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Jordan-Wigner transformations for tree structures.

Stefan Backens1, Alexander Shnirman2,3, Yuriy Makhlin4,5

  • 1Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, D-76131, Karlsruhe, Germany.

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This summary is machine-generated.

The Jordan-Wigner transformation is extended to tree structures, enabling spin-fermion mapping for complex systems. This facilitates simulating Majorana braiding in spin and qubit systems with nearest-neighbor interactions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Science
  • Theoretical Physics

Background:

  • The Jordan-Wigner transformation efficiently maps one-dimensional spin chains to fermionic systems.
  • Extending such mappings is crucial for simulating complex quantum systems.

Purpose of the Study:

  • To generalize the Jordan-Wigner spin-fermion mapping to arbitrary tree structures.
  • To enable simulations of fermionic and spin systems with nearest-neighbor coupling on trees.

Main Methods:

  • Extension of the Jordan-Wigner transformation to graph-based structures.
  • Introduction of auxiliary spins at junction points to facilitate the mapping.

Main Results:

  • A novel spin-fermion mapping applicable to arbitrary tree structures is developed.
  • The mapping allows for nearest-neighbor interactions in both spin and fermionic representations.

Conclusions:

  • The generalized mapping simplifies the simulation of Majorana braiding in spin and qubit systems.
  • This approach provides a powerful tool for quantum simulations on complex network topologies.