Broadcasting for semiclassical objects

[apkille]

@david-pl @Krastanov @amilsted

• Added an interface for broadcasting State objects, which enables use of DiffEq solvers
• With these changes, ODE problems for States can be naturally written as the following example:

using QuantumOptics, OrdinaryDiffEq, BenchmarkTools

b = SpinBasis(1//2)
psi0 = spindown(b)
u0 = ComplexF64[0.5, 0.75] 
sc = semiclassical.State(psi0, u0)
t₀, t₁ = (0.0, pi)
const σx = sigmax(b)

fquantum(t, q, u) = σx + cos(u[1])*identityoperator(σx)
fclassical!(du, u, q, t) = (du[1] = sin(u[2]); du[2] = 2*u[1])
f!(dstate, state, p, t) = semiclassical.dschroedinger_dynamic!(dstate, fquantum, fclassical!, state, t)
prob = ODEProblem(f!, sc, (t₀, t₁))

julia> @benchmark sol = solve($prob, DP5(); save_everystep=false)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  50.166 μs … 133.706 ms  ┊ GC (min … max):  0.00% … 99.93%
 Time  (median):     52.583 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   70.621 μs ±   1.339 ms  ┊ GC (mean ± σ):  23.35% ±  3.73%

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  50.2 μs         Histogram: frequency by time         69.8 μs <

 Memory estimate: 93.81 KiB, allocs estimate: 1136.

julia> @benchmark semiclassical.schroedinger_dynamic([$t₀, $t₁], $sc, $fquantum, $fclassical!)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  117.875 μs … 137.310 ms  ┊ GC (min … max):  0.00% … 99.87%
 Time  (median):     122.959 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   148.349 μs ±   1.379 ms  ┊ GC (mean ± σ):  15.47% ±  6.25%

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  118 μs           Histogram: frequency by time          163 μs <

 Memory estimate: 225.66 KiB, allocs estimate: 2637.

• Support is provided for both kets and density operators.
• Note: broadcasting for a custom type like State is weird, and really the only reason we're doing it is to have interoperability of semiclassical objects with SciML.
• Some of these interface decisions probably can be debated. I based most of them off of how State objects were recasted in the semiclassical.schroedinger_dynamic, semiclassical.master_dynamic, etc. functions.

[Krastanov]

Looks good to merge after a small import change.

[Krastanov]

And after the errors in the tests are fixed. Does this depend on the changes to QuantumOpticsBase in its broadcast PR? If so, we should bump the compat bound for it.

[Krastanov]

And same comment as in the QuantumOpticsBase PR on adding your examples from the PR description to the test runner, maybe as a new file.

[apkille]

And after the errors in the tests are fixed. Does this depend on the changes to QuantumOpticsBase in its broadcast PR? If so, we should bump the compat bound for it.

Yes, so we should merge this after we merge the QuantumOpticsBase PR.

[apkille]

@Krastanov Should be good to go.

[codecov]

Codecov Report

Attention: Patch coverage is 86.36364% with 9 lines in your changes missing coverage. Please review.

Project coverage is 96.66%. Comparing base (d2c71fe) to head (bb2d0f5).
Report is 11 commits behind head on master.

Files	Patch %	Lines
src/semiclassical.jl	86.36%	9 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #404      +/-   ##
==========================================
- Coverage   97.03%   96.66%   -0.38%     
==========================================
  Files          18       19       +1     
  Lines        1554     1678     +124     
==========================================
+ Hits         1508     1622     +114     
- Misses         46       56      +10     

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[apkille]

@Krastanov is there anything preventing this from getting merged?

[Krastanov]

This looks good to me.

There is a minor issue with isapprox not propagating its kwargs.

More importantly though, there are a few functions that codecov reports as not covered by tests. Could you add new tests for them, just to ensure the review is not missing anything? I am a bit skittish here as this touches a lot of basic interfaces.

[apkille]

@Krastanov good catch. Should be covered now.