Abstract
Blind quantum computing (BQC) allows a client with limited quantum technology to delegate her quantum computational tasks to a server who can perform universal quantum computation while retaining the client’s secret information. Firstly, in qubits transmission between the server and the client, the loss of qubits is inevitable due to the channel noise. Thus, we propose a fault-tolerant framework for blind quantum computing using logical GHZ states over depolarization channels. In our protocol, an encoded GHZ state by 7-qubit Calderbank–Shor–Steane code is sent by the quantum channel as a medium of quantum teleportation. The client only makes a single-qubit measurement on the third qubit of the logical GHZ state, and the remaining Bell state is shared between the client and the server. After decoding logical Bell state, the client and the server perform the measurement-based blind quantum computing protocol. Secondly, there are two classes of collective noises in the channel, which will affect the blind quantum computing. We modify our BQC protocol to overcome the collective-dephasing noise and the collective-rotating noise with logical states \(|H_{dp}\rangle \), \(|V_{dp}\rangle \), \(|H_{r}\rangle \) and \(|V_{r}\rangle \). Our protocol is robust against channel noise and qubits loss.


Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Bennett C.H., Brassard, G., Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, vol. 10–12, pp. 175–179 (1984)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)
Andrew, M.: Childs, secure assisted quantum computation. Quant. Inform. Comput. 5, 456–466 (2005)
Fisher, K.A.G., Broadbent, A., Shalm, L.K., Yan, Z., Lavoie, J., Prevedel, R., Jennewein, T., Resch, K.J.: Quantum computing on encrypted data. Nat. Commun. 5, 3074 (2014)
Fitzsimons, J.F.: Private quantum computation, an introduction to blind quantum computing and related protocols. NPJ Quant. Inform. 3, 23 (2017)
Pablo, A., Louis, S.: Blind quantum computation. Int. J. Quant. Inform. 4, 883–898 (2006)
Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation. In: 2009 50th Annual IEEE Symposium on Foundations of Computer Science, vol. 5, pp. 17–526 (2009)
Briegel, H., Browne, D., Dür, W., Raussendorf, R., Van den Nest, M.: Measurement-based quantum computation. Nat. Phys. 5, 19–26 (2009)
Broadbent, A., Fitzsimons, J., Kashefi, E.: Measurement-Based and Universal Blind Quantum Computation, vol. 4, pp. 3–86. Springer, Berlin (2010)
Barz, S., Kashefi, E., Broadbent, A., Fitzsimons, J.F., Zeilinger, A., Walther, P.: Demonstration of blind quantum computing. Science 335, 303–308 (2012)
Morimae, T., Fujii, K.: Secure entanglement distillation for double-server blind quantum computation. Phys. Rev. Lett. 111, 020502 (2013)
Li, Q., Chan, W.H., Wu, C.H., Wen, Z.H.: Triple-server blind quantum computation using entanglement swapping. Phys. Rev. A 89, 040302 (2014)
Tomoyuki, M., Keisuke, F.: Blind topological measurement-based quantum computation. Nat. Commun. 3, 1036 (2012)
Raussendorf, R., Harrington, J.: Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 99, 190504 (2007)
Morimae, T., Fujii, K.: Blind quantum computation protocol in which Alice only makes measurements. Phys. Rev. A 87, 050301 (2013)
Greganti, C., Roehsner, M.C., Barz, S., Morimae, T., Walther, P.: Demonstration of measurement-only blind quantum computing. N. J. Phys. 18, 013020 (2016)
Takeuchi, Y., Fujii, K., Ikuta, R., Yamamoto, T., Imoto, N.: Blind quantum computation over a collective-noise channel. Phys. Rev. A 93, 052307 (2016)
Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)
Dr, W., Briegel, H.J.: Entanglement purification and quantum error correction. Rep. Progress Phys. 70, 1381–1424 (2007)
Zanardi, P., Rasetti, M.: Noiseless quantum codes. Phys. Rev. Lett. 79, 3306–3309 (1997)
Sheng, Y.B., Zhou, L.: Deterministic entanglement distillation for secure double-server blind quantum computation. Cien. Rep. 5, 7815 (2015)
Kwiat, P.G., Berglund, A.J., Altepeter, J.B., White, A.G.: Experimental verification of decoherence-free subspaces. Science 260, 498–501 (2000)
Tian-Yu, Y.: Fault-tolerant quantum dialogue without information leakage based on entanglement swapping between two logical bell states. Commun. Theor. Phys. 63, 431–438 (2015)
Kumagai, H., Yamamoto, T., Koashi, M., Imoto, N.: Robustness of quantum communication based on a decoherence-free subspace using a counter-propagating weak coherent light pulse. Phys. Rev. A 87, 052325 (2013)
Wu, D., Lv, H.J., Xie, G.J.: Robust anti-collective noise quantum secure direct dialogue using logical bell states. Int. J. Theor. Phys. 55, 1–13 (2015)
Stucki, D., Gisin, N., Guinnard, O., Ribordy, G., Zbinden, H.: Quantum key distribution over 67 km with a plugplay system. N. J. Phys. 4, 41 (2002)
Yamamoto, T., Shimamura, J., Özdemir, Ş.K., Koashi, M., Imoto, N.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95, 040503 (2005)
Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Found. Phys. 24, 379–385 (1994)
Yang, C.W., Tsai, C.W., Hwang, T.: Fault tolerant deterministic quantum communications using GHZ states over collective-noise channels. Quant. Inform. Process. 12, 3043–3055 (2013)
Zhang, X.Q., Weng, J., Lu, W., Li, X.C., Luo, W.Q., Tan, X.Q.: Greenberger–Horne–Zeilinger states-based blind quantum computation with entanglement concentration. Sci. Rep. 7, 11104 (2017)
Ye, T.: Fault tolerant channel-encrypting quantum dialogue against collective noise. Sci. China Phys. Mech. Astron. 58, 1–10 (2015)
Gu, B., Mu, L., Ding, L.G., Zhang, C.Y., Li, C.Q.: Fault tolerant three-party quantum secret sharing against collective noise. Opt. Commun. 283, 3099–3103 (2010)
Gu, B., Pei, S.X., Song, B., Zhong, K.: Deterministic secure quantum communication over a collective-noise channel. Sci. China Ser. G Phys. Mech. Astron. 52, 1913–1917 (2009)
Xiao, M., Liu, L., Song, X.I.: Multi-server blind quantum computation over collective-noise channels. Quant. Inform. Process. 17, 63 (2018)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, 10th edn. Cambridge University Press, Cambridge (2011)
Acknowledgements
The research is partly supported by the Natural Science Foundation of Guangdong Province of China under Grant No. 2019A1515011069, the National Cryptography Development Fund of China under Grant No. MMJJ20180109, the Major Program of Guangdong Basic and Applied Research under Grant No. 2019B030302008 and the National Natural Science Foundation of China under Grant Nos. 62032009 and 62005321.
Author information
Authors and Affiliations
Corresponding author
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
Tan, X., Tao, H., Zhang, X. et al. Fault-tolerant blind quantum computing using GHZ states over depolarization channel. Quantum Inf Process 20, 297 (2021). https://doi.org/10.1007/s11128-021-03197-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-021-03197-8