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，用于更容易地表征和演化难以分析描述和传播的量子态[1]。贝叶斯推理是一种经常用作估计器的技术，利用似然函数来更新先验分布，该先验分布表示关于什么被估计的某种信念，以便产生更新的（后验）概率分布[2]。这种技术已经被用于诸如金刚石NV中心中的电子自旋的开放系统动力学[3]、核自旋的表征[4]和误差校正[5]等任务。光子集成电路（PIC）在过去十年中经历了重大发展，1已经允许台式量子光学实验按比例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，这是用高斯玻色子采样（GBS）证明的[7]。然而，PIC面临一个问题，因为光子芯片所需的任务和工作波长范围意味着仅仅一种均匀材料的特性不太可能是足够的，因此研究异质PIC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。更确切地说，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.