Robustness of quantum Fourier transform interferometry

Boson Sampling photonic networks can be used to obtain Heisenberg limited measurements of optical phase gradients, by using quantum Fourier transform interferometry. Here, we use phase-space techniques and the complex P-distribution, to simulate a $100$ qubit Fourier transform interferometer with additional random phases, to simulate decoherence. This is far larger than possible in conventional calculations of matrix permanents, which is the standard technique for such calculations. Our results show that this quantum metrology technique is robust against phase decoherence, and one can also measure lower order correlations without substantial degradation.