Evaluating the Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection.
During the calculation of this matrix function exponentially large number of determinants have to be computed.
We proposed a recursive algorithm providing a polynomial speedup in the exact calculation of the Torontonian compared to state-of-the-art algorithms.
Our algorithm recursively reuses the data used before to reach the computational advantage.
According to numerical analysis the complexity of the algorithm is ordo(n^1.06912 * 2^n).
With our algorithm, one can simulate threshold GBS up to 35-40 photon clicks without the needs of large-scale computational capacities.