Now that we have already seen the states of the multi-qubit systems, we want to apply gates to them. But how do we do this? David Elkouss (QuTech) will guide us through the steps and the possible kinds of gates. We will see the CNOT gate, a two-qubit gate that can generate entanglement!
So far you learned how to express a single qubit state in the braket notation and its representation on the Bloch sphere. In this video, David Elkouss (QuTech) will explain more in detail how these concepts extend to two and multiple qubit systems.
Which of the following properties for the matrix M defines unitarity?
When we write CNOT|ij>, we mean flip j if i=1. We could also redefine the gate to mean flip i if j=1. What is the matrix of this new CNOT?
For a more detailed explanation on controlled gates see section 4.3 in M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, 10th anniversary ed. Cambridge ; New York: Cambridge University Press, 2010.