3D Quantum Compiler Gate Decomposition

Target unitary U — 3D

Axis polar θ_n 90°

Axis azimuth φ_n 0°

Rotation angle θ 90°

Compiled sequence Rz(α)·Ry(β)·Rz(γ)

γ (1st, Rz)

0.00°

β (2nd, Ry)

0.00°

α (3rd, Rz)

0.00°

Verification

Max |ΔU| element error

0.0e+0

Arrow reached target?

–

How it works

Every pure qubit state is a point on the unit Bloch sphere. A quantum compiler decomposing a target unitary U into R_z(α)·R_y(β)·R_z(γ) is really choosing a 3-step rotation path on this sphere: spin about the vertical z-axis by γ, tip about the horizontal y-axis by β, then spin about z again by α. Press Play to watch the white arrow — starting at |0⟩, the north pole — execute exactly those three real rotations, about the real axes, by the real computed angles.

step 1: rotate about z-axis by gamma
step 2: rotate about y-axis by beta
step 3: rotate about z-axis by alpha
arrow tip after step 3 =?= gold target marker

The gold target marker is U|0⟩, computed straight from the target unitary matrix — it never moves once you set the sliders.
If the arrow's final position visually coincides with the target marker, that is the proof: the same matrix math from the 2D version underlies this animation, and the numerical error readout confirms it below tolerance.
Drag to orbit the sphere and check the alignment from any angle — a real geometric confirmation, not just a claimed one.

state vector |ψ⟩ target U|0⟩ Rz step (about z) Ry step (about y)

step 1/3 · Rz(γ)

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3D Quantum Compiler Gate Decomposition — Bloch Sphere Rotation Path