Bichen Zhang, Sven Jandura, Jahan Claes, Alex P. Burgers, Guido Pupillo, Shruti Puri, and Jeff D. Thompson, "High-fidelity gates and mid-circuit erasure conversion in an atomic qubit", Nature 622 7982, 279 (2023).

[24] Vadim N. Petruhanov and Alexander N. Pechen, "Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search", Photonics 10 2, 220 (2023).

[25] Mingyu Kang, Wesley C. Campbell, and Kenneth R. Brown, "Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion", PRX Quantum 4 2, 020358 (2023).

[26] T H Chang, T N Wang, H H Jen, and Y-C Chen, "High-fidelity Rydberg controlled-Z gates with optimized pulses", New Journal of Physics 25 12, 123007 (2023).

[27] Simone Notarnicola, Andreas Elben, Thierry Lahaye, Antoine Browaeys, Simone Montangero, and Benoît Vermersch, "A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator", New Journal of Physics 25 10, 103006 (2023).

[28] Daniel González-Cuadra, Torsten V. Zache, Jose Carrasco, Barbara Kraus, and Peter Zoller, "Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms", Physical Review Letters 129 16, 160501 (2022).

[29] Matteo Magoni, Radhika Joshi, and Igor Lesanovsky, "Molecular Dynamics in Rydberg Tweezer Arrays: Spin-Phonon Entanglement and Jahn-Teller Effect", Physical Review Letters 131 9, 093002 (2023).

[30] Vikas Buchemmavari, Sivaprasad Omanakuttan, Yuan-Yu Jau, and Ivan Deutsch, "Entangling quantum logic gates in neutral atoms via the microwave-driven spin-flip blockade", Physical Review A 109 1, 012615 (2024).

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[32] Shiqing Tang, Chong Yang, Dongxiao Li, and Xiaoqiang Shao, "Implementation of Quantum Algorithms via Fast Three-Rydberg-Atom CCZ Gates", Entropy 24 10, 1371 (2022).

[33] Simon J. Evered, Dolev Bluvstein, Marcin Kalinowski, Sepehr Ebadi, Tom Manovitz, Hengyun Zhou, Sophie H. Li, Alexandra A. Geim, Tout T. Wang, Nishad Maskara, Harry Levine, Giulia Semeghini, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin, "High-fidelity parallel entangling gates on a neutral-atom quantum computer", Nature 622 7982, 268 (2023).

[34] Yunzhe Zheng and Keita Kanno, "Minimizing readout-induced noise for early fault-tolerant quantum computers", Physical Review Research 6 2, 023129 (2024).

[35] Alice Pagano, Sebastian Weber, Daniel Jaschke, Tilman Pfau, Florian Meinert, Simone Montangero, and Hans Peter Büchler, "Error budgeting for a controlled-phase gate with strontium-88 Rydberg atoms", Physical Review Research 4 3, 033019 (2022).

[36] Yijiao Fu and Jinhui Wu, "One-Step Implementation of Collective Anti-Blockade in a Rydberg Ring", Photonics 10 10, 1172 (2023).

[37] Ignacio R. Sola, Seokmin Shin, and Bo Y. Chang, "Optimal protocols for entangling gates in N-qubit atomic systems", AIP Advances 13 11, 115102 (2023).

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[39] Korbinian Staudacher, Ludwig Schmid, Johannes Zeiher, Robert Wille, and Dieter Kranzlmüller, "Multi-controlled Phase Gate Synthesis with ZX-calculus applied to Neutral Atom Hardware", arXiv:2403.10864, (2024).

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