This is the native 2D representation of a braid: a planar braid diagram read top-to-bottom, exactly the notation used in braid-group theory itself (the 3D "spacetime block" picture is a visualization choice — the mathematics of B4 is defined on diagrams like this one). Four anyons sit in fixed horizontal slots; each button crosses two neighbouring strands and draws the crossing with a gap in the strand that passes underneath — the standard over/under convention in knot and braid diagrams, done here with no z-depth or camera at all.
Each crossing simultaneously applies the same elementary Ising-anyon braid matrix used in the 3D version, in the alternating fusion-tree basis:
B(odd) = e^(-iπ/8) · diag(1, i)
B(even) = F · B(odd) · F, F = (1/√2)[[1, 1],[1,-1]]
The top strip is a second, independent view of the same qubit: two phasor plots on the complex plane, one per fusion-channel amplitude (|1⟩ vacuum channel, |ψ⟩ non-trivial channel). Each dot's angle is the amplitude's phase and its distance from center is its magnitude; the dot never leaves the unit circle boundary combined (|c₀|²+|c₁|²=1) because every generator matrix is unitary. Because the braid diagram only encodes which strands cross and how many times, two diagrams that are topologically the same braid word always drive the phasors to the exact same final state — the same topological-protection argument as the 3D version, shown through a genuinely different, native-2D mechanism (planar diagram + phase-space plot instead of a 3D tube render).
- σᵢ / σᵢ⁻¹ — swap the anyons currently in slots i, i+1 (over vs. under crossing) and apply the corresponding unitary.
- Follow latest — keeps the diagram auto-scrolled to the newest crossing; turn it off and scroll with the mouse wheel to inspect earlier history.
- Reset braid — clears the diagram and returns the qubit to |1⟩ (vacuum fusion channel).
Real systems pursuing this: Majorana zero modes at the ends of topological superconducting nanowires (Microsoft's approach) and non-Abelian quasiparticles in the ν = 5/2 fractional quantum Hall state are the leading experimental candidates for Ising anyons.