Explore Bessel.jl for Chebychev coeffs

[goerz]

This might make the calculation of coefficients significantly faster:

See https://discourse.julialang.org/t/matrix-exponential-vector-for-various-scales/112022/17

[Fe-r-oz]

Do we need to normalize the spellings of Chebychev to Chebyshev in QuantumPropagators.jl ?

[goerz]

No, I always spell it Chebychev, and that will be the canonical spelling inside this package.

[Fe-r-oz]

Alrighty!

I am excited to explore Bessel.jl for chebychev coeff!

As you mentioned we have to use Bessel.jl instead of (besselj) from SpecialFunctions.jl, as it is typically 2-12x faster than specialfunction.jl implementations. Bessel.jl also have same names etc. besselj

if I recall correctly, the regular exponential just uses the modified Bessel function (besseli instead of bessel) and you kill the i in the definition of c and in the final phase factor

It seems that regular exponential uses besselj instead of besseli,, so there might be no need to kill i in c and phase factor, right?

[goerz]

To really "explore" this would require proper benchmarking in realistic settings. I have a WIP benchmarking repository that isn't quite ready to be pushed. Since the coefficients can typically be reused a lot, they are very unlikely to be a bottleneck in any optimization. Still, at some point, it would be nice to quantify it a bit more. This issue is more of a note to myself to look at this when my benchmarking code is in better shape. I don't think looking into this would be a good use of your time.

[Fe-r-oz]

Sounds good! I enjoyed your talk at Yao Community Call, that was comprehensive!

Looking forward to the workshop tutorial!