Question

In a two-qubit system, what is the final state after applying a CNOT gate to a control qubit in state |1⟩ and a target qubit in state |0⟩?

Accepted Answer

In a two-qubit system, the state of the system is described by the tensor product of the individual qubit states. When the control qubit is in state |1⟩ and the target qubit is in state |0⟩, the initial combined state is represented as |10⟩. A CNOT gate, or Controlled-NOT gate, is a quantum logic gate that flips the state of the target qubit if and only if the control qubit is in the state |1⟩. Since the control qubit is |1⟩, the CNOT gate triggers a bit-flip on the target qubit. A bit-flip operation changes a |0⟩ to a |1⟩ and a |1⟩ to a |0⟩. Applying this to the target qubit in the |10⟩ state changes the target qubit from |0⟩ to |1⟩, while the control qubit remains unchanged in its |1⟩ state. Therefore, the final state of the system is |11⟩.

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In a two-qubit system, what is the final state after applying a CNOT gate to a control qubit in state |1⟩ and a target qubit in state |0⟩?

In a two-qubit system, the state of the system is described by the tensor product of the individual qubit states. When the control qubit is in state |1⟩ and the target qubit is in state |0⟩, the initial combined state is repr....