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Coherent-Error Threshold for Surface Codes from Majorana Delocalization.

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We developed new methods to map quantum error correction with coherent errors to statistical mechanics models. This reveals a higher storage threshold for coherent errors compared to incoherent ones.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Statistical mechanics mappings are crucial for understanding quantum error correction.
  • Existing models primarily address incoherent noise, neglecting coherent errors like spurious gate rotations.

Purpose of the Study:

  • To develop a statistical mechanics mapping for the surface code considering coherent errors.
  • To compare the error correction properties of coherent versus incoherent noise.

Main Methods:

  • Mapped the surface code with coherent errors (X or Z rotations) to a 2D Ising model with complex couplings.
  • Further mapped this to a 2D Majorana scattering network.
  • Linked 2D networks to 1D fermions to analyze error-correcting phases.

Main Results:

  • Identified commonalities and differences between coherent and incoherent error correction.
  • Both error types map to a Z2-nontrivial 2D insulator in the error-correcting phase.
  • Coherent errors, beyond a threshold angle (ϕth ≈ 0.14π), map to a Majorana metal, unlike the Z2-trivial insulator for incoherent errors.
  • The derived threshold sin²(ϕth) ≈ 0.18 exceeds the incoherent threshold pth ≈ 0.11.

Conclusions:

  • The developed mapping provides new insights into quantum error correction with coherent noise.
  • Coherent errors allow for a higher storage threshold than previously considered for incoherent errors.
  • The findings suggest potential improvements in the resilience of quantum error correction codes.