Abstract
The high-speed implementation and robustness against of non-adiabatic holonomic quantum computation provide a new idea for overcoming the difficulty of the quantum system interacting with the environment easily decoherence, which realizing large-scale quantum computer construction. Here, we show that high-fidelity quantum gates to implement non-adiabatic holonomic quantum computation under electron spin states in Nitrogen-Vacancy(NV ) centers, providing an extensible experimental platform that has the potential for room-temperature quantum computing, which has increased attention recent years. Compared with the previous method, we can implement both the one- and two-qubit gates by varying the amplitude and phase of the microwave pulse applied to control the non-Abelian geometric phase acquired by NV centers. We also found that our proposed scheme may be implemented in the current experiment to discuss the gate fidelity with the experimental parameters. Therefore, the scheme adopts a new method to achieve high-fidelity non-adiabatic holonomic quantum computation.
Similar content being viewed by others
References
ÓBrien, J.L.: Optical quantum computing. Science 318, 1567–1570 (2007)
Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., ÓBrien, J.L.: Quantum computers. Nature(London) 464, 45–53 (2010)
Suter, D., Lim, K.: Scalable architecture for spin-based quantum computers with a single type of gate. Phys. Rev. A 65, 052309 (2002)
Sjöqvist, E., Pati, A.K., Ekert, A., Anandan, J.S., Ericsson, M., Oi, D.K.L., Vedral, V.: Geometric phases for mixed states in interferometry. Phys. Rev. Lett. 85, 2845 (2000)
Falci, G., Fazio, R., Palma, G.M., Siewert, J., Vedral, V.: Detection of geometric phases in superconducting nanocircuits. Nature(London) 407, 355–358 (2000)
Zhu, S.L., Wang, Z.D.: Implementation of universal quantum gates based on nonadiabatic geometric phases. Phys. Rev. Lett. 89, 097902 (2002)
Zhu, S.L.: Scaling of geometric phases close to the quantum phase transition in the spin chain. Phys. Rev. Lett. 96, 077206 (2006)
Mousolou, V.A., Sjöqvist, E.: Non-Abelian geometric phases in a system of coupled quantum bits. Phys. Rev. A 89, 022117 (2014)
Simeonov, L.S., Vitanov, N.V.: Generation of non-Abelian geometric phases in degenerate atomic transitions. Phys. Rev. A 96, 032102 (2017)
Abdumalikov Jr, A.A., Fink, J.M., Juliusson, K., Pechal, M., Berger, S., Wallraff, A., Filipp, S.: Experimental realization of non-Abelian non-adiabatic geometric gates. Nature(London) 496, 482–485 (2013)
Xu, G.F., Long, G.L.: Universal nonadiabatic geometric gates in two-qubit decoherence-free subspaces. Sci. Rep. 4, 6814 (2014)
Liang, Z.T., Yue, X.X., Lv, Q., Du, Y.X., Huang, W., Yan, H., Zhu, S.L.: Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers. Phys. Rev. A 93(R), 040305 (2016)
Berger, S., Pechal, M., Abdumalikov Jr, A.A., Eichler, C., Steffen, L., Fedorov, A., Wallraff, A., Filipp, S.: Exploring the effect of noise on the berry phase. Phys Rev. A 87(R), 060303 (2013)
Yale, C.G., Heremans, F.J., Zhou, B.B., Auer, A., Burkard, G., Awschalom, D.D.: Optical manipulation of the Berry phase in a solid-state spin qubit. Nat. Photon. 10, 184 (2016)
Albash, T., Lidar, D.A.: Decoherence in adiabatic quantum computation. Phys. Rev. A 91, 062320 (2015)
Sjöqvist, E.: Nonadiabatic holonomic single-qubit gates in off-resonant Λ systems. Phys. Lett. A 380, 65–67 (2016)
Duan, L.M., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Science 292, 1695–1697 (2001)
Recati, A., Calarco, T., Zanardi, P., Cirac, J.I., Zoller, P.: Holonomic quantum computation with neutral atoms. Phys. Rev. A 66, 032309 (2002)
Zhang, P., Wang, Z.D., Sun, J.D., Sun, C.P.: Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity. Phys. Rev. A 71, 042301 (2005)
Zhang, X.D., Zhang, Q., Wang, Z.D.: Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions. Phys. Rev. A 74, 34302 (2006)
Zanardi, P., Rasetti, M.: Holonomic quantum computation. Phys. Lett. A 264, 94–99 (1999)
Lidar, D.A., Chuang, I.L., Whaley, K.B.: Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594 (1998)
Knill, E., Laflamme, R., Viola, L.: Theory of quantum error correction for general noise. Phys. Rev. Lett. 84, 2525 (2000)
Nayak, C., Simon, S.H., Stern, A., Freedman, M., Das Sarma, S.: Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083 (2008)
Sjöqvist, E., Tong, D.M., Andersson, L.M., Hessmo, B., Johansson, M., Singh, K.: Non-adiabatic holonomic quantum computation. New J. Phys. 14, 103035 (2012)
Zhou, J., Liu, B.J., Hong, Z.P., Xue, Z.Y.: Fast holonomic quantum computation on solid-state spins with all-optical control. Sci. China Phys. Mech. 1, 010312 (2018)
Dong, P., Yu, L.B., Zhou, J.: Holonomic quantum computation on microwave photons with all resonant interactions. Laser Phys. Lett. 13, 085201 (2016)
Herr, D., Nori, F., Devitt, S.J.: Lattice surgery translation for quantum computation. New J. Phys. 19, 013034 (2017)
Liu, J., Dong, P., Zhou, J., Cao, Z.L.: Universal non-adiabatic holonomic quantum computation in decoherence-free subspaces with quantum dots inside a cavity. Laser Phys. Lett. 14, 055202 (2017)
Zhou, J., Yu, W.C., Gao, Y.M., Xue, Z.Y.: Cavity QED implementation of non-adiabatic holonomies for universal quantum gates in decoherence-free subspaces with nitrogen-vacancy centers. Opt. Express 23, 14027 (2015)
Liang, Z.T., Du, Y.X., Huang, W., Xue, Z.Y., Yan, H.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions. Phys. Rev. A 89, 062312 (2014)
Xu, G.F., Liu, C.L., Zhao, P.Z., Tong, D.M.: Nonadiabatic holonomic gates realized by a single-shot implementation. Phys. Rev. A 92, 052302 (2015)
Xue, Z.Y., Zhou, J., Chu, Y.M., Hu, Y.: Nonadiabatic holonomic quantum computation with all-resonant control. Phys. Rev. A 94, 022331 (2016)
Herterich, E., Sjöqvist, E.: Single-loop multiple-pulse nonadiabatic holonomic quantum gates. Phys. Rev. A 94, 052310 (2016)
Zhao, P.Z., Xu, G.F., Tong, D.M.: Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases. Phys. Rev. A 94, 062327 (2016)
Xu, G.F., Zhao, P.Z., Xing, T.H., Sjöqvist, E., Tong, D.M.: Composite nonadiabatic holonomic quantum computation. Phys. Rev. A 95, 032311 (2017)
Liu, B.J., Huang, Z.H., Xue, Z.Y., Zhang, X.D.: Superadiabatic holonomic quantum computation in cavity QED. Phys. Rev. A 95, 062308 (2017)
Zhao, P.Z., Xu, G.F., Ding, Q.M., Sjöqvist, E., Tong, D.M.: Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces. Phys. Rev. A 95, 062310 (2017)
Xue, Z.Y., Gu, F.L., Hong, Z.P., Yang, Z.H., Zhang, D.W., Hu, Y., You, J.Q.: Nonadiabatic holonomic quantum computation with dressed-state qubits. Phys. Rev. Applied 7, 054022 (2017)
Xu, G.F., Zhang, J., Tong, D.M., Sjöqvist, E., Kwek, L.C.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces. Phys. Rev. Lett. 109, 170501 (2012)
Abdumalikov Jr, A.A., Fink, J.M., Juliusson, K., Pechal, M., Berger, S., Wallra, A., Filipp, S.: Experimental realization of non-Abelian non-adiabatic geometric gates. Nature. 7446 (2013)
Zu, C., Wang, W.B., He, L., Zhang, W.G., Dai, C.Y., Wang, F., Duan, L.M.: Experimental realization of universal geometric quantum gates with solid-state spins. Nature. 7520 (2014)
Zhou, B.B., Jerger, P.C., Shkolnikov, V.O., Heremans, F.J., Burkard, G., Awschalom, D.D.: Holonomic quantum control by coherent optical excitation in diamond. Phys. Rev. Lett. 14, 140503 (2017)
Arroyo-Camejo, S., Lazariev, A., Hell, S.W., Balasubramanian, G.: Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin. Nat. Commun. 5, 4870 (2014)
Sekiguchi, Y., Niikura, N., Kuroiwa, R., Kano, H., Kosaka, H: Optical holonomic single quantum gates with a geometric spin under a zero field. Nat. Photon. 11, 309–314 (2017)
Yale, C.G., Heremans, F.J., Zhou, B.B., Auer, A., Burkard, G., Awschalom, D.D.: Optical manipulation of the Berry phase in a solid-state spin qubit. Nat. Photon. 110, 184–189 (2016)
Clark, S., Parkins, A.: Entanglement and entropy engineering of atomic two-qubit states. Phys. Rev. Lett. 90, 047905 (2003)
Vernooy, D.W., Ilchenko, V.S., Mabuchi, H., Streed, E.W., Kimble, H.J.: High-q measurements of fused-silica microspheres in the near infrared. Opt. Lett. 23, 247–249 (1998)
Tittel, W., Brendel, J., Zbinden, H., Gisin, N.: Quantum cryptography using entangled photons in energy-time bell states. Phys. Rev. Lett. 84, 4737 (2000)
Acknowledgments
This work are supported by the Project of Introduction and Cultivation for Young Innovative Talents in Colleges and Universities of Shandong Province and National Natural Science Foundation of China under Grant Nos. 11674253, 11674089, 11725524 and 61471356.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yan, GA., Lu, H. Room Temperature High-fidelity Non-adiabatic Holonomic Quantum Computation on Solid-state Spins in Nitrogen-vacancy Centers. Int J Theor Phys 59, 2223–2231 (2020). https://doi.org/10.1007/s10773-020-04500-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-020-04500-6