Embedding Fault-Tolerant Error Correction in Molecular Nanomagnets: advantages, limitations, and applications

Quantum technologies represent one of the most ambitious frontiers of contemporary physics, aiming to harness the fundamental principles of quantum mechanics, such as superposition and entanglement, to realize new generations of computational, communication, and sensing devices. These technologies promise capabilities far beyond those of their classical counterparts, from the discovery of new materials to the development of sensors with unprecedented precision. Yet, their full potential is limited by a common obstacle, the intrinsic fragility of quantum states to environmental noise and decoherence. The central motivation of this thesis lies precisely in this challenge: understanding how to protect quantum information and preserve coherence long enough to make quantum technologies more reliable. The work combines theoretical analysis, numerical modeling, and realistic system simulation to identify architectures and strategies capable of embedding error correction directly within the physical system, rather than treating it as an external layer. The first part of the thesis focuses on the foundations and implementation of Fault-Tolerant Quantum Error Correction (QEC) in realistic noisy regimes. In this context, a Fault-Tolerant embedded QEC protocol was developed for molecular nanomagnets (MNMs), which constitute one of the most versatile and controllable classes of molecular spin systems. Their multilevel spin structure enables the encoding and manipulation of logical information directly within the physical hardware, allowing error protection without introducing additional qubits or complex control sequences. Numerical studies demonstrate that this embedded architecture can significantly enhance coherence times and bring error-correction thresholds close to values accessible with present molecular technologies. These results establish MNMs as a promising physical platform for future qudit-based architectures, where multiple quantum levels can be coherently exploited to achieve fault-tolerant operations. The second part extends this framework to the domain of Quantum Sensing (QS). By integrating QEC principles within a sensing protocol, it was possible to design a dephasing-tolerant magnetic-field sensor that maintains coherence for several orders of magnitude longer than unprotected systems. This improvement directly translates into enhanced measurement sensitivity, proving that quantum error correction can serve not only as a defensive tool against noise but also as an active resource for sensitivity enhancement. The results highlight how the logical encoding of information can be leveraged to amplify the physical response of the system, without introducing systematic bias into the measurement process. The third part addresses the experimental implementation of quantum algorithms on current noisy intermediate-scale quantum (NISQ) devices. A non-variational algorithmic pipeline to approximate the ground state of antiferromagnetic Heisenberg rings was developed and tested both on IBM quantum processors and through ideal simulations. This work provided a realistic evaluation of the capabilities and limits of present hardware, as well as a benchmark for the effectiveness of error-mitigation strategies. The study confirms that, although techniques such as Zero Noise Extrapolation or Pauli Twirling can partially suppress errors, achieving true quantum advantage on NISQ machines remains hindered by noise accumulation and limited coherence. Finally, the thesis explores the phenomenon of Chirality-Induced Spin Selectivity (CISS) within a many-body theoretical framework, linking spin polarization to electron transport through chiral molecular bridges. This work sheds light on the microscopic origins of spin selectivity and hints at how this effect could be exploited to design molecular-scale components that can perform quantum-state initialization at higher temperatures. The study demonstrates how concepts from condensed matter and quantum information can converge toward common goals. Taken together, these results contribute to consolidating the bridge between quantum information science and condensed matter physics. They demonstrate that fault-tolerant protection can be naturally embedded within realistic spin systems, that logical encoding can enhance measurement sensitivity, and that molecular architectures can serve as fertile ground for scalable and noise-resilient quantum devices.