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==A General Introduction to Quantum Information== | ==A General Introduction to Quantum Information== | ||
Quantum computation is marked by a set of unitary matrices (quantum gates) acting on qubit states followed by measurement. The most used representation is the circuit model of computation, comprising straight lines and boxes. The horizontal lines represent qubits and boxes represent single qubit unitary gates. A two qubit unitary gate links one qubit from another via vertical lines. Some useful notations are given below.<br/> | Quantum computation is marked by a set of unitary matrices (quantum gates) acting on qubit states followed by measurement. The most used representation is the circuit model of computation, comprising straight lines and boxes. The horizontal lines represent qubits and boxes represent single qubit unitary gates. A two qubit unitary gate links one qubit from another via vertical lines. Some useful notations are given below.<br/> | ||
<math>|+\rangle=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle),\quad |-\rangle=\frac{1}{\sqrt{2}}(|0\rangle-|1\rangle)</math> | *<math>|+\rangle=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle),\quad |-\rangle=\frac{1}{\sqrt{2}}(|0\rangle-|1\rangle)</math> | ||
*X (NOT gate): <math>X|0\rangle\,\to\,\ |1\rangle,\quad X|1\rangle\,\to\,\ |0\rangle,\quad X|+\rangle\,\to\,\ |+\rangle,\quad *X|-\rangle\,\to\,\ -|-\rangle</math> | |||
*Z (Phase gate): <math>Z|+\rangle \,\to\,\ |-\rangle,\quad Z|-\rangle \,\to\,\ |+\rangle,\quad Z|0\rangle \,\to\,\ |0\rangle,\quad Z|1\rangle \,\to\,\ -|1\rangle </math></br> | |||
Thus, <math>|0\rangle </math>, <math>|1\rangle </math> are eigenstates of Z gate and <math>|+\rangle</math>, <math>|-\rangle </math> are eigenstates of X gate. | |||
*H (Hadamard gate): <math>H|0\rangle \,\to\,\ |+\rangle </math> or <math>H|1\rangle \,\to\,\ |-\rangle </math> | |||
===Unitary Operation=== | ===Unitary Operation=== | ||