We apply a controlled-NOT operator on two probabilistic bits where the second one is the controlled bit and the first one is the target bit.Which of the following matrix represent this operator?Group of answer choices⎛⎝⎜⎜⎜⎜1000010000100001⎞⎠⎟⎟⎟⎟(1000010000100001) ⎛⎝⎜⎜⎜⎜1000010000010010⎞⎠⎟⎟⎟⎟(1000010000010010) ⎛⎝⎜⎜⎜⎜0001001001001000⎞⎠⎟⎟⎟⎟(0001001001001000) ⎛⎝⎜⎜⎜⎜1000000100100100⎞⎠⎟⎟⎟⎟(1000000100100100) ⎛⎝⎜⎜⎜⎜1000001001000001⎞⎠⎟⎟⎟⎟(1000001001000001) PreviousNext
Question
We apply a controlled-NOT operator on two probabilistic bits where the second one is the controlled bit and the first one is the target bit.Which of the following matrix represent this operator?Group of answer choices⎛⎝⎜⎜⎜⎜1000010000100001⎞⎠⎟⎟⎟⎟(1000010000100001) ⎛⎝⎜⎜⎜⎜1000010000010010⎞⎠⎟⎟⎟⎟(1000010000010010) ⎛⎝⎜⎜⎜⎜0001001001001000⎞⎠⎟⎟⎟⎟(0001001001001000) ⎛⎝⎜⎜⎜⎜1000000100100100⎞⎠⎟⎟⎟⎟(1000000100100100) ⎛⎝⎜⎜⎜⎜1000001001000001⎞⎠⎟⎟⎟⎟(1000001001000001) PreviousNext
Solution
The controlled-NOT operator, also known as the CNOT gate, is a quantum logic gate that is an essential part of quantum computing. In a CNOT gate, one qubit (the control qubit) can flip the state of the second qubit (the target qubit) from |0⟩ to |1⟩ or vice versa.
The matrix representation of a CNOT gate with the second qubit as the control and the first as the target is:
⎛⎝⎜⎜⎜⎜1000010000010010⎞⎠⎟⎟⎟⎟
This matrix leaves the control qubit unchanged and flips the target qubit if the control qubit is |1⟩. The other matrices do not represent this operation.
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