Bit Oracle to Phase Oracle

Your library only has bit-flip oracles, but your algorithm wants phase oracles. Convert one to the other with a single helper qubit, and hand that helper back clean.

Objective

phase_from_bit_oracle(oracle, num_inputs) receives a Gate on num_inputs + 1 qubits acting as |x>|y> -> |x>|y XOR f(x)>. Return an (n + 1)-qubit circuit mapping |x>|0> -> (-1)^f(x) |x>|0>.

Constraints

• The helper qubit (index num_inputs) must end in |0>.
• Do not inspect the oracle: every non-oracle gate must be identical for every oracle.

Entry Point

Checks

• Exports phase_from_bit_oracle(oracle, num_inputs).
• Applies (-1)^f(x) on a full superposition and restores the helper qubit.
• The circuit is identical apart from the oracle box.