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I'm gradually teaching myself quantum computing, being an excellent programmer and fair at linear algebra and geometry.

To learn it, I'm writing a quantum computer emulator (complete with graphical representations). I'll share it when I get to some level of completion. The following is a screenshot of one piece of the program:

But here's why I'm posting.

**I'm struggling somewhat with the math needed to partition Phi into BetaA (real part) and BetaB (imaginary part).**I'm trying to write a function with input of Theta and Phi (polar coordinates for qubit), and have it output Alpha, BetaA, and BetaB. As we know...

|Alpha|

^{2}+ |Beta|

^{2}must = 1

...or, recognizing that Alpha doesn't need an imaginary part, we can simplify to...

Alpha

^{2}+ |Beta|

^{2}= 1

...and Alpha is fairly easy to get from Theta. It's...

Temp1 = (Cos(Theta) + 1) / 2

Alpha = Sqrt(Temp1)

...so, since Temp1 is still squared, we can say that...

Temp2 = 1 - Temp1

...and then...

|Beta|

^{2}must = Temp2

However, now that Temp2 part must be partitioned between BetaA (the real part) and BetaB (the imaginary part). That's where I'm a bit stuck.

**To simplify things further, let's just stick with the**I can easily sort out the signs once I get past the BetaA and BetaB partitioning.

__first quadrant__of the Phi Argand plane (the XY qubit plane).I can get VERY close just treating it as a linear relationship (before sqrt) to Phi, as follows (using Temp2 from above)...

BetaA = Sqrt(Temp2 * (1 - Phi / (PI/2)))

BetaB = Sqrt(Temp2 - BetaA

^{2})

In fact, this works perfectly when Phi=0, Phi=PI/4, and Phi=PI/2.

However, it's not quite right when Phi isn't on a multiple of 45 degrees.

**Some help with this BetaA and BetaB partitioning of Phi would be much appreciated.**

Also, if anything isn't clear, please don't hesitate to ask, and I'll attempt to be more clear.

Regards,

Elroy

p.s. Just FYI, being the old curmudgeon that I am, this certainly isn't homework. With my PhD, I've been to school quite enough. :p