Exact, zero-noise discrete algebra for quantum circuits — leaving physical noise where it actually belongs: in condensed-matter spectroscopy, not in computation.
| ζ | = eiπ/4 | ζ⁴ = −1 | √2 = ζ − ζ³ |
| amp(b) | = (c₀ + c₁ζ + c₂ζ² + c₃ζ³) / 2d | ci ∈ ℤ | |
| H | (a, b) → M(a+b), M(a−b) | d ← d + 1 | |
| M | (c₀,c₁,c₂,c₃) → (c₁−c₃, c₀+c₂, c₁+c₃, c₂−c₀) | ||
| ζk | ci → ±c(i+k) mod 4 | d unchanged | |
| |amp|² | = (S + X√2) / 22d | ||
| S | = c₀² + c₁² + c₂² + c₃² | Σ S = 22d | |
| X | = c₀c₁ + c₁c₂ + c₂c₃ − c₀c₃ | Σ X = 0 |