Louis Paletta

This page presents illustrative animations of the 2D signal-rule decoders introduced in Local decoder for the toric code with a high pseudo-threshold, L. Paletta (2026).

Layout

Each lattice site stores:

• Defect (−1 stabilizer outcome)
• 16 binary variables: 1- and 2-forward-signals, 1- and 2-anti-signals (by cardinal direction)
• 8 integer variables: 1- and 2-stacks (by cardinal direction)

The rule dynamically mediates an effective attractive interaction between defects via the propagation of 1- and 2-forward-signals. Stack and anti-signal dynamics erase forward-signals at the end, ensuring the decoder eventually returns to the zero configuration.

Visualization

Dynamics of the decoder as animated GIF, the step j of iteration i is indicated as i.j.

1. A single particle is represented per site, according to the following priority order:
   • defects > 1-forward-signals > 2-forward-signals
   • 1-stacks > 2-stacks > 1-anti-signals > 2-anti-signals
2. Multiple signals of the same type at a site are represented as a square.
3. The highest value of each local stack is shown in white.

Elementary Update Mechanisms

1. Matching of neighboring defects by applying a local Pauli correction in between.
2. 1-forward dynamics
   1. Creation of 1-forward-signals from defect sites; the associated local 1-stacks are incremented by 1.
   2. Propagation of 1-forward-signals by one lattice step.
3. 2-forward dynamics
   1. Creation of 2-forward-signals from 1-forward-signals and defect sites; the associated local stacks are incremented by 1.
   2. Propagation of 2-forward-signals by one lattice step.
4. Attraction of defects encountering 1- or 2-forward-signals by applying a local Pauli correction.
5. Anti-signal dynamics
   1. Creation of 1-anti-signals (resp. 2-anti-signals) triggered by decrementing the 1-stacks (resp. 2-stacks) when no defect is present.
   2. (Repeated three times) Propagation by one lattice step and recombination of anti-signals with forward-signals of the same type and direction.