The T Gate

The T gate is the expensive non-Clifford gate whose count Kronos tracks as the real price of a fault-tolerant fusion-chemistry calculation.

What it does

T = [[1,0],[0,e^(i*pi/4)]] is the square root of S. Adding T to the Clifford set {H,S,CNOT} makes it universal - but in error-corrected machines T gates must be produced by costly magic-state distillation.

Where it appears at Kronos

When Kronos estimates whether a low-activation-alloy simulation is feasible, the headline number is the T-count: the more T gates, the more distillation factories and runtime. Minimizing T-count is a central goal of Kronos's circuit design.

Honest note

Practical T-heavy materials runs require the large error-corrected machines expected ~mid-2030s.