Skip to main content

Quantum communication protocols as a benchmark for programmable quantum computers

Abstract

We point out that realization of quantum communication protocols in programmable quantum computers provides a deep benchmark for capabilities of real quantum hardware. Particularly, it is prospective to focus on measurements of entropy-based characteristics of the performance and to explore whether a “quantum regime” is preserved. We perform proof-of-principle implementations of superdense coding and quantum key distribution BB84 using 5- and 16-qubit superconducting quantum processors of IBM Quantum Experience. We focus on the ability of these quantum machines to provide an efficient transfer of information between distant parts of the processors by placing Alice and Bob at different qubits of the devices. We also examine the ability of quantum devices to serve as quantum memory and to store entangled states used in quantum communication. Another issue we address is an error mitigation. Although it is at odds with benchmarking, this problem is nevertheless of importance in a general context of quantum computation with noisy quantum devices. We perform such a mitigation and noticeably improve some results.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  1. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, p. 175

  2. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    ADS  Article  Google Scholar 

  3. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009)

    ADS  Article  Google Scholar 

  4. Korzh, B., Wen Lim, C.C., Houlmann, R., Gisin, N., Li, M.J., Nolan, D., Sanguinetti, B., Thew, R., Zbinden, H.: Provably secure and practical quantum key distribution over 307 km of optical fibre. Nat. Photon. 9, 163 (2015)

    ADS  Article  Google Scholar 

  5. Fröhlich, B., Lucamarini, M., Dynes, J.F., Comandar, L.C., Tam, W.W.-S., Plews, A., Sharpe, A.W., Yuan, Z., Shields, A.J.: Long-distance quantum key distribution secure against coherent attacks. Optica 4, 163 (2017)

    ADS  Article  Google Scholar 

  6. Liao, S.-K., et al.: Long-distance free-space quantum key distribution in daylight towards inter-satellite communication. Nat. Photon. 11, 509 (2017)

    Article  Google Scholar 

  7. Elliott, C., Colvin, A., Pearson, D., Pikalo, O., Schlafer, J., Yeh, H.: Current status of the DARPA quantum. Netw. Proc. SPIE 5815, 138 (2005)

    ADS  Article  Google Scholar 

  8. Peev, M., et al.: The SECOQC quantum key distribution network in Vienna. New J. Phys. 11, 075001 (2009)

    ADS  Article  Google Scholar 

  9. Kiktenko, E.O., Pozhar, N.O., Duplinskiy, A.V., Kanapin, A.A., Sokolov, A.S., Vorobey, S.S., Miller, A.V., Ustimchik, V.E., Anufriev, M.N., Trushechkin, A.T., Yunusov, R.R., Kurochkin, V.L., Kurochkin, YuV, Fedorov, A.K.: Demonstration of a quantum key distribution network in urban fibre-optic communication lines. Quantum Electron. 47, 798 (2017)

    ADS  Article  Google Scholar 

  10. Tysowski, P.K., Ling, X., Lütkenhaus, N., Mosca, M.: The engineering of a scalable multi-site communications system utilizing quantum key distribution (QKD). Quantum Sci. Technol. 3, 024001 (2018)

    ADS  Google Scholar 

  11. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    ADS  Article  Google Scholar 

  12. Jian-Yong, Hu, Bo, Yu., Jing, Ming-Yong, Xiao, Lian-Tuan, Jia, Suo-Tang, Qin, Guo-Qing, Long, Gui-Lu: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5, e16144 (2016)

    Article  Google Scholar 

  13. Zhang, Wei, Ding, Dong-Sheng, Sheng, Yu-Bo, Zhou, Lan, Shi, Bao-Sen, Guo, Guang-Can: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118, 220501 (2017)

    ADS  Article  Google Scholar 

  14. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    ADS  MathSciNet  Article  Google Scholar 

  15. Ren, Ji-Gang, et al.: Ground-to-satellite quantum teleportation. Nature 549, 70 (2017)

    ADS  Article  Google Scholar 

  16. 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 (1993)

    ADS  MathSciNet  Article  Google Scholar 

  17. Schoelkopf, R.J., Girvin, S.M.: Wiring up quantum systems. Nature 451(7179), 664 (2008)

    ADS  Article  Google Scholar 

  18. Blatt, R., Roos, C.F.: Quantum simulations with trapped ions. Nat. Phys. 8(4), 277 (2012)

    Article  Google Scholar 

  19. Kelly, J., Barends, R., Fowler, A.G., Megrant, A., Jeffrey, E., White, T.C., Sank, D., Mutus, J.Y., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Hoi, I.C., Neill, C., O’Malley, P.J.J., Quintana, C., Roushan, P., Vainsencher, A., Wenner, J., Cleland, A.N., Martinis, J.M.: State preservation by repetitive error detection in a superconducting quantum circuit. Nature 519(7541), 66 (2015)

    ADS  Article  Google Scholar 

  20. Ristè, D., Poletto, S., Huang, M.Z., Bruno, A., Vesterinen, V., Saira, O.P., DiCarlo, L.: Detecting bit-flip errors in a logical qubit using stabilizer measurements. Nat. Commun. 6(1), 6983 (2015)

    ADS  Article  Google Scholar 

  21. Córcoles, A., Magesan, E., Srinivasan, S.J., Cross, A.W., Steffen, M., Gambetta, J.M., Chow, J.M.: Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. Nat. Commun. 6(1), 6979 (2015)

    ADS  Article  Google Scholar 

  22. Gambetta, J.M., Chow, J.M., Steffen, M.: Building logical qubits in a superconducting quantum computing system. npj Quantum Inf. 3(1), 2 (2017)

    ADS  Article  Google Scholar 

  23. Ghosh, D., Agarwal, P., Pandey, P., Behera, B.K., Panigrahi, P.K.: Automated error correction in IBM quantum computer and explicit generalization. Quantum Inf. Process. 17(6), 153 (2018)

    ADS  MathSciNet  Article  Google Scholar 

  24. Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242 (2017)

    ADS  Article  Google Scholar 

  25. Barends, R., Lamata, L., Kelly, J., García-Álvarez, L., Fowler, A.G., Megrant, A., Jeffrey, E., White, T.C., Sank, D., Mutus, J.Y., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Hoi, I.C., Neill, C., O’Malley, P.J.J., Quintana, C., Roushan, P., Vainsencher, A., Wenner, J., Solano, E., Martinis, J.M.: Digital quantum simulation of fermionic models with a superconducting circuit. Nat. Commun. 6(1), 7654 (2015)

    ADS  Article  Google Scholar 

  26. Langford, N.K., Sagastizabal, R., Kounalakis, M., Dickel, C., Bruno, A., Luthi, F., Thoen, D.J., Endo, A., DiCarlo, L.: Experimentally simulating the dynamics of quantum light and matter at ultrastrong coupling. Nat. Commun. 8, 1715 (2017)

    ADS  Article  Google Scholar 

  27. Barends, R., Shabani, A., Lamata, L., Kelly, J., Mezzacapo, A., Heras, U.L., Babbush, R., Fowler, A.G., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Jeffrey, E., Lucero, E., Megrant, A., Mutus, J.Y., Neeley, M., Neill, C., O’Malley, P.J.J., Quintana, C., Roushan, P., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Solano, E., Neven, H., Martinis, J.M.: Digitized adiabatic quantum computing with a superconducting circuit. Nature 534(7606), 222 (2016)

    ADS  Article  Google Scholar 

  28. Roushan, P., Neill, C., Tangpanitanon, J., Bastidas, V.M., Megrant, A., Barends, R., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Fowler, A., Foxen, B., Giustina, M., Jeffrey, E., Kelly, J., Lucero, E., Mutus, J., Neeley, M., Quintana, C., Sank, D., Vainsencher, A., Wenner, J., White, T., Neven, H., Angelakis, D.G., Martinis, J.: Spectral signatures of many-body localization with interacting photons. arXiv:1709.07108 (2017)

  29. Ristè, D., da Silva, M.P., Ryan, C.A., Cross, A.W., Córcoles, A.D., Smolin, J.A., Gambetta, J.M., Chow, J.M., Johnson, B.R.: Demonstration of quantum advantage in machine learning. npj Quantum Inf. 3(1), 16 (2017)

    ADS  Article  Google Scholar 

  30. Reagor, M., Osborn, C.B., Tezak, N., Staley, A., Prawiroatmodjo, G., Scheer, M., Alidoust, N., Sete, E.A., Didier, N., da Silva, M.P., Acala, E., Angeles, J., Bestwick, A., Block, M., Bloom, B., Bradley, A., Bui, C., Caldwell, S., Capelluto, L., Chilcott, R., Cordova, J., Crossman, G., Curtis, M., Deshpande, S., El Bouayadi, T., Girshovich, D., Hong, S., Hudson, A., Karalekas, P., Kuang, K., Lenihan, M., Manenti, R., Manning, T., Marshall, J., Mohan, Y., O’Brien, W., Otterbach, J., Papageorge, A., Paquette, J.P., Pelstring, M., Polloreno, A., Rawat, V., Ryan, C.A., Renzas, R., Rubin, N., Russel, D., Rust, M., Scarabelli, D., Selvanayagam, M., Sinclair, R., Smith, R., Suska, M., To, T.W., Vahidpour, M., Vodrahalli, N., Whyland, T., Yadav, K., Zeng, W., Rigetti, C.T.: Demonstration of universal parametric entangling gates on a multi-qubit lattice. Sci. Adv. 4(2) (2018)

  31. Temme, Kristan, Bravyi, Sergey, Gambetta, Jay M.: Error mitigation for short-depth quantum circuits. Phys. Rev. Lett. 119, 180509 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  32. Li, Ying, Benjamin, Simon C.: Efficient variational quantum simulator incorporating active error minimization. Phys. Rev. X 7, 021050 (2017)

    Google Scholar 

  33. McClean, Jarrod R., Kimchi-Schwartz, Mollie E., Carter, Jonathan, de Jong, Wibe A.: Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states. Phys. Rev. A 95, 042308 (2017)

    ADS  Article  Google Scholar 

  34. Endo, S., Benjamin, S.C., Li, Y.: Practical Quantum Error Mitigation for Near-Future Applications. arXiv:1712.09271

  35. Zhukov, A.A., Remizov, S.V., Pogosov, W.V., Lozovik, YuE: Algorithmic simulation of far-from-equilibrium dynamics using quantum computer. Quantum Inf. Process. 17, 223 (2018)

    ADS  MathSciNet  Article  Google Scholar 

  36. Moll, Nikolaj, Barkoutsos, Panagiotis, Bishop, Lev S., Chow, Jerry M., Cross, Andrew, Egger, Daniel J., Filipp, Stefan, Fuhrer, Andreas, Gambetta, Jay M., Ganzhorn, Marc, Kandala, Abhinav, Mezzacapo, Antonio, Müller, Peter, Riess, Walter, Salis, Gian, Smolin, John, Tavernelli, Ivano, Temme, Kristan: Quantum optimization using variational algorithms on near-term quantum devices. Quantum Sci. Technol. 3, 030503 (2018)

    ADS  Article  Google Scholar 

  37. Devitt, S.J.: Performing quantum computing experiments in the cloud. Phys. Rev. A 94, 032329 (2016)

    ADS  Article  Google Scholar 

  38. Michielsen, K., Nocon, M., Willsch, D., Jin, F., Lippert, T., De Raedt, H.: Benchmarking gate-based quantum computers. Comput. Phys. Commun. 220, 44 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  39. Bai, G., Chiribella, G.: Test one to test many: a unified approach to quantum benchmarks. Phys. Rev. Lett. 120, 150502 (2018)

    ADS  Article  Google Scholar 

  40. Wootton, J.R.: Benchmarking of quantum processors with random circuits. arXiv:1806.02736

  41. García-Martín, D., Sierra, G.: Five Experimental Tests on the 5-Qubit IBM Quantum Computer. arXiv:1712.05642

  42. Dumitrescu, E.F., McCaskey, A.J., Hagen, G., Jansen, G.R., Morris, T.D., Papenbrock, T., Pooser, R.C., Dean, D.J., Lougovski, P.: Cloud quantum computing of an atomic nucleus. Phys. Rev. Lett. 120, 210501 (2018)

    ADS  Article  Google Scholar 

  43. Pokharel, B., Anand, N., Fortman, B., Lidar, D.: Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits. arXiv:1807.08768

  44. Kiktenko, E.O., Trushechkin, A.S., Lim, C.C.W., Kurochkin, Y.V., Fedorov, A.K.: Symmetric blind information reconciliation for quantum key distribution. Phys. Rev. Appl. 8, 044017 (2017)

    ADS  Article  Google Scholar 

  45. Tomamichel, M., Lim, C.C.W., Gisin, N., Renner, R.: Tight finite-key analysis for quantum cryptography. Nat. Commun. 3, 634 (2012)

    ADS  Article  Google Scholar 

  46. Magesan, E., Gambetta, J.M., Emerson, J.: Scalable and robust randomized benchmarking of quantum processes. Phys. Rev. Lett. 106, 180504 (2011)

    ADS  Article  Google Scholar 

  47. Proctor, T., Rudinger, K., Young, K., Sarovar, M., Blume-Kohout, R.: What randomized benchmarking actually measures. Phys. Rev. Lett. 119, 130502 (2017)

    ADS  MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

We acknowledge use of the IBM Quantum Experience for this work. The viewpoints expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum Experience team. E. O. K. was supported by RFBR (Project No. 18-37-00096). W. V. P. acknowledges a support from RFBR (Project No. 15-02-02128). Yu. E. L. acknowledges a support from RFBR (Project No. 17-02-01134) and the Program of Basic Research of HSE.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to W. V. Pogosov.

Additional information

E. O. K. was supported by RFBR (Project No. 18-37-00096). W. V. P. acknowledges a support from RFBR (Project No. 15-02-02128). Yu. E. L. acknowledges a support from RFBR (Project No. 17-02-01134) and the Program of Basic Research of HSE.

Appendices

Appendix A: Output distributions for superdense coding

Table 1 shows output distributions for the superdense coding protocol for the situation corresponding to Fig. 2a for different number of SWAPs, as obtained from 16-qubit IBMqx5 device. Here, \((a_1, a_2)\) is Alice’s input, while \((b_1,b_2)\) is Bob’s output. Results presented in the table provide output distributions in connection to the input data. In the ideal situation, the input and output must be the same, so that the corresponding matrix for each given \((a_1, a_2)\) should be identity (unit) matrix. We see from Table 1 that, in reality, even for the zero number of SWAPs this matrix is rather different from the identity matrix.

Table 1 The output distribution for superdense coding protocol for different number of SWAPs

Table 2 presents similar data for different values of delay time, as obtained from 5-qubit IBMqx4 device. We again see noticeable deviations from the ideal distribution even for zero waiting time.

Table 2 The output distribution for superdense coding protocol for different values of time delay

Tables 3 and 4 provide output distributions without error correction and with error correction, respectively, for different values of waiting time, as obtained from 16-qubit IBMQx5 device. We again see that the distributions are rather different from ideal ones even at \(t=0\), but the error correction, in general, indeed improves the results.

Table 3 The output distribution for superdense coding protocol for different values of time delay without any correction of coherent errors
Table 4 The output distribution for superdense coding protocol for different values of time delay with the correction of the coherent error

Measurements for the superdense coding protocol have been taken between April 25, 2018, and May 21, 2018.

Appendix B: Correction of the coherent error

Figure 12 shows the experimentally determined overlap (fidelity) between the prepared state and the Bell states \(|\varPsi _+ \rangle \) (blue circles) and \(|\varPsi _- \rangle \) (brown triangles) as a function of time, provided the initial target state was \(|\varPsi _+ \rangle \). Figure 12a corresponds to direct measurements, while Fig. 12b deals with the results after our error correction, which compensates the drift of the internal phase. Similar oscillations have been also revealed for Bell states \(|\varPhi _+ \rangle \) and \(|\varPhi _- \rangle \).

Fig. 12
figure 12

An overlap between the prepared state and the Bell states \(|\varPsi _+ \rangle \) (blue circles) and \(|\varPsi _- \rangle \) (brown triangles) as a function of time, provided the initial target state for \(|\varPsi \rangle \) was \(|\varPsi _+ \rangle \); a corresponds to direct measurements, b deals with the results after the correction of the coherent error (see in the text) (Color figure online)

Appendix C: Error distributions for BB84 protocol

Table 5 gives error distribution for different time delays and each possible choice of the basis and bit of information, as obtained from 5-qubit IBMQx4 device. In the ideal case, the errors should be absent.

Table 5 The error distribution for BB84 protocol for different values of time delay

Table 6 provides error distribution for different number of SWAPs and each possible choice of the basis and bit of information, as obtained from 5-qubit IBMQx4 device. Table 7 gives similar data, but using the encoding of the logical qubit into two physical qubits supplemented by post-selection procedure. The brackets contain fraction of algorithm’s runs used after the post-selection. The post-selection allowed us to improve the results, as seen from the comparison of data from Tables 6 and 7. We also note that the fraction of discarded data grows with the number of SWAPs, and this leads to the improvement in the performance.

Table 6 The error distribution for BB84 protocol for different number of SWAPs
Table 7 The error distribution for BB84 protocol for different number of SWAPs

Measurements for the BB84 protocol have been taken between April 4, 2018, and May 21, 2018.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhukov, A.A., Kiktenko, E.O., Elistratov, A.A. et al. Quantum communication protocols as a benchmark for programmable quantum computers. Quantum Inf Process 18, 31 (2019). https://doi.org/10.1007/s11128-018-2144-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-2144-y

Keywords

  • Quantum computer
  • Quantum communication protocol
  • Quantum algorithms
  • Superdense coding
  • Quantum benchmark