Topological Qubits & Majorana Zero Modes

Majorana fermions at the ends of a topological superconducting wire form a non-local qubit. Braiding operations perform fault-tolerant quantum gates — the quantum information is encoded in topology, not local physics.

Kitaev Wire — Majorana Zero Modes

Braiding Diagram — Non-Abelian Anyons

Qubit State |ψ⟩ = α|0⟩ + β|1⟩

|0⟩ amplitude:
1.000
|1⟩ amplitude:
0.000
Phase arg(β/α):
0°
No operations applied yet.
0
Braids applied
100%
Logical fidelity
∞
Error protection (topological gap)

Key Physics

γ₁† = γ₁, γ₂† = γ₂ (Majorana: particle = antiparticle)
{γᵢ, γⱼ} = 2δᵢⱼ (Clifford algebra)
Logical qubit: f = ½(γ₁ + iγ₂) — non-local fermion across wire ends
Braid operator σᵢ = exp(π/4 · γᵢγᵢ₊₁) — rotation by π/8 in qubit space

Microsoft Station Q target: Majorana qubits in InAs/Al heterostructures. Topological protection means local perturbations cannot flip the qubit — error rate ~ exp(-gap/kT).