The Hadamard Gate

     Applying a hadamard gate from |0>:                                                        

Apllying a Hadamard  gate from |1>:

 Perplexity:

https://www.perplexity.ai/search/Quantum-computing-are-aez3XV9LTOGsQJLV0HDlJQ

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The CNOT gate, controlled NOT gate, is very useful. In qiskit, it is the only directly

applicable controlled gate. If we want others, we need to be creative about it. Here is what 

the controlled-Z gate reduces to.

                                                               

Asking for expand definition:

The more utilitarian version:

                                      

That is because (and this is verifiable through matrix multiplication) HXH = Z, and

HZH = X. 

 Z on a Hadamard gate that was applied form|0>:                                                                        

Z on a Hadamard gate that was applied to |1>:

HZH:

In the same vein, this is a controlled Y-gate:

                                                                                

  And a controlled Hadamard:

                                                                           

Doing a test. With a 1 on qubit(0) I do indeed create a Hadamard gate on qubit(1):