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Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary.

Vincent Steffan1, Shin Ho Choe1, Nikolas P Breuckmann2

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Summary
This summary is machine-generated.

We introduce tile codes, a novel quantum error correction method offering flexibility and improved performance. These codes outperform existing constructions, providing a versatile tool for quantum error-correction code design.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Lattice-based Quantum Codes

Background:

  • The surface code is a leading quantum error correction code, but its flexibility is limited.
  • Existing constructions often struggle with balancing locality and code parameters.

Purpose of the Study:

  • To introduce a new class of quantum codes called tile codes.
  • To demonstrate the flexibility and improved performance of tile codes compared to existing methods.
  • To provide a unified framework for designing local lattice quantum codes.

Main Methods:

  • Development of a novel construction for quantum codes based on a planar 2D lattice.
  • Generalization of the surface code by allowing flexibility in locality and stabilizer weight.
  • Systematic exploration of code parameters, including different boundary conditions and stabilizer configurations.

Main Results:

  • Discovery of [[288,8,12]] codes with weight-6 stabilizers and [[288,8,14]] codes with weight-8 stabilizers, outperforming previous constructions.
  • Identification of a [[512,18,19]] code using weight-8 stabilizers, surpassing the rotated surface code by over 12 times.
  • Demonstration of tile codes' ability to maintain locality on lattices with open boundary conditions.

Conclusions:

  • Tile codes offer a simple yet powerful method for constructing high-performance quantum error correction codes.
  • The unified framework provided by tile codes facilitates systematic exploration of quantum code design.
  • Tile codes are a versatile tool for quantum error correction, adaptable to various boundary conditions and stabilizer types.