Question

Implement the X gate on a qubit in the state ∣0⟩. What is the resulting state? Implement the Y gate on a qubit in the state ∣+⟩. What is the resulting state? Implement the Z gate on a qubit in the state ∣1⟩. What is the resulting state?

Answer 1

The X gate transforms the state |0⟩ to |1⟩. The Y gate transforms the state |+⟩ to |-⟩. The Z gate leaves the state |1⟩ unchanged.

Step-by-step explanation:

The X gate is a quantum logic gate that corresponds to a rotation around the x-axis of the Bloch sphere by π radians. When applied to a qubit in the state |0⟩, it transforms the state to |1⟩. So, the resulting state after implementing the X gate on a qubit in the state |0⟩ is |1⟩.

The Y gate is another quantum logic gate that corresponds to a rotation around the y-axis of the Bloch sphere by π radians. When applied to a qubit in the state |+⟩ (the superposition of |0⟩ and |1⟩ states), it transforms the state to |-⟩ (the orthogonal state). So, the resulting state after implementing the Y gate on a qubit in the state |+⟩ is |-⟩.

The Z gate is a quantum logic gate that corresponds to a rotation around the z-axis of the Bloch sphere by π radians. When applied to a qubit in the state |1⟩, it leaves the state unchanged. So, the resulting state after implementing the Z gate on a qubit in the state |1⟩ remains |1⟩.