Topological Qubits

Majorana fermions in nanowires and anyons in fractional quantum Hall systems

Trapping Technique

1. Majorana zero modes localized at defects in superconducting-semiconductor nanowires
2. Topological phase requires specific material properties and magnetic field
3. Majorana modes appear at wire ends or domain walls between phases
4. Anyons emerge in fractional quantum Hall systems at specific filling factors
5. Anyons are quasiparticle excitations in 2D electron gas
6. Strong magnetic fields and low temperatures required for topological phases

Gate Mechanism

1. Braiding operations: physically moving Majorana modes around each other
2. Braiding creates non-Abelian phase factors, implementing quantum gates
3. Topological protection: gates are fault-tolerant by design
4. Measurement-based gates: measure topological charge to perform operations
5. Fusion rules: combining anyons creates entanglement
6. No local perturbations can affect topological qubits during braiding
7. Gate operations depend only on topology of braid, not precise path