Bruhat–Tits QEC: Staircase Redundancy vs Archimedean Codes

How to use this demo (click to collapse)

Prime buttons — choose the effective prime p of the Bruhat–Tits tree (2, 3, or 5).
Depth slider — how many levels of the tree to build.
Tree geometry tab — hover/click nodes; click to select and see its path.
Redundancy curve tab — the staircase; toggle Compare Archimedean for the smooth case.
Inject error — then click a node to see ultrametric error confinement (only that subtree is affected).
Reset — clear selections and return to default.

Effective prime p

Tree depth d

Current depth: 3

Controls

Live metrics

Total nodes

Tree depth

Redundancy R

Max R (all lvls)

Key insight — verify it yourself

In Archimedean codes, adding one qubit adds exactly +1 redundancy (a smooth curve). In a Bruhat–Tits tree code, adding one tree level adds +p^r redundancy at once (a staircase). Count the horizontal steps on the curve — between steps, redundancy cannot change, so QEC and classical objectivity can coexist there. Redundancy here = number of nodes at the deepest level (distinct environment fragments).

Node

Selected

Error subtree

Archimedean