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Magic state distillation with the ternary Golay code.

Shiroman Prakash1

  • 1Department of Physics and Computer Science, Dayalbagh Educational Institute, Dayalbagh, Agra 282005, India.

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|October 19, 2020
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Summary
This summary is machine-generated.

The 11-qutrit Golay code, a quantum error-correcting code, effectively distils magic states for fault-tolerant quantum computing. It achieves high thresholds and significant error suppression for both the strange and Norell states.

Keywords:
error correcting codesfault-tolerant quantum computingmagic state distillationquantum error correction

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Fault-Tolerant Quantum Computing

Background:

  • The ternary Golay code is a foundational classical error-correcting code.
  • Magic state distillation is crucial for fault-tolerant quantum computing.
  • Qutrit-based quantum computing offers potential advantages.

Purpose of the Study:

  • To investigate the application of the 11-qutrit Golay code for magic state distillation.
  • To evaluate the error suppression capabilities and thresholds of this code.
  • To explore its effectiveness in distilling specific magic qutrit states.

Main Methods:

  • An 11-qutrit quantum error correcting code derived from the ternary Golay code was applied.
  • The code was used for magic state distillation protocols.
  • Performance was analyzed in terms of error suppression and thresholds against noise.

Main Results:

  • The 11-qutrit Golay code successfully distils the 'strange state' with cubic error suppression and a high threshold.
  • It also distils the 'Norell state' with quadratic error suppression and a high threshold to depolarizing noise.
  • This demonstrates the code's efficacy in advanced quantum state preparation.

Conclusions:

  • The 11-qutrit Golay code is a powerful tool for magic state distillation in quantum computing.
  • Its high thresholds and error suppression capabilities are significant for achieving fault tolerance.
  • This work highlights the potential of Golay codes in advancing qutrit-based quantum information processing.