Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions

It is an open question how well tensor network states in the form of an infinite projected entangled pair states (iPEPS) tensor network can approximate gapless quantum states of matter. Here we address this issue for two different physical scenarios: i) a conformally invariant $(2+1)d$ quantum critical point in the incarnation of the transverse field Ising model on the square lattice and ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the $S=1/2$ antiferromagnetic Heisenberg and XY models on the square lattice. We find that the energetically best wave functions display {\em finite} correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite-$D$ iPEPS states. The framework is important i) to understand the mild limitations of the finite-$D$ iPEPS manifold in representing Lorentz-invariant, gapless many body quantum states and ii) to put forward a practical scheme in which the finite correlation length $\xi(D)$ combined with field theory inspired formulae can be used to extrapolate the data to infinite correlation length, i.e. to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics.Comment: 16 pages, 11 figure

Electronic Payment Systems Observatory (ePSO). Newsletter Issues 9-15

Abstract not availableJRC.J-Institute for Prospective Technological Studies (Seville

Creación de mapas batimétricos usando vehículos submarinos autónomos en el río Magdalena

The goal is to develop a guidance and navigation algorithm for an AUV to perform high resolution scanning of the constantly changing river bed of the Magdalena River, the main river of Colombia, from the river mouth to a distance of 10 Km upriver, which is considered to be the riskiest section to navigate. Using geometric control we design the required thrust for an under-actuated autonomous underwater vehicle to realize the desired mission.El objetivo es desarrollar un algoritmo de orientación y navegación para un AUV (Autonomous Underwater Vehicle) para realizar el escaneado de alta resolución del cambiante lecho del río Magdalena, principal río de Colombia, desde su desembocadura hasta una distancia de 10 Km río arriba, que se considera la sección de mayor riesgo para navegar. Usando control geométrico se diseñó el empuje necesario para unvehículo submarino autónomo subactuado para realizar la misión deseada

HE-MAN -- Homomorphically Encrypted MAchine learning with oNnx models

Machine learning (ML) algorithms are increasingly important for the success of products and services, especially considering the growing amount and availability of data. This also holds for areas handling sensitive data, e.g. applications processing medical data or facial images. However, people are reluctant to pass their personal sensitive data to a ML service provider. At the same time, service providers have a strong interest in protecting their intellectual property and therefore refrain from publicly sharing their ML model. Fully homomorphic encryption (FHE) is a promising technique to enable individuals using ML services without giving up privacy and protecting the ML model of service providers at the same time. Despite steady improvements, FHE is still hardly integrated in today's ML applications. We introduce HE-MAN, an open-source two-party machine learning toolset for privacy preserving inference with ONNX models and homomorphically encrypted data. Both the model and the input data do not have to be disclosed. HE-MAN abstracts cryptographic details away from the users, thus expertise in FHE is not required for either party. HE-MAN 's security relies on its underlying FHE schemes. For now, we integrate two different homomorphic encryption schemes, namely Concrete and TenSEAL. Compared to prior work, HE-MAN supports a broad range of ML models in ONNX format out of the box without sacrificing accuracy. We evaluate the performance of our implementation on different network architectures classifying handwritten digits and performing face recognition and report accuracy and latency of the homomorphically encrypted inference. Cryptographic parameters are automatically derived by the tools. We show that the accuracy of HE-MAN is on par with models using plaintext input while inference latency is several orders of magnitude higher compared to the plaintext case