Skip to main content
SpringerLink
Log in

Calculation of \(\pi \) on the IBM quantum computer and the accuracy of one-qubit operations

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

A quantum algorithm for the calculation of \(\pi \) is proposed and implemented on the five-qubit IBM quantum computer with superconducting qubits. We find \(\pi =3.157\pm 0.017\). The error is due to the noise of quantum one-qubit operations and measurements. The results can be used for estimating the errors of the quantum computer and suggest that the errors are purely random.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Koch, J., Yu, T.M., Gambetta, J., Houck, A.A., Schuster, D.I., Majer, J., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007). https://doi.org/10.1103/PhysRevA.76.042319

    Article  ADS  Google Scholar 

  2. Chow, J.M., Gambetta, J.M., Magesan, E., Abraham, D.W., Cross, A.W., Johnson, B.R., Masluk, N.A., Ryan, C.A., Smolin, J.A., Srinivasan, S.J., Steffen, M.: Implementing a strand of a scalable fault-tolerant quantum computing fabric. Nat. Commun. 5, 4015 (2014)

    Article  ADS  Google Scholar 

  3. Temme, K., Bravyi, S., Gambetta, J.M.: Error mitigation for short-depth quantum circuits. Phys. Rev. Lett. 119, 180509 (2017). https://doi.org/10.1103/PhysRevLett.119.180509

    Article  ADS  MathSciNet  Google Scholar 

  4. Kandala, A., Temme, K., Córcoles, A.D., Mezzacapo, A., Chow, J.M., Gambetta, J.M.: Error mitigation extends the computational reach of a noisy quantum processor. Nature 567, 491 (2019)

    Article  ADS  Google Scholar 

  5. 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, 6979 (2015). https://doi.org/10.1038/ncomms7979

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  7. Doronin, S.I., Fel’dman, E.B., Zenchuk, A.I.: Solving systems of linear algebraic equations via unitary transformations on quantum processor of IBM Quantum Experience. Quantum Inf. Process. 19(2), 68 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  8. 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, 242 (2017)

    Article  ADS  Google Scholar 

  9. Li, Y., Benjamin, S.C.: Efficient variational quantum simulator incorporating active error minimization. Phys. Rev. X 7, 021050 (2017). https://doi.org/10.1103/PhysRevX.7.021050

    Article  Google Scholar 

Download references

Acknowledgements

This work was performed as a part of a state task (State Registration No. AAAA-A19-119071190017-7). This work is partially supported by the Russian Foundation for Basic Research (Grants Nos. 19-32-80004 and 20-03-00147). The authors are grateful to D. E. Feldman for useful discussion.

Author information

Authors and Affiliations

  1. Institute of Problems of Chemical Physics of Russian Academy of Sciences, Chernogolovka, Moscow Region, Russia, 142432

    G. A. Bochkin, S. I. Doronin, E. B. Fel’dman & A. I. Zenchuk

Authors
  1. G. A. Bochkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. I. Doronin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. B. Fel’dman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. I. Zenchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. A. Bochkin.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bochkin, G.A., Doronin, S.I., Fel’dman, E.B. et al. Calculation of \(\pi \) on the IBM quantum computer and the accuracy of one-qubit operations. Quantum Inf Process 19, 257 (2020). https://doi.org/10.1007/s11128-020-02759-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02759-6

Keywords

Search

Navigation