quantum reading notes, QAOA

superposition is a linear combination of states

quantum gates are matrices

Hadamard gate creates superposition. 

H on |0> gives to sqrt(2)( |0> + |1> ), whereas H on |1> gives sqrt(2) ( |0> - |1> ) 

Controlled NOT gate is on two qubit systems: 

Quantum Approximate Optimization Algorithm (QAOA) can solve Max-Cut of graphs, an NP-complete problem. 

For n vertices and m edges, the vertices can be either k(i) = +1 or -1. A cut can be defined as k(i)xk(j)= -1. 

The n-vertices can implemented as n qubits. The 2^n assignments for the vertices will correspond to the 2^n dimenstional Hilbert space generated by n qubits. So, if <i,j> is a cut, the related qubit will land onto different bases. 

QIN: In the above implementation, each vertice is allowed either 1 or 0. So, expand this for my network aging model, I may be able to expand the vertice to sub-vertices, which allows for 1 or 0 separately. Can I? 

Reference: 

Quantgates training materials