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Subsystem fault tolerance with the Bacon-Shor code.

Panos Aliferis1, Andrew W Cross

  • 1Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review Letters
|August 7, 2007
PubMed
Summary
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Gauge subsystems in the Bacon-Shor code enable simple fault-tolerant error correction (FTEC) without entangled states. This method achieves a new lower bound for quantum accuracy thresholds, improving prior results significantly.

Area of Science:

  • Quantum information science
  • Quantum computing
  • Error correction codes

Background:

  • The Bacon-Shor code offers a framework for quantum error correction.
  • Efficient fault-tolerant error correction (FTEC) is crucial for scalable quantum computation.

Purpose of the Study:

  • To investigate the role of gauge subsystems in the Bacon-Shor code for FTEC.
  • To develop simpler and more efficient FTEC methods.
  • To establish a new lower bound for the quantum accuracy threshold.

Main Methods:

  • Utilizing gauge subsystems within the Bacon-Shor code.
  • Implementing FTEC without requiring entangled ancillary states.
  • Employing nearest-neighbor two-qubit measurements for error correction.

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Main Results:

  • Demonstrated simple and efficient FTEC methods.
  • Showcased FTEC implementation without entangled ancillary states.
  • Proved a quantum accuracy threshold lower bound of 1.94 x 10^-4 for adversarial stochastic noise.

Conclusions:

  • Gauge subsystems significantly simplify and enhance FTEC in the Bacon-Shor code.
  • The developed FTEC methods are resource-efficient, utilizing only nearest-neighbor measurements.
  • The improved lower bound on the quantum accuracy threshold advances the field of fault-tolerant quantum computing.