javafxpert/grok-bloch

Application that helps user understand the Bloch Sphere

grok-bloch's Issues

Phase Calculation On Unitary Matrices

Initialize a qubit to |0> and apply HZH gate should be equivalent to applying the X gate directly. The resulting state is |1> with phase=0. The current implementation carries a phase of 1.16 $\pi$. While the global phase technically doesn't matter, this is a bit confusing.

Built same circuit in Grok Bloch and IBM QE Circuit Composer, got different statevector and phases

This is my one qubit circuit:

When I build this in grok bloch, I get this state vector, with only one value for phase:

But circuit composer gives me a phase value for each state, and the statevector is different:

The state vectors are in different formats, so let's convert to confirm they're different:

sqrt(0.5) * e^(i * 3pi/2) = 0-0.707i

the grok bloch statevector
[ |0⟩, |1⟩ ] = [ 0.707+0i, 0-0.707i  ] 

the circuit composer statevector
[ |0⟩, |1⟩ ] = [ 0-0.707i, -0.707+0i ]

And let's compare the phases

grok bloch phases
[ arg(0.707+0i),  arg(0-0.707i) ] = [ 0, -π/2 ] = [ 0, 3π/2 ]

circuit composer phases
[ arg(0-0.707i),  arg(-0.707+0i) ] = [ -π/2, π ]

Which is the correct way to grok the bloch?
How many phases does a qubit have?

Thanks