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Updated: May 18, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
From Majorana fermions to topological order
Barbara M Terhal1, Fabian Hassler, David P DiVincenzo
1Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany.
Physical Review Letters
|September 26, 2012
Summary
This study demonstrates that a 2D network of Majorana fermions exhibits topological order, revealing Kitaev
Area of Science:
- Condensed Matter Physics
- Quantum Computing
- Topological Materials
Background:
- Superconducting islands host Majorana fermions, which are exotic quantum particles.
- Understanding topological order is crucial for robust quantum computation.
Purpose of the Study:
- To investigate the topological properties of a 2D network of Majorana fermions.
- To explore the emergence of Kitaev's toric code in this system.
- To analyze the phase transition to a nontopological phase.
Main Methods:
- Analysis of a fermionic Hamiltonian describing the system.
- Application of fourth-order perturbation theory.
- Utilizing a Jordan-Wigner transformation to map the model.
- Investigating the nonperturbative regime and phase transitions.
Main Results:
- Topological order is identified in a specific parameter space region.
- Kitaev's toric code emerges from the system's Hamiltonian.
- A mapping to signed 2D Ising models with gauge bits was established.
- The nonperturbative regime and phase transition dynamics were elucidated.
Conclusions:
- The proposed system exhibits topological order and can be mapped to Ising models.
- This model offers insights into topological quantum computation.
- Adiabatic manipulation of the Hamiltonian can be used for quantum computation.
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