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5.2.1 The NOT gate

The NOT gate is denoted by the operator, cap x hat and, in the basis of the logical qubits vertical line zero mathematical right angle bracket and vertical line one mathematical right angle bracket, is represented by the matrix

cap x hat equals matrix row 1column 1 01 row 2column 1 10 full stop

which is also the Pauli-X operator, sigma hat sub x, mentioned earlier. In a circuit diagram representing a quantum algorithm, the symbol for the NOT gate is shown in Figure 7.

Figure 7 The symbol used in a quantum circuit for a NOT gate, cap x hat

In quantum computing, the truth table specifies outcomes for the logical states vertical line zero mathematical right angle bracket and vertical line one mathematical right angle bracket. In Table 3 the general superposition state is also included for reference.

Table 3 Quantum NOT gate truth table

Input Output
vertical line zero mathematical right angle bracket vertical line one mathematical right angle bracket
vertical line one mathematical right angle bracket vertical line zero mathematical right angle bracket
a sub zero times absolute value of zero mathematical right angle bracket prefix plus of a sub one times one mathematical right angle bracket a sub zero times absolute value of one mathematical right angle bracket prefix plus of a sub one times zero mathematical right angle bracket
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OpenLearn - Introduction to quantum computing
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