Fixing 2 mode Grover search

[MartinBombar]

Overview

Changing the 2 mode Grover search to make it correspond better to the kiwat reference and to grover algorithm.

What was wrong

In the old version, the state after initialization would be the wrong state (2 of the terms had a phase of \ pi ).
Also the inversion circuit would amplify the state having opposite polarization to the marked state. ({0;P:H} marked would amplify {0;P:V})

What was changed :

Both the issues were fixed.
In initialization : the components before the BS were lowered to mode 1 allowing to create the right superposition
In the inversion : the components between the BS were lowered to mode 1 allowing to amplify the right state.
In the circuit evaluation : Now the circuit is initialized to pcvl.BasicState("|0,{P:H}, 0, 0>") and not pcvl.BasicState("|{P:H},0, 0, 0>")

Please note that changing the mode for the initialization is not just a symetric change, it creates a totally different state :
Older version :
State after initialization : -0.5*|{P:H},0>+0.5*|0,{P:H}>-0.5*|{P:V},0>+0.5*|0,{P:V}>
New version :
State after initialization : 0.5*|{P:H},0>+0.5*|0,{P:H}>+0.5*|{P:V},0>+0.5*|0,{P:V}>

[Aubaert]

Hello,

Thank you for your contribution, and congrats on finding this error.
The changes will appear in the documentation when we release the 1.2 version of perceval.

Cheers,
The perceval team

[philippe3263]

here a full introduction with a full description of grover using photonic
https://arxiv.org/abs/2509.04266