Skip to main content
SpringerLink
Log in

Quantum Cost Optimization Algorithm for Entanglement-based Asymmetric Quantum Error Correction

  • Research
  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The importance of reversible operations has been increasing day by day to overcome the drawbacks of irreversible computation. Quantum computers perform operations exponentially faster by taking advantage of reversible operations. Reversible operations play an essential role in developing energy and cost-efficient circuits. The efficiency of a quantum circuit is measured in terms of Quantum cost and Quantum depth. In this paper, we propose an optimization algorithm for Entanglement-based Quantum error correction, which plays a crucial role in various applications like quantum teleportation, secure communications, quantum key distribution, etc. We performed the experiments using Qiskit and RCViewer+ tools. Qiskit tool is used to run the quantum algorithms and measure the quantum depth; the RCViewer+ tool is used to measure the quantum cost. The proposed algorithm optimizes the quantum cost and depth compared to the existing approaches.

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

Similar content being viewed by others

Data Availability

The data is available at the GitHub Repository upon the request and the link is https://github.com/mummadiswathi/Quantum

References

  1. Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5(3), 183–191 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17(6), 525–532 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  3. Swathi, M., Rudra, B.: Implementation of reversible logic gates with quantum gates. 2021 IEEE 11th Annual Computing and Communication Workshop and Conference (CCWC) (2021). IEEE

  4. Harrow, A., Hayden, P., Leung, D.: Superdense coding of quantum states. Phys. Rev. Lett. 92(18), 187901 (2004)

    Article  ADS  Google Scholar 

  5. Horodecki, R., et al.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Bouwmeester, D., et al.: Experimental quantum teleportation. Nature 390(6660), 575–579 (1997)

    Article  ADS  MATH  Google Scholar 

  7. Caves, C.M.: Quantum error correction and reversible operations. J. Supercond. 12(6), 707–718 (1999)

    Article  ADS  Google Scholar 

  8. Swathi, M., Rudra, B.: A novel architecture for binary code to gray code converter using quantum cellular automata. Edge Analytics: Select Proceedings of 26th International Conference-ADCOM 2020. Singapore: Springer Singapore (2022)

  9. Nielsen, M.A., Caves, C.M.: Reversible quantum operations and their application to teleportation. Phys. Rev. A 55(4), 2547 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  10. Aharonov, D.: Quantum computation. Annu. Rev. Comput. Phys. VI 259–346 (1999)

  11. Razeghi, M.: Technology of Quantum Devices. Springer, New York (2010)

    Book  Google Scholar 

  12. Patel, R.B., et al.: A quantum Fredkin gate. Sci. Adv. 2(3), e1501531 (2016)

    ADS  Google Scholar 

  13. Remón, P., et al.: Reversible molecular logic: a photophysical example of a Feynman gate. ChemPhysChem 10(12), 2004–2007 (2009)

    Article  Google Scholar 

  14. Yuriychuk, I.M., Hu, Z., Deibuk, V.G.: Effect of the noise on generalized Peres gate operation. International Conference on Computer Science, Engineering and Education Applications. Springer, Cham (2019)

  15. Fedorov, A., et al.: Implementation of a Toffoli gate with superconducting circuits. Nature 481(7380), 170–172 (2012)

    Article  ADS  Google Scholar 

  16. Thapliyal, H., Ranganathan, N.: Design of reversible sequential circuits optimizing quantum cost, delay, and garbage outputs. ACM J. Emerg. Technol. Comput. Syst. (JETC) 6(4), 1–31 (2010)

    Article  Google Scholar 

  17. Streltsov, A., Kampermann, H., Bruß, D.: Quantum cost for sending entanglement. Phys. Rev. Lett. 108(25), 250501 (2012)

    Article  ADS  Google Scholar 

  18. Mamun, S.A., Menville, D.: Quantum cost optimization for reversible sequential circuit. arXiv preprint. arXiv:1407.7098 (2014)

  19. Paler, A., Basmadjian, R.: Energy Cost of Quantum Circuit Optimisation: Predicting That Optimising Shor’s Algorithm Circuit Uses 1 GWh. ACM Trans. Quantum. Comput. 3(1), 1–14 (2022)

    Article  MathSciNet  Google Scholar 

  20. Swathi, M., Rudra, B.: Experimental analysis of a quantum encoder in various quantum systems. 2022 IEEE 13th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON) (2022). IEEE

  21. Maity, H., et al.: The quantum cost optimized design of 2: 4 decoder using the new reversible logic block. Micro Nanosyst. 12(3), 146–148 (2020)

    Article  Google Scholar 

  22. Qiu, X., Chen, L.: Quantum cost of dense coding and teleportation. arXiv preprint. arXiv:2202.12544 (2022)

  23. Mummadi, S., Rudra, B.: Fundamentals of Quantum Computation and Basic Quantum Gates. Handbook of Research on Quantum Computing for Smart Environments. IGI Global, 1–24 (2023)

  24. De Martini, F., et al.: Experimental realization of the quantum universal NOT gate. Nature 419(6909), 815–818 (2002)

    Article  ADS  Google Scholar 

  25. Swathi, M., Rudra, B.: Novel Encoding method for Quantum Error Correction. 2022 IEEE 12th Annual Computing and Communication Workshop and Conference (CCWC) (2022). IEEE

  26. Slimani, A., Benslama, A., Misra, N.K.: Optimal designs of reversible/quantum decoder circuit using new quantum gates. Int. J. Theor. Phys. 61(3), 1–19 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hofmann, H.F., Takeuchi, S.: Quantum phase gate for photonic qubits using only beam splitters and postselection. Phys. Rev. A 66(2), 024308 (2002)

    Article  ADS  Google Scholar 

  28. Lu, L.-C., et al.: General quantum entanglement purification protocol using a controlled-phase-flip gate. Ann. Phys. 532(4), 2000011 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  29. Swathi, M., Rudra, B.: A novel approach for asymmetric quantum error correction with syndrome measurement. IEEE Access 10, 44669–44676 (2022). https://doi.org/10.1109/ACCESS.2022.3170039

    Article  Google Scholar 

  30. Behera, B.K., et al.: Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer. Quantum Inf. Process. 18(4), 1–13 (2019)

    MATH  Google Scholar 

  31. Swathi, M., Rudra, B.: An efficient approach for quantum entanglement purification. Int. J. Quantum Inf. 2250004 (2022)

  32. Aleksandrowicz, G., et al.: Qiskit: An open-source framework for quantum computing (2019). Accessed 16 March

  33. Mummadi, S., Rudra, B.: Practical demonstration of quantum key distribution protocol with error correction mechanism. Int. J. Theor. Phys. 62(4), 86 (2023)

    Article  MathSciNet  MATH  Google Scholar 

  34. Chiani, M., Valentini, L.: Short codes for quantum channels with one prevalent pauli error type. IEEE J. Sel. Areas Inf. Theory 1(2), 480–486 (2020)

    Article  Google Scholar 

  35. Ryan-Anderson, C., Bohnet, J., Lee, K., Gresh, D., Hankin, A., Gaebler, J., Francois, D., Chernoguzov, A., Lucchetti, D., Brown, N., et al.: Realization of real-time fault-tolerant quantum error correction. Phys. Rev. X 11(4), 041058 (2021)

    Google Scholar 

  36. Behera, B.K., Seth, S., Das, A., Panigrahi, P.K.: Demonstration of entanglement purification and swapping protocol to design quantum repeater in ibm quantum computer. Quantum Inf. Process. 18(4), 1–13 (2019)

    MATH  Google Scholar 

  37. Asadi, M.A., Mosleh, M., Haghparast, M.: An efficient design of reversible ternary full-adder/full-subtractor with low quantum cost. Quantum Inf. Process. 19(7), 1–21 (2020)

    Article  Google Scholar 

  38. Cheng, K.W., Tseng, C.C.: Quantum full adder and subtractor. Electron Lett 38(22), 1343–1344 (2002)

    Article  ADS  Google Scholar 

  39. Tipsmark, A., et al.: Experimental demonstration of a Hadamard gate for coherent state qubits. Phys. Rev. A 84(5), 050301 (2011)

    Article  ADS  Google Scholar 

  40. Aharonov, D.: A simple proof that Toffoli and Hadamard are quantum universal. arXiv preprint quant-ph/0301040 (2003)

Download references

Acknowledgements

We are extremely grateful to the IBM team for providing access to IBM Quantum Experience (QE). The discussions and opinions developed in this paper are only those of the authors and do not reflect the opinions of IBM or IBM QE team.

Funding

Not Applicable.

Author information

Authors and Affiliations

  1. Department of Information Technology, National Institute of Technology Karnataka, Surathkal, Mangalore, 575025, Karnataka, India

    Swathi Mummadi

  2. Department of Computer Science and Engineering, B V Raju Institute of Technology, Narsapur, Medak, 502313, Telangana, India

    Swathi Mummadi

  3. Department of Information Technology, National Institute of Technology Karnataka, Surathkal, Mangalore, 575025, Karnataka, India

    Bhawana Rudra

Authors
  1. Swathi Mummadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bhawana Rudra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Swathi Mummadi.

Ethics declarations

Conflicts of interest

We do not have any conflict of interest.

Additional information

Publisher's Note

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

Appendix A RCViewer+ Tool Results

Appendix A RCViewer+ Tool Results

The quantum cost is measured in quantum computation based on the number of single and multi-qubit gates. We used the RCViewer+ tool to measure the quantum cost of existing and optimized circuits.

Fig. 12
figure 12

Quantum Cost Measurement

Full size image

Quantum cost calculation is a crucial process involved in assessing the expense of executing a quantum algorithm, holding significant implications for the advancement and implementation of quantum computing systems. The RCViewer tool proves indispensable in facilitating these quantum cost evaluations, serving as a valuable resource for researchers, engineers, and quantum computing experts. One of the standout features of the RCViewer tool, instrumental in quantum cost estimation, is its real-time capacity to visualize and scrutinize log data. This functionality empowers users to closely monitor the performance of quantum algorithms during execution, allowing for the collection of vital data concerning the quantum operations required at each algorithmic step. This data forms the foundation for precise determinations of the overall quantum cost of the algorithm.

Furthermore, the RCViewer tool offers a critical capability for quantum cost assessment through its aptitude for conducting statistical analyses on log data. Users can employ this functionality to perform statistical tests on the gathered data, helping identify any variables that may exert a substantial influence on the quantum cost of the algorithm. Armed with this insight, users can strategically optimize the algorithm, ultimately reducing its quantum resource requirements.

The results of the RCViewer+ tool of existing and optimized circuits are shown in Figs. 12 and 13.

Figure 12 shows the detailed cost analysis of the proposed error correction model with the total gate count, garbage/ancilla qubits, and single and multi-input gates. By combining all these values the calculated quantum cost is 33. The optimized results are shown in the following Fig. 13.

Fig. 13
figure 13

Optimized Quantum cost

Full size image

As shown in Fig. 13, after applying the optimization steps, the cost of the quantum circuit is reduced from 33 to 29.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mummadi, S., Rudra, B. Quantum Cost Optimization Algorithm for Entanglement-based Asymmetric Quantum Error Correction. Int J Theor Phys 62, 236 (2023). https://doi.org/10.1007/s10773-023-05497-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-023-05497-4

Keywords

Search

Navigation