Gates

 The Quirk site has a built-in Teleportation circuit that looks like mine,

only fancier with a probabilistic message, and thus probabilistic output. 

Been trying to see how, and why this was done.

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The Bloch sphere is in three dimensions and complex. It maps to a Riemann 

spherical Surface. Below:

                                                                          

   On or off is on the Z-axis, phase on the Y, time on the X.                                                             

                                                                                

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The Pauli X, Y, Z gates, along with the CNot are a complete set and allow us to create

any other gate one might want, including the Hadamard...

                                                                         

The X:

                                                                                          

The Y

                                                                      

                                                                                       

The Z:

                                                                             

                                              

The Hadamard:

                                                                           

The CNOT:

                                                                            

I asked Bing/Chat is there is an advantage to adding gates to a circuit. I was told

it means one has more to work with in defining operations down the road. It also has 

disadvantages in that each new gate means having to do somthing physical to the Qubits, 

opening the door to more incoherence.

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Still working on findng what that Message gate was put together...