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Universal Quantum Computation with Gapped Boundaries.

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This study presents methods for topological quantum computation using gapped boundaries. A new topological charge measurement primitive enables universal quantum computing with topological phases.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Topological Phases of Matter

Background:

  • Topological quantum computation (TQC) offers inherent protection against errors.
  • Gapped boundaries of two-dimensional topological phases are potential platforms for TQC.

Purpose of the Study:

  • To develop systematic methods for encoding quantum information and performing operations using gapped boundaries.
  • To introduce and implement a primitive for topological charge measurement.
  • To explore the physical realization of TQC in specific topological phases.

Main Methods:

  • Encoding quantum information topologically within gapped boundaries.
  • Developing and implementing a symmetry-protected topological charge measurement primitive.
  • Analyzing the Z_{3} toric code (D(Z_{3})) as a concrete physical example.

Main Results:

  • A general computational primitive for topological charge measurement is introduced.
  • A symmetry-protected implementation of this primitive is presented.
  • The Z_{3} toric code provides a qutrit encoding and an abstract universal gate set.

Conclusions:

  • Gapped boundaries of D(Z_{3}) can be realized in bilayer fractional quantum Hall systems.
  • A practical implementation of topological charge measurement could lead to a universal quantum computer.
  • This work demonstrates a pathway towards realizing universal quantum computation based on Abelian topological phases.