CCZ From Clifford+T

Fault-tolerant hardware speaks Clifford+T. CCZ is diagonal, so it can be built from phases on parities of the three inputs without any Hadamards.

Objective

Return a three-qubit circuit equal to CCZ.

Constraints

• Allowed gates: cx, t, tdg.
• At most 6 CX and at most 7 T/Tdg gates.

Entry Point

Checks

• Exports build_ccz().
• Uses only CX, T and Tdg within budget.
• The unitary equals CCZ.