Quantum logic gates

A ''quantum logic gate'' is a device which performs a fixed unitary operation on selected qubits in a fixed period of time. The gates listed below are common enough to have their own names. The matrices describing n qubit gates are written in the computational basis \{ |x\rangle\}, where x is a binary string of length n . The diagrams provide schematic representation of the gates. ==Hadamard gate== The Hadamard gate is a common single qubit gate H defined as Image:Img44.png The matrix is written in the computational basis \{|0\rangle, |1\rangle \} and the diagram on the right provides a schematic representation of the gate H acting on a qubit in state |x\rangle, with x=0,1. ==Phase gate== The phase shift gate \mathbf{\phi } defined as \left| \,0\right\rangle \mapsto \left| \,0\right\rangle and \left| \,1\right\rangle \mapsto e^{i\phi }\left| \,1\right\rangle , or, in matrix notation, Image:Img59.png ==Controlled NOT gate== The controlled-NOT (C-NOT) gate, also known as the XOR or the measurement gate is one of the most popular two-qubit gate. It flips the second (target) qubit if the first (control) qubit is \left| \,1\right\rangle and does nothing if the control qubit is \left| \,0\right\rangle . The gate is represented by the unitary matrix Image:Img76.png where x,y=0\mbox{ or }1 and \oplus denotes XOR or addition modulo 2. If we apply the C-NOT to Boolean data in which the target qubit is |0\rangle and the control is either |0\rangle or |1\rangle then the effect is to leave the control unchanged while the target becomes a copy of the control, ''i.e.'' |x\rangle |0\rangle \mapsto |x\rangle |x\rangle \qquad x=0,1. Category:Evolutions and Operations Category:Quantum Computation Category:Handbook of Quantum Information

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Monday, October 26, 2015 - 17:56