Controlled Hadamard Without CH

H is a Z rotated by 45 degrees around the Y axis. Use that to turn a controlled-Z into a controlled-Hadamard.

Objective

Return a two-qubit circuit equal to CH with control q0 and target q1.

Constraints

• Allowed gates: ry, cx, cz.

Entry Point

Checks

• Exports build_controlled_hadamard().
• The unitary equals CH(0, 1) up to global phase.