Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Flexible Computing Systems For AI Acceleration At The Extreme Edge Of The IoT

Embedding intelligence in extreme edge devices allows distilling raw data acquired from sensors into actionable information, directly on IoT end-nodes. This computing paradigm, in which end-nodes no longer depend entirely on the Cloud, offers undeniable benefits, driving a large research area (TinyML) to deploy leading Machine Learning (ML) algorithms on micro-controller class of devices. To fit the limited memory storage capability of these tiny platforms, full-precision Deep Neural Networks (DNNs) are compressed by representing their data down to byte and sub-byte formats, in the integer domain. However, the current generation of micro-controller systems can barely cope with the computing requirements of QNNs. This thesis tackles the challenge from many perspectives, presenting solutions both at software and hardware levels, exploiting parallelism, heterogeneity and software programmability to guarantee high flexibility and high energy-performance proportionality. The first contribution, PULP-NN, is an optimized software computing library for QNN inference on parallel ultra-low-power (PULP) clusters of RISC-V processors, showing one order of magnitude improvements in performance and energy efficiency, compared to current State-of-the-Art (SoA) STM32 micro-controller systems (MCUs) based on ARM Cortex-M cores. The second contribution is XpulpNN, a set of RISC-V domain specific instruction set architecture (ISA) extensions to deal with sub-byte integer arithmetic computation. The solution, including the ISA extensions and the micro-architecture to support them, achieves energy efficiency comparable with dedicated DNN accelerators and surpasses the efficiency of SoA ARM Cortex-M based MCUs, such as the low-end STM32M4 and the high-end STM32H7 devices, by up to three orders of magnitude. To overcome the Von Neumann bottleneck while guaranteeing the highest flexibility, the final contribution integrates an Analog In-Memory Computing accelerator into the PULP cluster, creating a fully programmable heterogeneous fabric that demonstrates end-to-end inference capabilities of SoA MobileNetV2 models, showing two orders of magnitude performance improvements over current SoA analog/digital solutions.

PCM-based in-memory computing: architectures, circuits and applications

Analog In-memory Computing (AIMC) has been proposed in the context of Beyond Von Neumann architectures as a valid strategy to reduce internal data transfers energy consumption and latency, and to improve compute efficiency. The aim of AIMC is to perform computations within the memory unit, typically leveraging the physical features of memory devices. Among resistive Non-volatile Memories (NVMs), Phase-change Memory (PCM) has become a promising technology due to its intrinsic capability to store multilevel data. Hence, PCM technology is currently investigated to enhance the possibilities and the applications of AIMC. This thesis aims at exploring the potential of new PCM-based architectures as in-memory computational accelerators. In a first step, a preliminar experimental characterization of PCM devices has been carried out in an AIMC perspective. PCM cells non-idealities, such as time-drift, noise, and non-linearity have been studied to develop a dedicated multilevel programming algorithm. Measurement-based simulations have been then employed to evaluate the feasibility of PCM-based operations in the fields of Deep Neural Networks (DNNs) and Structural Health Monitoring (SHM). Moreover, a first testchip has been designed and tested to evaluate the hardware implementation of Multiply-and-Accumulate (MAC) operations employing PCM cells. This prototype experimentally demonstrates the possibility to reach a 95% MAC accuracy with a circuit-level compensation of cells time drift and non-linearity. Finally, empirical circuit behavior models have been included in simulations to assess the use of this technology in specific DNN applications, and to enhance the potentiality of this innovative computation approach.