In December 2020, there was this claim of quantum advantage/supremacy by a team of USTC using Gaussian boson sampling. Here is the paper and here is an explanatory news article in Nature. To get an idea of how that works, I wanted to try to replicate a reduced version in Qiskit. Is this possible? Are there predefined functions I can exploit for doing photon-like circuits (if not how I can implement the boson-to-qubit mapping)?
The original paper on the theory of boson sampling by Scott Aaronson and Alex Arkhipov can be found here.
I looked in Qiskit documentation and I did not find any boson-qubit mapping (Holstein-Primakoff, Dyson-Maleev or Schwinger bosons). I just found out that there is a
BosonicOperator in Qiskit Chemistry module but I do not know what is its purpose without mappings.
I would also like to have an estimation of the minimum number of qubits I will be needing. I am not trying to test quantum advantage. The paper reported a 76 photons coincidence which is a lot for even the best of supercomputers. The calculation involves permanents which are in practice exponentially difficult to calculate with ordinary computers. My goal is to simulate boson sampling
to calculate the result of a very small permanent (if possible the smallest one) that I can verify later on my PC.
Note: according to Is it possible to "calculate" the absolute value of a permanent using Boson Sampling? you cannot calculate permanents directly using boson sampling.