Abstract

Compared with the idea of universal quantum computation, a direct synthesis of a multiqubit logic gate can greatly improve the efficiency of quantum information processing tasks. Here we propose an efficient scheme to implement a three-qubit controlled-not (Toffoli) gate of neutral atoms based on unconventional Rydberg pumping. By adjusting the strengths of Rabi frequencies of driving fields, the Toffoli gate can be achieved within one step, which is also insensitive to the fluctuation of the Rydberg-Rydberg interaction. Considering different atom alignments, we can obtain a high-fidelity Toffoli gate at the same operation time ∼7 μs. In addition, our scheme can be further extended to the four-qubit case without altering the operating time.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (8)

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).
[Crossref]

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).
[Crossref]

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

J.-L. Wu, S.-L. Su, Y. Wang, J. Song, Y. Xia, and Y.-Y. Jiang, “Effective rabi dynamics of rydberg atoms and robust high-fidelity quantum gates with a resonant amplitude-modulation field,” Opt. Lett. 45(5), 1200–1203 (2020).
[Crossref]

Y.-H. Kang, Z.-C. Shi, B.-H. Huang, J. Song, and Y. Xia, “Flexible scheme for the implementation of nonadiabatic geometric quantum computation,” Phys. Rev. A 101(3), 032322 (2020).
[Crossref]

Z.-C. Shi, C. Zhang, L.-T. Shen, Y. Xia, X. X. Yi, and S.-B. Zheng, “Implementation of universal quantum gates by periodic two-step modulation in a weakly nonlinear qubit,” Phys. Rev. A 101(4), 042314 (2020).
[Crossref]

Y.-H. Kang, Z.-C. Shi, J. Song, and Y. Xia, “Heralded atomic nonadiabatic holonomic quantum computation with rydberg blockade,” Phys. Rev. A 102(2), 022617 (2020).
[Crossref]

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(2), 022308 (2020).
[Crossref]

2019 (5)

X.-Y. Zhu, E. Liang, and S.-L. Su, “Rydberg-atom-based controlled arbitrary-phase gate and its applications,” J. Opt. Soc. Am. B 36(7), 1937–1944 (2019).
[Crossref]

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(17), 170503 (2019).
[Crossref]

J. L. Wu and S. L. Su, “Universal speeded-up adiabatic geometric quantum computation in three-level systems via counterdiabatic driving,” J. Phys. A: Math. Theor. 52(33), 335301 (2019).
[Crossref]

J.-L. Wu and S.-L. Su, “Auxiliary-qubit-driving-induced entanglement and logic gate,” EPL 126(3), 30001 (2019).
[Crossref]

D. Tiarks, S. Schmidt-Eberle, T. Stolz, G. Rempe, and S. Dürr, “A photon–photon quantum gate based on rydberg interactions,” Nat. Phys. 15(2), 124–126 (2019).
[Crossref]

2018 (8)

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).
[Crossref]

X.-R. Huang, Z.-X. Ding, C.-S. Hu, L.-T. Shen, W. Li, H. Wu, and S.-B. Zheng, “Robust rydberg gate via landau-zener control of förster resonance,” Phys. Rev. A 98(5), 052324 (2018).
[Crossref]

X.-F. Shi and T. A. B. Kennedy, “Simulating magnetic fields in rydberg-dressed neutral atoms,” Phys. Rev. A 97(3), 033414 (2018).
[Crossref]

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

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).
[Crossref]

S. L. Su, “Rydberg quantum controlled-phase gate with one control and multiple target qubits,” Chin. Phys. B 27(11), 110304 (2018).
[Crossref]

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. A 97(4), 042336 (2018).
[Crossref]

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. A 97(5), 053803 (2018).
[Crossref]

2017 (7)

S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth, “Calculation of rydberg interaction potentials,” J. Phys. B: At., Mol. Opt. Phys. 50(13), 133001 (2017).
[Crossref]

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).
[Crossref]

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).
[Crossref]

J. Lee, M. J. Martin, Y.-Y. Jau, T. Keating, I. H. Deutsch, and G. W. Biedermann, “Demonstration of the jaynes-cummings ladder with rydberg-dressed atoms,” Phys. Rev. A 95(4), 041801 (2017).
[Crossref]

O. Lahad and O. Firstenberg, “Induced cavities for photonic quantum gates,” Phys. Rev. Lett. 119(11), 113601 (2017).
[Crossref]

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. A 96(2), 022321 (2017).
[Crossref]

D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, “High-fidelity rydberg quantum gate via a two-atom dark state,” Phys. Rev. A 96(4), 042306 (2017).
[Crossref]

2016 (5)

S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
[Crossref]

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of rydberg-mediated single-photon nonlinearities by electrically tuned förster resonances,” Nat. Commun. 7(1), 12480 (2016).
[Crossref]

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(6), 062307 (2016).
[Crossref]

D. Maslov, “Advantages of using relative-phase toffoli gates with an application to multiple control toffoli optimization,” Phys. Rev. A 93(2), 022311 (2016).
[Crossref]

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).
[Crossref]

2015 (4)

E. Zahedinejad, J. Ghosh, and B. C. Sanders, “High-fidelity single-shot toffoli gate via quantum control,” Phys. Rev. Lett. 114(20), 200502 (2015).
[Crossref]

S. Ravets, H. Labuhn, D. Barredo, T. Lahaye, and A. Browaeys, “Measurement of the angular dependence of the dipole-dipole interaction between two individual rydberg atoms at a förster resonance,” Phys. Rev. A 92(2), 020701 (2015).
[Crossref]

I. I. Beterov and M. Saffman, “Rydberg blockade, förster resonances, and quantum state measurements with different atomic species,” Phys. Rev. A 92(4), 042710 (2015).
[Crossref]

T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, “Robust quantum logic in neutral atoms via adiabatic rydberg dressing,” Phys. Rev. A 91(1), 012337 (2015).
[Crossref]

2014 (7)

D. Tiarks, S. Baur, K. Schneider, S. Dürr, and G. Rempe, “Single-photon transistor using a förster resonance,” Phys. Rev. Lett. 113(5), 053602 (2014).
[Crossref]

S. Ravets, H. Labuhn, D. Barredo, L. Béguin, T. Lahaye, and A. Browaeys, “Coherent dipole–dipole coupling between two single rydberg atoms at an electrically-tuned förster resonance,” Nat. Phys. 10(12), 914–917 (2014).
[Crossref]

D. Petrosyan and K. Mølmer, “Binding potentials and interaction gates between microwave-dressed rydberg atoms,” Phys. Rev. Lett. 113(12), 123003 (2014).
[Crossref]

M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, “Implementation of an experimentally feasible controlled-phase gate on two blockaded rydberg atoms,” Phys. Rev. A 89(3), 032334 (2014).
[Crossref]

D. Paredes-Barato and C. S. Adams, “All-optical quantum information processing using rydberg gates,” Phys. Rev. Lett. 112(4), 040501 (2014).
[Crossref]

S. Baur, D. Tiarks, G. Rempe, and S. Dürr, “Single-photon switch based on rydberg blockade,” Phys. Rev. Lett. 112(7), 073901 (2014).
[Crossref]

D. D. B. Rao and K. Mølmer, “Robust rydberg-interaction gates with adiabatic passage,” Phys. Rev. A 89(3), 030301 (2014).
[Crossref]

2013 (4)

I. I. Beterov, M. Saffman, E. A. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, “Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and rydberg blockade,” Phys. Rev. A 88(1), 010303 (2013).
[Crossref]

T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, “Adiabatic quantum computation with rydberg-dressed atoms,” Phys. Rev. A 87(5), 052314 (2013).
[Crossref]

B. Eastin, “Distilling one-qubit magic states into toffoli states,” Phys. Rev. A 87(3), 032321 (2013).
[Crossref]

L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, “Direct measurement of the van der waals interaction between two rydberg atoms,” Phys. Rev. Lett. 110(26), 263201 (2013).
[Crossref]

2012 (4)

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(4), 042310 (2012).
[Crossref]

J. Qian, G. Dong, L. Zhou, and W. Zhang, “Phase diagram of rydberg atoms in a nonequilibrium optical lattice,” Phys. Rev. A 85(6), 065401 (2012).
[Crossref]

F. Reiter and A. S. Sørensen, “Effective operator formalism for open quantum systems,” Phys. Rev. A 85(3), 032111 (2012).
[Crossref]

A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, “Implementation of a toffoli gate with superconducting circuits,” Nature 481(7380), 170–172 (2012).
[Crossref]

2011 (4)

L.-T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84(6), 064302 (2011).
[Crossref]

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106(9), 090502 (2011).
[Crossref]

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via rydberg blockade,” Phys. Rev. Lett. 107(13), 133602 (2011).
[Crossref]

Y. L. Zhou and C. Z. Li, “Robust quantum gates via a photon triggering electromagnetically induced transparency,” Phys. Rev. A 84(4), 044304 (2011).
[Crossref]

2010 (4)

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with rydberg atoms,” Rev. Mod. Phys. 82(3), 2313–2363 (2010).
[Crossref]

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).
[Crossref]

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).
[Crossref]

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).
[Crossref]

2009 (1)

M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, “Mesoscopic rydberg gate based on electromagnetically induced transparency,” Phys. Rev. Lett. 102(17), 170502 (2009).
[Crossref]

2008 (1)

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).
[Crossref]

2007 (1)

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).
[Crossref]

2002 (1)

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
[Crossref]

2001 (1)

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).
[Crossref]

2000 (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), 2208–2211 (2000).
[Crossref]

Adams, C. S.

D. Paredes-Barato and C. S. Adams, “All-optical quantum information processing using rydberg gates,” Phys. Rev. Lett. 112(4), 040501 (2014).
[Crossref]

Amthor, T.

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).
[Crossref]

Ates, C.

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).
[Crossref]

Barredo, D.

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. A 97(5), 053803 (2018).
[Crossref]

S. Ravets, H. Labuhn, D. Barredo, T. Lahaye, and A. Browaeys, “Measurement of the angular dependence of the dipole-dipole interaction between two individual rydberg atoms at a förster resonance,” Phys. Rev. A 92(2), 020701 (2015).
[Crossref]

S. Ravets, H. Labuhn, D. Barredo, L. Béguin, T. Lahaye, and A. Browaeys, “Coherent dipole–dipole coupling between two single rydberg atoms at an electrically-tuned förster resonance,” Nat. Phys. 10(12), 914–917 (2014).
[Crossref]

Baur, M.

A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, “Implementation of a toffoli gate with superconducting circuits,” Nature 481(7380), 170–172 (2012).
[Crossref]

Baur, S.

D. Tiarks, S. Baur, K. Schneider, S. Dürr, and G. Rempe, “Single-photon transistor using a förster resonance,” Phys. Rev. Lett. 113(5), 053602 (2014).
[Crossref]

S. Baur, D. Tiarks, G. Rempe, and S. Dürr, “Single-photon switch based on rydberg blockade,” Phys. Rev. Lett. 112(7), 073901 (2014).
[Crossref]

Béguin, L.

S. Ravets, H. Labuhn, D. Barredo, L. Béguin, T. Lahaye, and A. Browaeys, “Coherent dipole–dipole coupling between two single rydberg atoms at an electrically-tuned förster resonance,” Nat. Phys. 10(12), 914–917 (2014).
[Crossref]

L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, “Direct measurement of the van der waals interaction between two rydberg atoms,” Phys. Rev. Lett. 110(26), 263201 (2013).
[Crossref]

Bergamini, S.

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(6), 062307 (2016).
[Crossref]

I. I. Beterov, M. Saffman, E. A. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, “Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and rydberg blockade,” Phys. Rev. A 88(1), 010303 (2013).
[Crossref]

Bernien, H.

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(17), 170503 (2019).
[Crossref]

Beterov, I. I.

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).
[Crossref]

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).
[Crossref]

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(6), 062307 (2016).
[Crossref]

I. I. Beterov and M. Saffman, “Rydberg blockade, förster resonances, and quantum state measurements with different atomic species,” Phys. Rev. A 92(4), 042710 (2015).
[Crossref]

I. I. Beterov, M. Saffman, E. A. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, “Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and rydberg blockade,” Phys. Rev. A 88(1), 010303 (2013).
[Crossref]

Biedermann, G. W.

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).
[Crossref]

J. Lee, M. J. Martin, Y.-Y. Jau, T. Keating, I. H. Deutsch, and G. W. Biedermann, “Demonstration of the jaynes-cummings ladder with rydberg-dressed atoms,” Phys. Rev. A 95(4), 041801 (2017).
[Crossref]

T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, “Robust quantum logic in neutral atoms via adiabatic rydberg dressing,” Phys. Rev. A 91(1), 012337 (2015).
[Crossref]

T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, “Adiabatic quantum computation with rydberg-dressed atoms,” Phys. Rev. A 87(5), 052314 (2013).
[Crossref]

Bienias, P.

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of rydberg-mediated single-photon nonlinearities by electrically tuned förster resonances,” Nat. Commun. 7(1), 12480 (2016).
[Crossref]

Boddeda, R.

S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
[Crossref]

Borregaard, J.

S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
[Crossref]

Brion, E.

S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
[Crossref]

Browaeys, A.

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. A 97(5), 053803 (2018).
[Crossref]

S. Ravets, H. Labuhn, D. Barredo, T. Lahaye, and A. Browaeys, “Measurement of the angular dependence of the dipole-dipole interaction between two individual rydberg atoms at a förster resonance,” Phys. Rev. A 92(2), 020701 (2015).
[Crossref]

S. Ravets, H. Labuhn, D. Barredo, L. Béguin, T. Lahaye, and A. Browaeys, “Coherent dipole–dipole coupling between two single rydberg atoms at an electrically-tuned förster resonance,” Nat. Phys. 10(12), 914–917 (2014).
[Crossref]

M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, “Implementation of an experimentally feasible controlled-phase gate on two blockaded rydberg atoms,” Phys. Rev. A 89(3), 032334 (2014).
[Crossref]

L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, “Direct measurement of the van der waals interaction between two rydberg atoms,” Phys. Rev. Lett. 110(26), 263201 (2013).
[Crossref]

Büchler, H. P.

S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth, “Calculation of rydberg interaction potentials,” J. Phys. B: At., Mol. Opt. Phys. 50(13), 133001 (2017).
[Crossref]

H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of rydberg-mediated single-photon nonlinearities by electrically tuned förster resonances,” Nat. Commun. 7(1), 12480 (2016).
[Crossref]

M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, “Mesoscopic rydberg gate based on electromagnetically induced transparency,” Phys. Rev. Lett. 102(17), 170502 (2009).
[Crossref]

Calarco, T.

M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, “Implementation of an experimentally feasible controlled-phase gate on two blockaded rydberg atoms,” Phys. Rev. A 89(3), 032334 (2014).
[Crossref]

Chen, X.-Y.

L.-T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84(6), 064302 (2011).
[Crossref]

Chen, Y.-H.

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. A 97(4), 042336 (2018).
[Crossref]

Chicireanu, R.

L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, “Direct measurement of the van der waals interaction between two rydberg atoms,” Phys. Rev. Lett. 110(26), 263201 (2013).
[Crossref]

Cirac, J. I.

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).
[Crossref]

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), 2208–2211 (2000).
[Crossref]

Cook, R. L.

T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, “Robust quantum logic in neutral atoms via adiabatic rydberg dressing,” Phys. Rev. A 91(1), 012337 (2015).
[Crossref]

Cote, R.

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).
[Crossref]

Côté, R.

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), 2208–2211 (2000).
[Crossref]

da Silva, M. P.

A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, “Implementation of a toffoli gate with superconducting circuits,” Nature 481(7380), 170–172 (2012).
[Crossref]

Dalal, A.

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).
[Crossref]

Das, S.

S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
[Crossref]

de Léséleuc, S.

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. A 97(5), 053803 (2018).
[Crossref]

Deutsch, I. H.

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).
[Crossref]

J. Lee, M. J. Martin, Y.-Y. Jau, T. Keating, I. H. Deutsch, and G. W. Biedermann, “Demonstration of the jaynes-cummings ladder with rydberg-dressed atoms,” Phys. Rev. A 95(4), 041801 (2017).
[Crossref]

T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, “Robust quantum logic in neutral atoms via adiabatic rydberg dressing,” Phys. Rev. A 91(1), 012337 (2015).
[Crossref]

T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, “Adiabatic quantum computation with rydberg-dressed atoms,” Phys. Rev. A 87(5), 052314 (2013).
[Crossref]

Ding, Z.-X.

X.-R. Huang, Z.-X. Ding, C.-S. Hu, L.-T. Shen, W. Li, H. Wu, and S.-B. Zheng, “Robust rydberg gate via landau-zener control of förster resonance,” Phys. Rev. A 98(5), 052324 (2018).
[Crossref]

Dong, G.

J. Qian, G. Dong, L. Zhou, and W. Zhang, “Phase diagram of rydberg atoms in a nonequilibrium optical lattice,” Phys. Rev. A 85(6), 065401 (2012).
[Crossref]

Duan, L. M.

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).
[Crossref]

Dürr, S.

D. Tiarks, S. Schmidt-Eberle, T. Stolz, G. Rempe, and S. Dürr, “A photon–photon quantum gate based on rydberg interactions,” Nat. Phys. 15(2), 124–126 (2019).
[Crossref]

D. Tiarks, S. Baur, K. Schneider, S. Dürr, and G. Rempe, “Single-photon transistor using a förster resonance,” Phys. Rev. Lett. 113(5), 053602 (2014).
[Crossref]

S. Baur, D. Tiarks, G. Rempe, and S. Dürr, “Single-photon switch based on rydberg blockade,” Phys. Rev. Lett. 112(7), 073901 (2014).
[Crossref]

Eastin, B.

B. Eastin, “Distilling one-qubit magic states into toffoli states,” Phys. Rev. A 87(3), 032321 (2013).
[Crossref]

Ebadi, S.

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(17), 170503 (2019).
[Crossref]

Entin, V. M.

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).
[Crossref]

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(6), 062307 (2016).
[Crossref]

I. I. Beterov, M. Saffman, E. A. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, “Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and rydberg blockade,” Phys. Rev. A 88(1), 010303 (2013).
[Crossref]

Fedorov, A.

A. Fedorov, L. Steffen, M. Baur, M. P. da Silva, and A. Wallraff, “Implementation of a toffoli gate with superconducting circuits,” Nature 481(7380), 170–172 (2012).
[Crossref]

Fedoruk, M. P.

I. I. Beterov, M. Saffman, E. A. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, “Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and rydberg blockade,” Phys. Rev. A 88(1), 010303 (2013).
[Crossref]

Firstenberg, O.

O. Lahad and O. Firstenberg, “Induced cavities for photonic quantum gates,” Phys. Rev. Lett. 119(11), 113601 (2017).
[Crossref]

S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth, “Calculation of rydberg interaction potentials,” J. Phys. B: At., Mol. Opt. Phys. 50(13), 133001 (2017).
[Crossref]

Fleischhauer, M.

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via rydberg blockade,” Phys. Rev. Lett. 107(13), 133602 (2011).
[Crossref]

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).
[Crossref]

Gao, Y.

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).
[Crossref]

Gerritsma, R.

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(2), 022308 (2020).
[Crossref]

Ghosh, J.

E. Zahedinejad, J. Ghosh, and B. C. Sanders, “High-fidelity single-shot toffoli gate via quantum control,” Phys. Rev. Lett. 114(20), 200502 (2015).
[Crossref]

Giese, C.

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).
[Crossref]

Gill, A. T.

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(4), 042310 (2012).
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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).
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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).
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H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of rydberg-mediated single-photon nonlinearities by electrically tuned förster resonances,” Nat. Commun. 7(1), 12480 (2016).
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A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via rydberg blockade,” Phys. Rev. Lett. 107(13), 133602 (2011).
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T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, “Adiabatic quantum computation with rydberg-dressed atoms,” Phys. Rev. A 87(5), 052314 (2013).
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S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
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M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, “Implementation of an experimentally feasible controlled-phase gate on two blockaded rydberg atoms,” Phys. Rev. A 89(3), 032334 (2014).
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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(17), 170503 (2019).
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T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, “Robust quantum logic in neutral atoms via adiabatic rydberg dressing,” Phys. Rev. A 91(1), 012337 (2015).
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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).
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S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth, “Calculation of rydberg interaction potentials,” J. Phys. B: At., Mol. Opt. Phys. 50(13), 133001 (2017).
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H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of rydberg-mediated single-photon nonlinearities by electrically tuned förster resonances,” Nat. Commun. 7(1), 12480 (2016).
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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).
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X.-R. Huang, Z.-X. Ding, C.-S. Hu, L.-T. Shen, W. Li, H. Wu, and S.-B. Zheng, “Robust rydberg gate via landau-zener control of förster resonance,” Phys. Rev. A 98(5), 052324 (2018).
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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. A 96(2), 022321 (2017).
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Y.-H. Kang, Z.-C. Shi, B.-H. Huang, J. Song, and Y. Xia, “Flexible scheme for the implementation of nonadiabatic geometric quantum computation,” Phys. Rev. A 101(3), 032322 (2020).
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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. A 97(4), 042336 (2018).
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X.-R. Huang, Z.-X. Ding, C.-S. Hu, L.-T. Shen, W. Li, H. Wu, and S.-B. Zheng, “Robust rydberg gate via landau-zener control of förster resonance,” Phys. Rev. A 98(5), 052324 (2018).
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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. A 96(2), 022321 (2017).
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S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
[Crossref]

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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(4), 042310 (2012).
[Crossref]

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).
[Crossref]

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).
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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).
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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), 2208–2211 (2000).
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J. Lee, M. J. Martin, Y.-Y. Jau, T. Keating, I. H. Deutsch, and G. W. Biedermann, “Demonstration of the jaynes-cummings ladder with rydberg-dressed atoms,” Phys. Rev. A 95(4), 041801 (2017).
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T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, “Robust quantum logic in neutral atoms via adiabatic rydberg dressing,” Phys. Rev. A 91(1), 012337 (2015).
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T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, “Adiabatic quantum computation with rydberg-dressed atoms,” Phys. Rev. A 87(5), 052314 (2013).
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Jin, Z.

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).
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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).
[Crossref]

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Y.-H. Kang, Z.-C. Shi, B.-H. Huang, J. Song, and Y. Xia, “Flexible scheme for the implementation of nonadiabatic geometric quantum computation,” Phys. Rev. A 101(3), 032322 (2020).
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Y.-H. Kang, Z.-C. Shi, J. Song, and Y. Xia, “Heralded atomic nonadiabatic holonomic quantum computation with rydberg blockade,” Phys. Rev. A 102(2), 022617 (2020).
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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. A 97(4), 042336 (2018).
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T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, “Robust quantum logic in neutral atoms via adiabatic rydberg dressing,” Phys. Rev. A 91(1), 012337 (2015).
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T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, “Adiabatic quantum computation with rydberg-dressed atoms,” Phys. Rev. A 87(5), 052314 (2013).
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S. Ravets, H. Labuhn, D. Barredo, L. Béguin, T. Lahaye, and A. Browaeys, “Coherent dipole–dipole coupling between two single rydberg atoms at an electrically-tuned förster resonance,” Nat. Phys. 10(12), 914–917 (2014).
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S. Ravets, H. Labuhn, D. Barredo, T. Lahaye, and A. Browaeys, “Measurement of the angular dependence of the dipole-dipole interaction between two individual rydberg atoms at a förster resonance,” Phys. Rev. A 92(2), 020701 (2015).
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S. Ravets, H. Labuhn, D. Barredo, L. Béguin, T. Lahaye, and A. Browaeys, “Coherent dipole–dipole coupling between two single rydberg atoms at an electrically-tuned förster resonance,” Nat. Phys. 10(12), 914–917 (2014).
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T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, “Adiabatic quantum computation with rydberg-dressed atoms,” Phys. Rev. A 87(5), 052314 (2013).
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J. Lee, M. J. Martin, Y.-Y. Jau, T. Keating, I. H. Deutsch, and G. W. Biedermann, “Demonstration of the jaynes-cummings ladder with rydberg-dressed atoms,” Phys. Rev. A 95(4), 041801 (2017).
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M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, “Mesoscopic rydberg gate based on electromagnetically induced transparency,” Phys. Rev. Lett. 102(17), 170502 (2009).
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X.-R. Huang, Z.-X. Ding, C.-S. Hu, L.-T. Shen, W. Li, H. Wu, and S.-B. Zheng, “Robust rydberg gate via landau-zener control of förster resonance,” Phys. Rev. A 98(5), 052324 (2018).
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H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of rydberg-mediated single-photon nonlinearities by electrically tuned förster resonances,” Nat. Commun. 7(1), 12480 (2016).
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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).
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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. A 97(5), 053803 (2018).
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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(17), 170503 (2019).
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A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via rydberg blockade,” Phys. Rev. Lett. 107(13), 133602 (2011).
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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).
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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), 2208–2211 (2000).
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I. I. Beterov, M. Saffman, E. A. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, “Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and rydberg blockade,” Phys. Rev. A 88(1), 010303 (2013).
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I. I. Beterov, M. Saffman, E. A. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, “Quantum gates in mesoscopic atomic ensembles based on adiabatic passage and rydberg blockade,” Phys. Rev. A 88(1), 010303 (2013).
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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).
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J. Lee, M. J. Martin, Y.-Y. Jau, T. Keating, I. H. Deutsch, and G. W. Biedermann, “Demonstration of the jaynes-cummings ladder with rydberg-dressed atoms,” Phys. Rev. A 95(4), 041801 (2017).
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S. Weber, C. Tresp, H. Menke, A. Urvoy, O. Firstenberg, H. P. Büchler, and S. Hofferberth, “Calculation of rydberg interaction potentials,” J. Phys. B: At., Mol. Opt. Phys. 50(13), 133001 (2017).
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H. Gorniaczyk, C. Tresp, P. Bienias, A. Paris-Mandoki, W. Li, I. Mirgorodskiy, H. P. Büchler, I. Lesanovsky, and S. Hofferberth, “Enhancement of rydberg-mediated single-photon nonlinearities by electrically tuned förster resonances,” Nat. Commun. 7(1), 12480 (2016).
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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).
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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).
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M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, “Implementation of an experimentally feasible controlled-phase gate on two blockaded rydberg atoms,” Phys. Rev. A 89(3), 032334 (2014).
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M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, “Mesoscopic rydberg gate based on electromagnetically induced transparency,” Phys. Rev. Lett. 102(17), 170502 (2009).
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M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, “Implementation of an experimentally feasible controlled-phase gate on two blockaded rydberg atoms,” Phys. Rev. A 89(3), 032334 (2014).
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M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, “Implementation of an experimentally feasible controlled-phase gate on two blockaded rydberg atoms,” Phys. Rev. A 89(3), 032334 (2014).
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A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via rydberg blockade,” Phys. Rev. Lett. 107(13), 133602 (2011).
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S. Das, A. Grankin, I. Iakoupov, E. Brion, J. Borregaard, R. Boddeda, I. Usmani, A. Ourjoumtsev, P. Grangier, and A. S. Sørensen, “Photonic controlled-phase gates through rydberg blockade in optical cavities,” Phys. Rev. A 93(4), 040303 (2016).
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Figures (6)

Fig. 1.
Fig. 1. (a) The diagram of atom level configuration. $|0\rangle _{m}$ and $|1\rangle _{m}$ are ground states, and $|r\rangle _{m}$ is excited Rydberg state, $m=\left \lbrace 1,~2,~3\right \rbrace$ . Atom 1 and Atom 2 are control qubits, driven by a classical field of Rabi frequency $\Omega '$ with blue detuning $\Delta$ , respectively. Atom 3 is target qubit driven by classical fields with Rabi frequencies $\Omega _1$ and $\Omega _2$ . $U_{12}$ , $U_{13}$ and $U_{23}$ denote the RRI strengths. (b) Schematic representation of three interacting Rydberg atoms.
Fig. 2.
Fig. 2. (a) The level transitions between ground states $|000\rangle$ and $|001\rangle$ and excited Rydberg states under URP condition as $U_{13}=U_{23}=\Delta \gg \Omega '\gg \left \lbrace \Omega _1, \Omega _2 \right \rbrace$ . (b) The effective transitions between ground states and dressed states under the condition $U_{12}\gg \Omega '$ and other situations are the same with above. The red cross marks indicate that the transition processes are forbidden.
Fig. 3.
Fig. 3. (a) The average fidelities of the Toffoli gate governed by full (effective) Hamiltonian with different Rabi frequencies $\Omega _1=\left \lbrace 0.025\Omega ', 0.05\Omega ', 0.075\Omega '\right \rbrace$ , where $U_{13}=U_{23}=\Delta$ , $U_{12}=\Delta /8$ , and $\Delta =50\Omega '$ . (b) The variation tendency of the average fidelities with different mismatching rate $\eta _{\Delta }$ between $U$ and $\Delta$ , where $U_{13}=U_{23}=U$ , $\eta _{\Delta }=(U-\Delta )/\Delta$ , $U_{12}=\Delta /8$ , $\Delta =50\Omega '$ , and $\Omega _1=0.05\Omega '$ . (c) The variation trend of the average fidelities with different mismatching rate $\eta _{(\Omega ')}=(\Omega ''-\Omega ')/\Omega '$ , where $\Omega ''$ is the Rabi frequency driven the control qubit Atom 2 and the other parameters are the same as (a) when $\Omega _1=0.05\Omega '$ . (d) The variation trend of the average fidelities with different distances between control qubits when $\Omega _1=0.05\Omega '$ , $U_{13}=U_{23}=\Delta$ , and $\Delta =50\Omega '$ , where the value of distance $R$ corresponds to $U_{12}=\Delta$ . The insets show the structures of different distances and the enlarged view of the average fidelity for $U_{12}=2\Delta$ , respectively.
Fig. 4.
Fig. 4. The variation tendency of the fidelities of Toffoli gate scheme with different Rabi frequencies $\Omega _1=\left \lbrace 0.025\Omega ', 0.05\Omega ', 0.075\Omega '\right \rbrace$ versus decay rate $\gamma$ and the other parameters are same as Fig. 3(a).
Fig. 5.
Fig. 5. (a) Schematic representation of four interacting Rydberg atoms under the same distance among control qubits. (b) Schematic representation under the different distance among control qubits. The distances between target qubit and control qubits are all the same.
Fig. 6.
Fig. 6. (a) The population of state $|\phi \rangle$ and $|\psi \rangle$ governed by full and effective Hamiltonian of four-qubit Toffoli gate with $U_{12}=U_{13}=U_{23}=\Delta /27$ . (b) The population of state $|\phi \rangle$ and $|\psi \rangle$ governed by full and effective Hamiltonian of four-qubit Toffoli gate with $U_{13}=\Delta /64$ and $U_{12}=U_{23}=\Delta /8$ . The other same parameter conditions are $U_{14}=U_{24}=U_{34}=\Delta$ , $\Delta =50\Omega '$ and $\Omega _1=0.05\Omega '$ .

Tables (1)

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Table 1. The average fidelities of the Toffoli gate under different experimental parameters. The variable parameters are U 12 = 2 π × ( 50 / 8 , 50 , 50 / 64 ) MHz, U = 2 π × ( 49.5 , 50 , 50.5 ) MHz and Ω = 2 π × ( 1 , 2 ) MHz. Other same parameters are selected as ( Ω 1 ,   Ω ,   Δ ) = 2 π × ( 0.05 ,   1 ,   50 ) MHz and γ = 3.125 kHz.

Equations (11)

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U Toffoli = i , j , k = 0 1 | i , j , i j k i , j , k | ,
H I = Ω e i Δ t ( | 0 1 r | + | 0 2 r | ) + Ω 1 | 0 3 r | + Ω 2 | 1 3 r | + H . c . + j k U j k | r r j k r r | ,
H I R = α , β = 0 1 Ω 1 ( | α β 0 α β r | + e i Δ t | α r 0 α r r | + e i Δ t | r α 0 r α r | + e 2 i Δ t | r r 0 r r r | ) + Ω 2 ( | α β 1 α β r | + e i Δ t | α r 1 α r r | + e i Δ t | r α 1 r α r | + e 2 i Δ t | r r 1 r r r | ) + Ω ( e i Δ t | 0 α β r α β | + | 0 α r r α r | + e i ( Δ U 12 ) t | 0 r α r r α | + e i U 12 t | 0 r r r r r | + e i Δ t | α 0 β α r β | + | α 0 r α r r | + e i ( Δ U 12 ) t | r 0 α r r α | + e i U 12 t | r 0 r r r r | ) + H . c . ,
H I R = H I R ( 1 ) + H I R ( 2 ) + H I R ( 3 ) + H I R ( 4 ) ,
H I R ( 1 ) = Ω 1 | 000 00 r | + Ω 2 | 001 00 r | + Ω ( | 00 r r 0 r | + | 00 r 0 r r | + e i U 12 t | 0 r r r r r | + e i U 12 t | r 0 r r r r | ) + H . c . , H I R ( 2 ) = Ω 1 | 010 01 r | + Ω 2 | 011 01 r | + Ω | 01 r r 1 r | + H . c . , H I R ( 3 ) = Ω 1 | 100 10 r | + Ω 2 | 101 10 r | + Ω | 10 r 1 r r | + H . c . , H I R ( 4 ) = Ω 1 | 110 11 r | + Ω 2 | 111 11 r | + H . c . .
H e f f I R ( 1 ) = [ V H e 1 V + + V ( H e 1 ) V + ] / 2 = [ Ω 1 2 | 000 000 | + Ω 2 2 | 001 001 | + Ω 1 Ω 2 ( | 000 001 | + | 001 000 | ) ] / U 12 ,
H eff H I R ( 4 ) = Ω 1 | 110 11 r | + Ω 2 | 111 11 r | + H . c . .
F ¯ ( ε , O ) = j tr ( O O j O ε ( O j ) ) + d 2 d 2 ( d + 1 ) ,
ρ ˙ = i [ H I , ρ ] + γ 2 j = 1 6 ( 2 σ j ρ σ j σ j σ j ρ ρ σ j σ j ) ,
H I = Ω e i Δ t ( | 0 1 r | + | 0 2 r | + | 0 3 r | ) + Ω 1 | 0 4 r | + Ω 2 | 1 4 r | + H . c . + m n U m n | r r m n r r | ,
H eff = Ω 1 | 1110 111 r | + Ω 2 | 1111 111 r | + H . c . .

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