Quantum golf

Rules

Start at |+⟩ = (|0⟩ + |1⟩)/√2. Reach the gold hole with as few H and T presses as possible. Drag the sphere to change your view.

H makes a half-turn around the diagonal between the x and z axes. T turns the point 45° around the z axis.

This is approximate synthesis of a quantum state: use a small set of gates to approach a target. The hole sets the allowed error ε. A smaller hole needs a closer match.