Quantum Computing Hardware
Which correctly describes what a single-qubit X gate does?
- AIt swaps |0⟩ and |1⟩, turning |0⟩ into |1⟩ and |1⟩ into |0⟩ (the equivalent of a classical NOT)
- BIt turns |0⟩ into a superposition in which the amplitudes of |0⟩ and |1⟩ have equal magnitude
- CIt flips only the sign of the amplitude of |1⟩, without changing the measurement probabilities
Show answer and explanation
Answer: A. It swaps |0⟩ and |1⟩, turning |0⟩ into |1⟩ and |1⟩ into |0⟩ (the equivalent of a classical NOT)
The X gate turns |0⟩ into |1⟩ and |1⟩ into |0⟩, the equivalent of NOT in classical logic circuits. Applied to a superposition α|0⟩ + β|1⟩, it swaps the amplitudes to give β|0⟩ + α|1⟩. On the Bloch sphere it is a 180° rotation about the x axis, and in superconducting qubits and similar platforms it is implemented by a microwave pulse tuned to the qubit's resonance frequency (a π pulse). The gate that turns |0⟩ into an equal superposition is the Hadamard (H) gate, and the one that flips the sign of |1⟩ is the Z gate.
- A. Correct. It is a 180° rotation about the x axis of the Bloch sphere.
- B. This is what the Hadamard (H) gate does.
- C. This is what the Z gate does.