Lecture 6. Basic elements of quantum circuits

In this Lecture we discussed some properties of basic elements in quantum circuits and gave a general definition of quantum circuits. We define a quantum circuit as some composition of state preparations, unitary gates from some dictionary (e.g., $C\mathrm{NOT}+\mathcal{U}(2)$), one-qubit measurements, classical data processing circuits, and classical control. We also proved some useful relations for these elements.