Bell decomp

[jakeffbulmer]

This is the residency demo project by myself and Yuan @sylviemonet. We are implementing the decomposition in https://arxiv.org/abs/2104.07561

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Context:
There are several ways to decompose a linear optical unitary transformation into 2x2 unitary elements. Here, we implement a new decomposition by Bell and Walmsley (https://arxiv.org/abs/2104.07561). This decomposition is lower in depth than e.g. 'rectangular' mesh in strawberryfields, as many of the phases are applied in parallel, resulting in just N+2 layers of phase shifters for an NxN unitary, instead of the 2N+1 layers of phase-shifters needed for the standard 'rectangular' decomposition.

Description of the Change:
We add a new gate: sMZgate, which has a phase shifter (Rgate) on each arm of the interferometer. We add functions to strawberryfields.decompositions: rectangular_compact and triangular_compact. These implement the rectangular/triangular decompositions described in https://arxiv.org/abs/2104.07561. We also add this functionality to the Interferometer operation, which can be accessed using the options mesh='rectangular_compact' and mesh='triangular_compact'.

Benefits:
Future devices may wish to use this decomposition instead of the conventional rectangular scheme, as it allows for a shorter depth, and so could lead to more compact footprint and lower loss. Therefore, having the decomposition available through strawberryfields could be useful for programming these future devices.

Possible Drawbacks:
We have used a different datastructure to store the phases as compared to the existing strawberryfields decompositions. This means that how the decomposition is handled inside Interferometer is different to the other mesh options.

Related GitHub Issues:

[jakeffbulmer]

I think we've implemented all your changes! Thanks very much for the review @josh146 !!

[josh146]

Thanks @jakeffbulmer and @sylviemonet! Looks really nice, happy to approve on my end (conditional on a few suggested changes to improve docstring rendering)

[josh146]

Oh, it also looks like there is still one Codecov/pylint warning:

You can fix this by adding the comment:

def _decompose(self, reg, **kwargs):
    """docstring"""
    # pylint: disable=too-many-branches