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*Controlled-U(CU): uses two inputs, control qubit and target qubit. It operates U on the second(target) qubit only when the first (source) qubit is 1. C-U gates are used to produce entangled states, when the target qubit is <math>|+\rangle</math> and control qubit is not an eigenstate of U. In the given equation 'i' denotes the source qubit and 'j', the target qubit. Following are two important C-U gates. | *Controlled-U(CU): uses two inputs, control qubit and target qubit. It operates U on the second(target) qubit only when the first (source) qubit is 1. C-U gates are used to produce entangled states, when the target qubit is <math>|+\rangle</math> and control qubit is not an eigenstate of U. In the given equation 'i' denotes the source qubit and 'j', the target qubit. Following are two important C-U gates. | ||
<math> | <math> | ||
\text{Controlled-NOT(CX): }CX_{ij}|+\rangle_i|0\rangle_j\,\to\,\ \frac{1}{\sqrt{2}} (|0_i0_j\rangle+|1_i1_j\rangle)</math></br> | \text{Controlled-NOT(CX or C-NOT): }CX_{ij}|+\rangle_i|0\rangle_j\,\to\,\ \frac{1}{\sqrt{2}} (|0_i0_j\rangle+|1_i1_j\rangle)</math></br> | ||
<math>\text{Controlled-Phase(CZ): }CZ_{ij}|+\rangle_i|+\rangle_j\,\to\,\ \frac{1}{\sqrt{2}} (|0_i+_j\rangle+|1_i-_j\rangle)</math> | <math>\text{Controlled-Phase(CZ): }CZ_{ij}|+\rangle_i|+\rangle_j\,\to\,\ \frac{1}{\sqrt{2}} (|0_i+_j\rangle+|1_i-_j\rangle)</math> | ||