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I coded up a simple implementation of our coupled first-order differential equations.

This code uses a loop along with our set of coupled differential equations and matrix math to create arrays of 4-vector quaternions.

Still need to figure out how to plot these. The previous code used a scatter plot, but that's not very useful for  two qubits. At this point an animation solution may be best, but I was never able to figure out how to make animations actually work in python. Making 4D plots can be problematic with multiple qubits since I was previously using color as the 4th dimension (the real component), though perhaps color intensity could be used to similar effect. Then we could use hue to distinguish qubits.

I created a section to check conservation of our candidate conserved quantity. I didn't bother cutting off the real part, but in testing that part seems to be conserved too. I'm a pessimist, so that's probably a glitch. I encourage y'all to scrutinize my work.
sdbonin/SOQresearch