Quantum Computing Hardware
Starting from the two-qubit state |00⟩ (the left digit is the first qubit), an H gate is applied to the first qubit, followed by a CNOT gate with the first qubit as control and the second as target. What is the resulting state?
- A(|00⟩ + |11⟩)/√2
- B(|00⟩ + |10⟩)/√2
- C(|01⟩ + |10⟩)/√2
Show answer and explanation
Answer: A. (|00⟩ + |11⟩)/√2
The H gate puts the first qubit into superposition, giving (|00⟩ + |10⟩)/√2. The CNOT gate flips the target only when the control is 1, so |10⟩ becomes |11⟩ and the state becomes (|00⟩ + |11⟩)/√2. This is an entangled state called a Bell state, in which the measurement results of the two qubits always agree. The combination of an H gate and a CNOT gate is the most basic circuit for creating entanglement.
- A. Correct. The CNOT gate turns |10⟩ into |11⟩.
- B. This is the state right after the H gate; it leaves out the action of the CNOT gate.
- C. This is a different Bell state, obtained when the same circuit starts from |01⟩.