dr luca innocenti

Shadow estimation via quantum extreme learning machines

Shadow tomography is a general methodology used to estimate properties of input states while avoiding the resource scaling with the state dimension that is intrinsic to traditional tomographic approaches. In contrast, quantum extreme learning machines and quantum reservoir computing are quantum machine learning methods aimed at learning from a training dataset how to optimally post-process measurement data to retrieve target functions of input data. While these two methods appear quite distinct—one relying on machine learning training methods and the other firmly rooted in standard quantum estimation theory—we will highlight and discuss the deep connections between them. Specifically, we will examine how the framework of shadow tomography for general POVMs (Positive Operator-Valued Measures) allows for a precise understanding of the post-processing learned using quantum extreme learning machines through the concept of dual measurement. Additionally, we will discuss a formal approach to quantum extreme learning machines that demonstrates how both methodologies can be viewed as quantum estimation techniques differing only in their assumptions about prior knowledge of the measurement apparatus.