Bayesian Inference for Heterogeneous Integrated Photonic systems

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Machine learning (ML) techniques have found employment in the quantum sciences for easier characterisation and evolution of quantum states that are difficult to describe and propagate analytically [1].Bayesian inference is one such technique that is often used as an estimator, making use of a likelihood function to update a prior distribution that represents some belief about what is being estimated in or-der to produce an updated (posterior) probability distribution [2]. This technique has been used tasks like open system dynamics of an electron spin in a diamond NV centre [3], characterisation of nuclear spins [4], and error correction [5].Photonic integrated circuits (PICs) has undergone significant development in the past decade which1has allowed benchtop quantum optics experiments to be scaled down into prototype photonic chips[6], allowing recent advances like the claim of quantum advantage from Xanadu on a programmablephotonic chip which was demonstrated with Gaussian Boson Sampling (GBS) [7]. However, PICs facean issue in that the range of tasks and operating wavelengths that will be demanded of photonic chips,mean that the properties of just one homogeneous material is unlikely to be sufficient, so research intoheterogeneous PICs and hybrid integrated quantum photonics platforms become necessary for furtheradvances in quantum information. More precisely, such platforms should be scalable and offer a highlevel of optical control.