MCX, MCPhase gate

[gyu-don]

How qiskit realize it especially when it's for hardware?

[gyu-don]

Qiskit has 4 ways to decomposite MCX gates. Almost all implementations are described in [Barenco]

• Decomposite by Gray code
• Decomposite by V-chain
• Decomposite by V-chain but dirty ancilla accepted (refer [Barenco], Lemma 7.2)
• Decomposite by the recursive process (refer [Barenco], Lemma 7.3)

And MCPhase gate is implemented by Gray code decomposition.

[gyu-don]

Gray code implementation is done in #137. I will implement a recursive process and won't implement the V-chain process.

[gyu-don]

Done in #138