Error Correction Using Quantum Computation

Khalik Khan, Sapna Jain

SEST, Jamia Hamdard, New Delhi, India

Cite: Khan K., Jain S. Error Correction Using Quantum Computation. J. Digit. Sci. 5(1), 12 – 22 (2023). https://doi.org/10.33847/2686-8296.5.1_2

Abstract. Quantum Error Correction (QEC) is an important technique for protecting quantum information against decoherence and errors. This involves the design and implementation of algorithms and techniques to minimize error rates and increase the stability of quantum circuits. One of the key parameters in QEC is the distance of the error- correcting code, which determines the number of errors that can be corrected. Another important parameter is the error probability, which quantifies the likelihood of errors occurring in the  quantum system. In this context, the goal of a simulation sweeps like the one performed in the code is to studythe performance of the QEC code for different values of the distance and error probability, and to optimize the code for maximum accuracy. By varying these parameters and observing the performance of the code, researchers can gain insights into how to design better codes and improve the reliability of quantum computing systems. We also discuss the challenges that need to be addressed for quantum computing to realize its potential in solving practical Error correction problems.
Keywords: quantum, error corection, decoherence, algoritm. 

References

  1. Aharonov, D., Ben-Or, M., Eban, E., & Hassidim, A. (2020). Quantum Error Correction with only Two Qubits. Physical Review Letters, 124(10), 100504.
  2. Calderbank, A. R., Shor, P. W., & Steane, A. M. (1996). Quantum Error Correction and Orthogonal Geometry. Physical Review Letters, 78(3), 405- 408.
  3. Gottesman, D. (1997). Stabilizer Codes and Quantum Error Correction. PhD thesis, California Institute of Technology.
  4. Kitaev, A. Y. (1997). Quantum Error Correction with Imperfect Gates. Quantum Communications and Measurement, 181-188.
  5. Knill, E., Laflamme, R., & Zurek, W.H. (1996). Resilient Quantum Computation: Error Models and Thresholds. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1969), 365- 384.
  6. Lidar, D. A., & Brun, T. A. (2013). Quantum Error Correction. Cambridge University Press.
  7. Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.
  8. Preskill, J. (1998). Reliable Quantum Computers. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering   Sciences, 454(1969), 385-410.
  9. Raussendorf, R., & Harrington, J. (2007). Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions. Physical Review Letters, 98(19), 190504.
  10. Shor, P. W. (1995). Scheme for Reducing Decoherence in Quantum Computer Memory. Physical Review A, 52(4), R2493-R2496.
  11. Steane, A. (1996). Error Correcting Codes in Quantum Theory. Physical Review Letters, 77(5), 793-797.
  12. Terhal, B. M. (2015). Quantum Error Correction for Quantum Memories. Reviews of Modern Physics, 87(2), 307-346.
  13. Tureci, H. E., & Imamoglu, A. (2003). Fault-Tolerant Quantum Computation with Strongly Coupled Qubits. Physical Review A, 67(6), 062322.
  14. Vedral, V. (2010). Introduction to Quantum Information Science. Oxford University Press.
  15. Zeng, B., & Jiang, L. (2019). Recent Advances in Quantum Error Correction. Quantum Science and Technology, 4(3), 030501.

Published online 25.06.2023