Bayesian Inference for Heterogeneous Integrated Photonic systems

机器学习（ML）技术已经在量子科学中找到了应用，可以更容易地表征和演化难以描述和解析传播的量子态。贝叶斯推理就是这样一种技术，它经常被用作估计器，利用似然函数来更新先验分布，该分布表示关于被估计内容的某些信念，从而产生更新的（后验）概率分布[2]。该技术已被用于钻石NV中心电子自旋[3]的开放系统动力学、核自旋[4]的表征和误差校正[5]等任务。光子集成电路（PICs）在过去十年中经历了重大发展，这使得台式量子光学实验可以缩小到原型光子芯片[6]，允许最近的进展，如Xanadu在可编程光子芯片上的量子优势，该芯片用高斯玻色子采样（GBS）[7]进行了演示。然而，PICs面临的一个问题是，光子芯片所要求的任务范围和工作波长，意味着仅仅一种均质材料的特性不太可能是足够的，因此研究异质PICs和混合集成量子光子学平台对于量子信息的进一步发展是必要的。更准确地说，这样的平台应该是可扩展的，并提供高水平的光学控制。

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.