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This study explores 3D color codes for quantum computing, finding error thresholds of 1.9% for bit-flip and 27.6% for phase-flip errors. These findings are crucial for developing robust quantum computers.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Three-dimensional (3D) color codes offer enhanced fault tolerance for quantum computing.
  • They provide protected quantum gates with lower overhead and better robustness against measurement errors.

Purpose of the Study:

  • To investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on a body-centered cubic lattice.
  • To estimate thresholds for 1D stringlike and 2D sheetlike logical operators under ideal syndrome measurement conditions.

Main Methods:

  • Utilizing a connection between quantum error correction and statistical mechanics.
  • Employing parallel tempering Monte Carlo simulations.
  • Studying disorder-temperature phase diagrams of novel 3D statistical-mechanical models (four- and six-body random coupling Ising models).

Main Results:

  • Estimated threshold error rate for 1D stringlike logical operators: p_{3DCC}^{(1)} ≃ 1.9%.
  • Estimated threshold error rate for 2D sheetlike logical operators: p_{3DCC}^{(2)} ≃ 27.6%.

Conclusions:

  • The 3D color code on the body-centered cubic lattice demonstrates significant potential for fault-tolerant quantum computation.
  • The established thresholds provide critical benchmarks for designing and implementing robust quantum memory and gates.