the braid → the qubit (soft-GL Bloch)
each braid is a gate: apply σ1/σ2 and watch the topological qubit rotate on the Bloch sphere. faint dots are 400 random braid words applied to |0⟩ — they scatter over the whole sphere, showing the braids reach every gate (universal). the bright arrow is the current state. drag to rotate.
the braid worldlines & the relation
three anyon worldlines running down the page; a crossing is a braid generator (σ1 crosses strands 1–2, σ2 crosses 2–3). the panel shows the Yang–Baxter relation σ1σ2σ1 = σ2σ1σ2 — the two braids are topologically the same, so they are the same gate. that sameness IS the protection: only the crossing pattern matters, not the wiggles.
toddler corner
ELI5: we built a qubit hidden inside three anyons (axiom 4). Now: how do you actually *compute* with it? You braid them — you literally swap their positions, looping one around another, like plaiting three strands of hair. Each swap is a computation step, a "gate." And here\u2019s the beautiful, almost unfair part: the answer depends ONLY on the pattern of crossings — who went over whom, how many times — and NOT on the exact wiggly path. So your hand can shake, the anyons can wander, and as long as you don\u2019t undo a crossing, you get the EXACT same answer. The computation is protected by knot-topology itself, not by keeping anything perfectly still. And with just two kinds of braid you can reach every possible operation — a whole computer made of braids. That\u2019s the last rung: axiom one was a single bit, and now, five steps up, we have a bit that computes by being braided, and can\u2019t be knocked off course because the answer is written in the knot. The five axioms are now one machine.