<p>Conventional computing is based on the concept of bits which are classical entities that are either 0 or 1 and can be represented by stable magnets. The field of quantum computing relies on qubits which are a complex linear combination of 0 and 1. Recently, the concept of probabilistic computing with probabilistic (<em>p-</em>)bits was introduced where <em>p-</em>bits are robust classical entities that fluctuate between 0 and 1. <em>P-</em>bits can be naturally represented by low-barrier nanomagnets. Probabilistic computers (<em>p-</em>computers) based on <em>p-</em>bits are domain-based hardware accelerators for Monte Carlo algorithms that can efficiently address probabilistic tasks like sampling, optimization and machine learning. </p> <p>In this dissertation, starting from the intrinsic physics of nanomagnets, we show that a compact hardware implementation of a <em>p-</em>bit based on stochastic magnetic tunnel junctions (s-MTJs) can operate at high-speeds in the order of nanoseconds, a prediction that has recently received experimental support.</p> <p>We then move to the system level and illustrate by simulation and by experiment how multiple interconnected <em>p-</em>bits can be utilized to train a Boltzmann machine built with hardware <em>p-</em>bits. We observe that even non-ideal s-MTJs can be utilized for probabilistic computing when combined with hardware-aware learning.</p> <p>Finally, we show how to build a <em>p-</em>computer to accelerate a wide variety of problems ranging from optimization and sampling to quantum computing and machine learning. The common theme for all these applications is the underlying Monte Carlo and Markov chain Monte Carlo algorithms and their parallelism enabled by a unique <em>p-</em>computer architecture.</p>

<p dir="ltr">Antiferromagnetic spintronics promises next-generation information processing devices with ultra-fast speeds and ultra-low power consumption. Inspired by the recent demonstration of signatures of Tunnel Magnetoresistance (TMR) in non-colinear chiral antiferromagnets of the Mn₃X family, we study the thermal stability of such magnets in both low and high barrier limits. A stochastic Landau-Lifshitz-Gilbert (s-LLG) based numerical assessment of the dynamics reveals that strong exchange fields in Mn₃Sn could lead to thermally-driven rapid fluctuations of the order parameter, viz., octupole moment. However, distinct Random Telegraph Noise (RTN)-like signals distinguish the high barrier limit from the low barrier limit - suggesting different physical phenomena in the two regimes. To that end, the correlation time for thermal fluctuations has been explored analytically following an approach inspired by Langer's theory in the high barrier limit and dephasing mechanisms in the low barrier limit. It has been shown that the dynamics in chiral antiferromagnetic nanoparticles in both regimes are an order of magnitude faster than easy plane ferromagnetic particles. The thermal instability of chiral antiferromagnets could lead to picosecond-scale random number generation in probabilistic bits -- paving the path toward ultra-fast probabilistic computation. </p>

<p dir="ltr">The limitations of the traditional von Neumann computing architecture, particularly evident in the slowdown of Moore's law, have spurred the development of alternative domain-specific computing paradigms. This dissertation explores novel materials-physics based solutions for two promising alternatives: quantum computing and probabilistic computing, with a specific focus on leveraging magnetic spin textures and their unique properties. We demonstrate that magnetic spin textures, with their inherent topology and chirality, offer distinctive advantages in addressing key challenges in both computing paradigms. These textures' ability to couple with various degrees of freedom, such as electrical, thermal, mechanical, and optical, makes them particularly suitable for hybrid device implementations. Our work presents four contributions to the field.</p><p dir="ltr">First, we propose a novel approach of using skyrmions --- topologically protected rigid-object like spin textures --- to nucleate and braid Majorana modes in topological superconductor-magnetic multilayer heterostructures. We show analytically and numerically that skyrmion--vortex bound pairs can be braided in experimentally relevant timescales. Inspired by circuit quantum electrodynamics methods, we propose a novel readout scheme based on the dispersive coupling between vortex confinement states and Majorana bound states. This work paves the way for experimentally demonstrating the non-Abelian statistics of Majorana bound states, which might be a crucial step towards the development of fault-tolerant topological quantum computers.</p><p dir="ltr">Second, we study thermal relaxation mechanisms and timescales of spin-split chiral antiferromagnets. The class of spin-split antiferromagnets, including altermagnets, have recently emerged as excellent candidates for ultra-fast and low-energy spintronics applications. Due the lack of dipolar order, they are unaffected by stray fields. However, the spin-split bands still offer electrical control and readout of these antiferromagnets unlike the conventional antiferromagnets. While a lot of promising phenomena in these materials has already been experimentally demonstrated, thermal relaxation mechanisms of such magnets remain unexplored. Using reaction rate theories and statistical physics tools, we study the thermal dynamics of chiral antiferromagnets. We show that these materials thermally relax at ultra-fast picosecond-order timescales. Further, by building on the analogy between XY magnets and current biased Josephson junctions, we propose a novel approach to electrically tune the thermal barrier in chiral antiferromagnets. Although such chiral antiferromagnets may not be suitable for non-volatile memory type of applications, they emerge as promising candidates for the building blocks of probabilistic computers.</p><p dir="ltr">We then turn our attention to the strongly correlated quantum system of quantum spin liquids. We show that spin textures exchange coupled to a Kitaev spin liquid (KSL) can induce emergent gauge fields on the Majorana fermions in the spin liquid. These emergent gauge fields may trap zero energy modes if they are able to thread a net flux through the KSL. We derive analytical expressions for the gauge fields in the presence of spin textures and outline the conditions to obtain a net flux. Zero energy Majorana fermion modes trapped on such spin textures may eventually be used for fault tolerant quantum computing.</p><p dir="ltr">Finally, in the last project, we bring the quantum and probabilistic computing paradigms together by proposing a quantum two level system as a sensor for the building blocks of a probabilistic computer. we show that quantum spin defects such as Nitrogen vacancy centers (NV) can be used as novel probes for characterizing probabilistic bits. We show that various NV sensing protocols can be leveraged to create a complete picture of this nascent magnet based probabilistic bits including their energy barrier and attempt times.</p><p dir="ltr">Our findings suggest that magnetic spin textures, particularly their topological and chiral properties, could provide crucial solutions to current challenges in alternative computing platforms. This work bridges the gap between materials physics, device physics and the applications in alternative computing platforms.</p>