Application of entropy and signal energy for ultrasound-based classification of three-dimensional printed polyetherketoneketone components.

This paper describes a preliminary method for the classification of annealed and unannealed polyetherketoneketone (PEKK) components manufactured using a material extrusion three-dimensional (3D) printing process. PEKK is representative of a class of high-performance thermoplastics that are increasingly employed as feedstocks for use in 3D printing. PEKK components may be used continuously at elevated temperatures, are chemically resistant, and able to withstand large mechanical loads. These properties render PEKK suitable as a metal component replacement in aerospace applications, high-temperature industrial applications, and surgical implants. The structure of PEKK is semi-crystalline with the specific crystallinity correlating to the final properties during application, making determination of this property crucial. This study compares three different signal processing techniques intended to distinguish annealed (high crystallinity) from unannealed (low crystallinity) components using backscattered ultrasound. The first is energy-based and is unable to detect annealing. The second two are based on different entropies of the backscattered signal: a limiting form of Renyi's entropy and a limiting form of joint entropy. The joint entropy values for the annealed and unannealed specimens fall into two non-overlapping intervals and have a statistical separation of two standard deviations.

A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits.

Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit's generators.