Stabilizer Tableau

Overview

Tracks n qutrits using a 2n×2n matrix over GF(3). Clifford gates update the tableau in O(n²) time.

Clifford Gates

Gate	Operation	Effect
H (Hadamard)	X ↔ Z swap	Superposition creation
S (Phase)	Z → ZX	Relative phase
CSUM (Controlled-SUM)	X_a → X_a, Z_b → Z_b + X_a	Entanglement

Gottesman-Knill Theorem

Stabilizer circuits (H, S, CSUM + measurements) can be efficiently simulated classically — no exponential overhead.

This enables quantum-inspired parallelism on classical hardware.

Tableau Structure

tableau[n][2n] : GF(3) matrix
  rows 0..n-1   : X generators
  rows n..2n-1  : Z generators

See Also

• Ternary State Space — underlying GF(3) arithmetic
• SYCL Acceleration — parallel tableau updates