Single-Qubit Gate Decomposition: Rz·Ry·Rz Compiler

This is the core job of a quantum programming language's compiler laid bare: turning an arbitrary target rotation into the specific gate sequence real hardware can run. Dial in a target unitary U — a rotation axis and angle on the Bloch sphere, or a familiar preset gate (X, Y, Z, Hadamard, S, T) — and the tool performs the actual Euler-angle (ZYZ) matrix decomposition, computing real α, β, γ angles for the universal sequence R_z(α)·R_y(β)·R_z(γ) directly from U's 2×2 complex matrix elements. Nothing is faked: the tool multiplies the three decomposed gates back together and shows you the reconstructed matrix next to the original target, with a live numerical error readout that has to fall below tolerance for the PASS badge to appear. A circuit diagram and a 2D Bloch-circle projection trace the qubit state through each of the three rotation steps so you can see, not just read, that the compiled sequence really does land on the target.