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Fault-tolerant conversion between the Steane and Reed-Muller quantum codes.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Quantum Computation

Background:

  • Steane's 7-qubit code generates Clifford gates but lacks universality.
  • The 15-qubit Reed-Muller code has fault-tolerant T and control-control-Z gates, enabling universality with Clifford gates.

Purpose of the Study:

  • To introduce a novel method for achieving universal fault-tolerant quantum computation.
  • To demonstrate fault-tolerant conversion between Steane's code and the Reed-Muller code.

Main Methods:

  • Developing a scheme for fault-tolerant state interconversion between the 7-qubit Steane code and the 15-qubit Reed-Muller code.
  • Leveraging the distinct fault-tolerant gate sets of each code.

Main Results:

  • A new pathway to universal fault-tolerant quantum computation is established.
  • The conversion scheme provides a practical method for implementing universal gates.
  • The results suggest both codes represent the same subsystem code in different gauges.

Conclusions:

  • The developed fault-tolerant conversion technique enables universal quantum computation.
  • This method extends to the broader family of quantum Reed-Muller codes.
  • The findings offer a new perspective on the relationship between different quantum error-correcting codes.