Occupations interface

[aryavorskiy]

This PR extends #157 by providing a more thought-out occupations interface. It also fixes the #102 issue, because the statistics is now stored in the occupations object.

To implement the occupations interface, one must implement these methods for the object:

• Ordering by defining == and isless
• Conversion from the occupations represented as a Vector{Int}, aka convert(::Type{YourType}, v::AbstractVector) so that basisstate could work normally
• QuantumOpticsBase.state_transition!(buffer, occ, at_inds, a_inds) for transition coefficients
• similar (if mutable) or QuantumOpticsBase.allocate_buffer (if immutable) for allocating a buffer

Maybe this should be documented for someone who needs, for example, anyon statistics or extra performance?

[aryavorskiy]

Also this PR introduces (as an example of the interface and for performance reasons) fermion states as bitstrings. This introduces up to 5x speedup in operator creation (below - 36 modes, 4 fermions)

Vector occupations:
BenchmarkTools.Trial: 36 samples with 1 evaluation.
 Range (min … max):  136.681 ms … 153.661 ms  ┊ GC (min … max): 0.00% … 5.47%
 Time  (median):     140.449 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   141.117 ms ±   3.466 ms  ┊ GC (mean ± σ):  1.03% ± 1.61%

   █   ▃   █▃ ▃    █▃  ▃ █    ▃
  ▇█▇▇▁█▇▇▇██▁█▁▇▁▇██▁▁█▁█▁▁▁▁█▁▁▇▇▁▁▁▁▁▇▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇ ▁
  137 ms           Histogram: frequency by time          154 ms <

 Memory estimate: 23.86 MiB, allocs estimate: 58.

Bitstring occupations:
BenchmarkTools.Trial: 135 samples with 1 evaluation.
 Range (min … max):  33.617 ms … 44.738 ms  ┊ GC (min … max): 0.00% … 11.08%
 Time  (median):     35.879 ms              ┊ GC (median):    0.00%
 Time  (mean ± σ):   37.058 ms ±  2.687 ms  ┊ GC (mean ± σ):  3.78% ±  5.34%

      ▅█▅ ▃▃▅▃▅▅
  ▄▄▄███████████▅█▇▅▁▄▁▅▄▅▇▄▁▄▇▅▄▄▁▄██▅▄▄▇▁▄▅▄▁▁▅▄▅▁▅▁▁▁▅▄▄▁▄ ▄
  33.6 ms         Histogram: frequency by time        43.8 ms <

 Memory estimate: 23.86 MiB, allocs estimate: 57.

[Krastanov]

Thanks, Alexander, this is great! Sorry for the slow response, it is end of the semester and we are a bit short staffed. I will try to review this in the next couple of days.

[aryavorskiy]

Thanks, Alexander, this is great! Sorry for the slow response, it is end of the semester and we are a bit short staffed. I will try to review this in the next couple of days.

It's OK, I understand, I also have end of semester now :)

This was the last-est commit before review, had to unify the interface for fermionstates/bosonstates

[Krastanov]

Sorry for the long wait on review! This is awesome, thank you for taking the time to implement it. Looking through it, I do not see anything that raises any flags for me. I added a commit to bump the version number. When the tests pass I will merge and make a release.

I will make a new issue to track:

• defaulting to the faster FermionBitstring implementation
• documenting the required interface
• anyon statistics