Fixing threshold clicks

[nquesada]

This PR adds the functions that allow to find the scaling factor of an adjacency matrix so that it has given mean click number when sampled with threshold detectors, addressing issue #100 .

[nquesada]

We can now add the possibility of doing torontonian sampling fixing the mean number of clicks, instead of the mean photon number which we took as a proxy for the former.
We can either:

1. Modify torontonian_sample_graph(A, n_mean) so that its second argument is the mean number of clicks.
2. Make a new function.

I am in favour of option 1 but it would require some reworking in sf apps. Any thoughts @josh146 @trbromley ?

[codecov]

Codecov Report

Merging #136 into master will increase coverage by 0.06%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #136      +/-   ##
==========================================
+ Coverage   97.61%   97.68%   +0.06%     
==========================================
  Files          12       12              
  Lines         839      864      +25     
==========================================
+ Hits          819      844      +25     
  Misses         20       20

Impacted Files	Coverage Δ
thewalrus/quantum.py	100% <100%> (ø)	⬆️

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[josh146]

Just left a couple of quick questions :)

[trbromley]

Thanks @nquesada - would be cool to have this feature and use it in the apps layer.

In terms of how this fits in to SF and the apps layer, I had more of a look just now.
The apps layer has this in sample.sample():

    mean_photon_per_mode = n_mean / float(nodes)

    # pylint: disable=expression-not-assigned,pointless-statement
    with p.context as q:
        sf.ops.GraphEmbed(A, mean_photon_per_mode=mean_photon_per_mode) | q

        if loss:
            for _q in q:
                sf.ops.LossChannel(1 - loss) | _q

        if threshold:
            sf.ops.MeasureThreshold() | q
        else:
            sf.ops.MeasureFock() | q

That is, it uses SF's GraphEmbed rather than directly calling torontonian_sample_graph.

I think it might be good to update torontonian_sample_graph separately, but for users to have access in SF and apps, we'd need to update decompositions.graph_embed(). In there, it would be easy to have find_scaling_adjacency_matrix_torontonian as well as the find_scaling_adjacency_matrix which is currently there, depending on whether we want to set n_mean or n_clicks. In terms of the user interface, how about:

• User can input mean_photon_per_mode, and we rescale to have that mean photon number.
  OR
• User can input mean_click_per_mode, and we rescale to have that number of clicks.

If they input both, they will get an exception. In this way, we don't break any existing SF and apps code, and can do a separate PR to apps.sample.sample() to allow for sampling based on mean click number.

[codecov-io]

Codecov Report

Merging #136 into master will increase coverage by 0.06%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #136      +/-   ##
==========================================
+ Coverage   97.61%   97.68%   +0.06%     
==========================================
  Files          12       12              
  Lines         839      864      +25     
==========================================
+ Hits          819      844      +25     
  Misses         20       20

Impacted Files	Coverage Δ
thewalrus/quantum.py	100% <100%> (ø)	⬆️

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Δ = absolute <relative> (impact), ø = not affected, ? = missing data
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[codecov]

Codecov Report

Merging #136 into master will increase coverage by 0.06%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #136      +/-   ##
==========================================
+ Coverage   97.61%   97.68%   +0.06%     
==========================================
  Files          12       12              
  Lines         839      864      +25     
==========================================
+ Hits          819      844      +25     
  Misses         20       20

Impacted Files	Coverage Δ
thewalrus/quantum.py	100% <100%> (ø)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
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[nquesada]

@trbromley what you propose sounds good. It also implies that no more changes are needed from this side at the moment.