Unselective ground-state blockade of Rydberg atoms for implementing quantum gates

Abstract

A dynamics regime of Rydberg atoms, unselective ground-state blockade (UGSB), is proposed in the context of Rydberg antiblockade (RAB), where the evolution of two atoms is suppressed when they populate in an identical ground state. UGSB is used to implement a SWAP gate in one step without individual addressing of atoms. Aiming at circumventing common issues in RAB-based gates including atomic decay, Doppler dephasing, and fluctuations in the interatomic coupling strength, we modify the RAB condition to achieve a dynamical SWAP gate whose robustness is much greater than that of the nonadiabatic holonomic one in the conventional RAB regime. In addition, on the basis of the proposed SWAP gates, we further investigate the implementation of a three-atom Fredkin gate by combining Rydberg blockade and RAB. The present work may facilitate to implement the RAB-based gates of strongly coupled atoms in experiment.

Graphical abstract

Keywords

Rydberg atoms / unselective ground-state blockade / SWAP gate / Fredkin gate

References

[1] 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(10), 2208 (2000)

[2] T. F. Gallagher, Rydberg Atoms, Cambridge University Press, 2005

[3] M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys. 82(3), 2313 (2010)

[4] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Dipole blockade and quantum information processing in mesoscopic atomic ensembles, Phys. Rev. Lett. 87(3), 037901 (2001)

[5] E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, Observation of Rydberg blockade between two-atoms, Nat. Phys. 5(2), 110 (2009)

[6] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Observation of collective excitation of two individual atoms in the Rydberg blockade regime, Nat. Phys. 5(2), 115 (2009)

[7] D. Møller, L. B. Madsen, and K. Mølmer, Quantum gates and multiparticle entanglement by Rydberg excitation blockade and adiabatic passage, Phys. Rev. Lett. 100(17), 170504 (2008)

[8] H. Z. Wu, Z. B. Yang, and S. B. Zheng, Implementation of a multiqubit quantum phase gate in a neutral atomic ensemble via the asymmetric Rydberg blockade, Phys. Rev. A 82(3), 034307 (2010)

[9] H. Wu, X. R. Huang, C. S. Hu, Z. B. Yang, and S. B. Zheng, Rydberg-interaction gates via adiabatic passage and phase control of driving fields, Phys. Rev. A96(2), 022321 (2017)

[10] P. Z. Zhao, X. D. Cui, G. F. Xu, E. Sjöqvist, and D. M. Tong, Rydberg-atom-based scheme of nonadiabatic geometric quantum computation, Phys. Rev. A96(5), 052316 (2017)

[11] Y. H. Kang, Y. H. Chen, Z. C. Shi, B. H. Huang, J. Song, and Y. Xia, Nonadiabatic holonomic quantum computation using Rydberg blockade, Phys. Rev. A97(4), 042336 (2018)

[12] D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, High-fidelity Rydberg quantum gate via a two-atom dark state, Phys. Rev. A96(4), 042306 (2017)

[13] I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, Adiabatic passage of radio-frequency-assisted Förster resonances in Rydberg atoms for two-qubit gates and the generation of bell states, Phys. Rev. A 97(3), 032701 (2018)

[14] X. F. Shi, Deutsch, Toffoli, and CNOT gates via Rydberg blockade of neutral atoms, Phys. Rev. Appl. 9(5), 051001 (2018)

[15] C. P. Shen, J. L. Wu, S. L. Su, and E. Liang, Construction of robust Rydberg controlled-phase gates, Opt. Lett. 44(8), 2036 (2019)

[16] K. Y. Liao, X. H. Liu, Z. Li, and Y. X. Du, Geometric Rydberg quantum gate with shortcuts to adiabaticity, Opt. Lett. 44(19), 4801 (2019)

[17] B. J. Liu, S. L. Su, and M. H. Yung, Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms, Phys. Rev. Research 2(4), 043130 (2020)

[18] 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(2), 021054 (2020)

[19] 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(6), 062309 (2020)

[20] A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, Robust Mølmer–Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing, Phys. Rev. A 101(3), 030301 (2020)

[21] C. Y. Guo, L. L. Yan, S. Zhang, S. L. Su, and W. Li, Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms, Phys. Rev. A102(4), 042607 (2020)

[22] X. F. Shi, Transition slow-down by Rydberg interaction of neutral atoms and a fast controlled-NOT quantum gate, Phys. Rev. Appl. 14(5), 054058 (2020)

[23] X. F. Shi, Rydberg quantum computation with nuclear spins in two-electron neutral atoms, Front. Phys. 16(5), 52501 (2021)

[24] C. Ates, T. Pohl, T. Pattard, and J. M. Rost, Antiblockade in Rydberg excitation of an ultracold lattice gas, Phys. Rev. Lett. 98(2), 023002 (2007)

[25] T. Pohl and P. R. Berman, Breaking the dipole blockade: Nearly resonant dipole interactions in few-atom systems, Phys. Rev. Lett. 102(1), 013004 (2009)

[26] J. Qian, Y. Qian, M. Ke, X. L. Feng, C. H. Oh, and Y. Wang, Breakdown of the dipole blockade with a zero area phase-jump pulse, Phys. Rev. A 80(5), 053413 (2009)

[27] T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, Evidence of antiblockade in an ultracold Rydberg gas, Phys. Rev. Lett. 104(1), 013001 (2010)

[28] W. Li, C. Ates, and I. Lesanovsky, Nonadiabatic motional effects and dissipative blockade for Rydberg atoms excited from optical lattices or microtraps, Phys. Rev. Lett. 110(21), 213005 (2013)

[29] S. L. Su, F. Q. Guo, J. L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, Rydberg antiblockade regimes: Dynamics and applications, EPL 131(5), 53001 (2020)

[30] S. L. Su, E. Liang, S. Zhang, J. J. Wen, L. L. Sun, Z. Jin, and A. D. Zhu, One-step implementation of the Rydberg–Rydberg-interaction gate, Phys. Rev. A 93(1), 012306 (2016)

[31] S. L. Su, Y. Gao, E. Liang, and S. Zhang, Fast Rydberg antiblockade regime and its applications in quantum logic gates, Phys. Rev. A 95(2), 022319 (2017)

[32] S. L. Su, Y. Tian, H. Z. Shen, H. Zang, E. Liang, and S. Zhang, Applications of the modified Rydberg antiblockade regime with simultaneous driving, Phys. Rev. A 96(4), 042335 (2017)

[33] S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, One-step construction of the multiple-qubit Rydberg controlled phase gate, Phys. Rev. A 98(3), 032306 (2018)

[34] J. L. Wu, J. Song, and S. L. Su, Resonant-interaction induced Rydberg antiblockade and its applications, Phys. Lett. A 384(1), 126039 (2020)

[35] T. H. Xing, X. Wu, and G. F. Xu, Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation, Phys. Rev. A 101(1), 012306 (2020)

[36] F. Q. Guo, J. L. Wu, X. Y. Zhu, Z. Jin, Y. Zeng, S. Zhang, L. L. Yan, M. Feng, and S. L. Su, Complete and nondestructive distinguishment of many-body Rydberg entanglement via robust geometric quantum operations, Phys. Rev. A 102(6), 062410 (2020)

[37] D. D. B. Rao, and K. Mølmer, Dark entangled steady states of interacting Rydberg atoms, Phys. Rev. Lett. 111(3), 033606 (2013)

[38] A. W. Carr, and M. Saffman, Preparation of entangled and antiferromagnetic states by dissipative Rydberg pumping, Phys. Rev. Lett. 111(3), 033607 (2013)

[39] X. Q. Shao, J. B. You, T. Y. Zheng, C. H. Oh, and S. Zhang, Stationary three-dimensional entanglement via dissipative Rydberg pumping, Phys. Rev. A 89(5), 052313 (2014)

[40] S. L. Su, Q. Guo, H. F. Wang, and S. Zhang, Simplified scheme for entanglement preparation with Rydberg pumping via dissipation, Phys. Rev. A 92(2), 022328 (2015)

[41] J. Song, C. Li, Z. J. Zhang, Y. Y. Jiang, and Y. Xia, Implementing stabilizer codes in noisy environments, Phys. Rev. A 96(3), 032336 (2017)

[42] X. Q. Shao, D. X. Li, Y. Q. Ji, J. H. Wu, and X. X. Yi, Ground-state blockade of Rydberg atoms and application in entanglement generation, Phys. Rev. A 96(1), 012328 (2017)

[43] X. Y. Zhu, Z. Jin, E. Liang, S. Zhang, and S. L. Su, Preparation of steady 3D dark state entanglement in dissipative Rydberg atoms via electromagnetic induced transparency, Ann. Phys. (Berlin) 532(6), 2000059 (2020)

[44] T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, Entanglement of two individual neutral atoms using Rydberg blockade, Phys. Rev. Lett. 104(1), 010502 (2010)

[45] L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, Demonstration of a neutral atom controlled-NOT quantum gate, Phys. Rev. Lett. 104(1), 010503 (2010)

[46] X. L. Zhang, L. Isenhower, A. T. Gill, T. G. Walker, and M. Saffman, Deterministic entanglement of two neutral atoms via Rydberg blockade, Phys. Rev. A 82(3), 030306 (2010)

[47] H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, High-fidelity control and entanglement of Rydberg-atom qubits, Phys. Rev. Lett. 121(12), 123603 (2018)

[48] 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 highfidelity multiqubit gates with neutral atoms, Phys. Rev. Lett. 123(17), 170503 (2019)

[49] 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(8), 857 (2020)

[50] H. Jo, Y. Song, M. Kim, and J. Ahn, Rydberg atom entanglements in the weak coupling regime, Phys. Rev. Lett. 124(3), 033603 (2020)

[51] J. B. Balewski, A. T. Krupp, A. Gaj, S. Hofferberth, R. Löw, and T. Pfau, Rydberg dressing: Understanding of collective many-body effects and implications for experiments, New J. Phys. 16(6), 063012 (2014)

[52] Y. Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, and G. W. Biedermann, Entangling atomic spins with a Rydbergdressed spin-flip blockade, Nat. Phys. 12(1), 71 (2016)

[53] D. X. Li and X. Q. Shao, Unconventional Rydberg pumping and applications in quantum information processing, Phys. Rev. A 98(6), 062338 (2018)

[54] X. Q. Shao, D. X. Li, Y. Q. Ji, J. H. Wu, and X. X. Yi, Ground-state blockade of Rydberg atoms and application in entanglement generation, Phys. Rev. A 96(1), 012328 (2017)

[55] Y. J. Zhao, B. Liu, Y. Q. Ji, S. Q. Tang, and X. Q. Shao, Robust generation of entangled state via ground state antiblockade of Rydberg atoms, Sci. Rep. 7(1), 16489 (2017)

[56] Y. H. Chen, Z. C. Shi, J. Song, Y. Xia, and S. B. Zheng, Accelerated and noise-resistant generation of highfidelity steady-state entanglement with Rydberg atoms, Phys. Rev. A 97(3), 032328 (2018)

[57] D. X. Li, T. Y. Zheng, and X. Q. Shao, Adiabatic preparation of multipartite GHZ states via Rydberg ground-state blockade, Opt. Express 27(15), 20874 (2019)

[58] X. Q. Shao, Selective Rydberg pumping via strong dipole blockade, Phys. Rev. A 102(5), 053118 (2020)

[59] H. Z. Wu, Z. B. Yang, and S. B. Zheng, Quantum state swap for two trapped Rydberg atoms, Chin. Phys. B21(4), 040305 (2012)

[60] X. F. Shi, F. Bariani, and T. A. B. Kennedy, Entanglement of neutral-atom chains by spin-exchange Rydberg interaction, Phys. Rev. A 90(6), 062327 (2014)

[61] A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, Designing frustrated quantum magnets with laser-dressed Rydberg atoms, Phys. Rev. Lett. 114(17), 173002 (2015)

[62] 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, Photon. Res. 9(5), 814 (2021)

[63] E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, Non-adiabatic holonomic quantum computation, New J. Phys. 14(10), 103035 (2012)

[64] G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, Nonadiabatic holonomic quantum computation in decoherence-free subspaces, Phys. Rev. Lett. 109(17), 170501 (2012)

[65] G. Feng, G. Xu, and G. Long, Experimental realization of nonadiabatic holonomic quantum computation, Phys. Rev. Lett. 110(19), 190501 (2013)

[66] 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, Nature551(7682), 579 (2017)

[67] 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, Science365(6453), 570 (2019)

[68] D. F. V. James and J. Jerke, Effective Hamiltonian theory and its applications in quantum information, Can. J. Phys. 85(6), 625 (2007)

[69] B. J. Liu, X. K. Song, Z. Y. Xue, X. Wang, and M. H. Yung, Plug-and-play approach to nonadiabatic geometric quantum gates, Phys. Rev. Lett. 123(10), 100501 (2019)

[70] P. Z. Zhao, K. Z. Li, G. F. Xu, and D. M. Tong, General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation, Phys. Rev. A 101(6), 062306 (2020)

[71] E. Brion, L. H. Pedersen, and K. Mølmer, Implementing a neutral atom Rydberg gate without populating the Rydberg state, J. Phys. B40(9), S159 (2007)

[72] J. L. Wu, S. L. Su, Y. Wang, J. Song, Y. Xia, and Y. Jiang, Effective Rabi dynamics of Rydberg atoms and robust high-fidelity quantum gates with a resonant amplitudemodulation field, Opt. Lett. 45(5), 1200 (2020)

[73] H. D. Yin, X. X. Li, G. C. Wang, and X. Q. Shao, One step implementation of Toffoli gate for neutral atoms based on unconventional Rydberg pumping, Opt. Express28(24), 35576 (2020)

[74] H. D. Yin and X. Q. Shao, Gaussian soft control-based quantum fan-out gate in ground-state manifolds of neutral atoms, Opt. Lett. 46(10), 2541 (2021)

[75] I. I. Beterov, I. I. Ryabtsev, D. B. Tretyakov, and V. M. Entin, Quasiclassical calculations of black body radiationinduced depopulation rates and effective lifetimes of Rydberg ns, np, and nd alkali-metal atoms with n≤80, Phys. Rev. A79(5), 052504 (2009)

[76] M. Saffman, Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges, J. Phys. B49(20), 202001 (2016)

[77] I. I. Ryabtsev, I. I. Beterov, D. B. Tretyakov, V. M. Entin, and E. A. Yakshina, Doppler- and recoil-free laser excitation of Rydberg states via three-photon transitions, Phys. Rev. A84(5), 053409 (2011)

[78] X. F. Shi, Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms, Phys. Rev. Appl. 11(4), 044035 (2019)

[79] X. F. Shi, Suppressing motional dephasing of ground-Rydberg transition for high-fidelity quantum control with neutral atoms, Phys. Rev. Appl. 13(2), 024008 (2020)

[80] J. L. Wu, Y. Wang, J. X. Han, S. L. Su, Y. Xia, Y. Jiang, and J. Song, Resilient quantum gates on periodically driven Rydberg atoms, Phys. Rev. A103(1), 012601 (2021)

[81] S. de Léséleuc, D. Barredo, V. Lienhard, A. Browaeys, and T. Lahaye, Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states, Phys. Rev. A97(5), 053803 (2018)

[82] 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 twodimensional neutral atom qubit array, Phys. Rev. Lett. 123(23), 230501 (2019)

[83] D. S. Weiss and M. Saffman, Quantum computing with neutral atoms, Phys. Today70(7), 44 (2017)

[84] A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16(2), 132 (2020)

[85] L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G. O. Reymond, and C. Jurczak, Quantum computing with neutral atoms, Quantum4, 327 (2020)

[86] S. L. Su, F. Q. Guo, L. Tian, X. Y. Zhu, L. L. Yan, E. J. Liang, and M. Feng, Nondestructive Rydberg parity meter and its applications, Phys. Rev. A 101(1), 012347 (2020)

[87] E. Fredkin and T. Toffoli, Conservative logic, Int. J. Theor. Phys. 21(3–4), 219 (1982)

[88] I. L. Chuang and Y. Yamamoto, Quantum bit regeneration, Phys. Rev. Lett. 76(22), 4281 (1996)

[89] H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, Quantum fingerprinting, Phys. Rev. Lett. 87(16), 167902 (2001)

[90] B. K. Behera, T. Reza, A. Gupta, and P. K. Panigrahi, Designing quantum router in IBM quantum computer, Quantum Inform. Process. 18(11), 328 (2019)

[91] W. Feng and D. Wang, Quantum Fredkin gate based on synthetic three-body interactions in superconducting circuits, Phys. Rev. A 101(6), 062312 (2020)

[92] M. D. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Realization of threequbit quantum error correction with superconducting circuits, Nature 482(7385), 382 (2012)

[93] A. M. Souza, G. A. Álvarez, and D. Suter, Robust dynamical decoupling, Phil. Trans. R. Soc. A370(1976), 4748 (2012)

[94] G. T. Genov, D. Schraft, N. V. Vitanov, and T. Halfmann, Arbitrarily accurate pulse sequences for robust dynamical decoupling, Phys. Rev. Lett. 118(13), 133202 (2017)

[95] B. J. Liu, Y. S. Wang, and M. H. Yung, Global property condition-based non-adiabatic geometric quantum control, arXiv: 2008.02176 (2020)

[96] A. Vepsäläinen, S. Danilin, and G. S. Paraoanu, Optimal superadiabatic population transfer and gates by dynamical phase corrections, Quantum Sci. Technol. 3(2), 024006 (2018)

[97] A. Vepsäläinen, S. Danilin, and G. S. Paraoanu, Superadiabatic population transfer in a three-level superconducting circuit, Sci. Adv. 5(2), eaau5999 (2019)

[98] C. Wang, J. X. Han, J. L. Wu, Y. Wang, Y. Jiang, Y. Xia, and J. Song, Generation of three-dimensional entanglement between two antiblockade Rydberg atoms with detuning-compensation-induced effective resonance, Laser Phys. 30(4), 045201 (2020)

[99] J. X. Han, J. L. Wu, Y. Wang, Y. Y. Jiang, Y. Xia, and J. Song, Multi-qubit phase gate on multiple resonators mediated by a superconducting bus, Opt. Express 28(2), 1954 (2020)

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