Resources in quantum computation for discrete and continuous-variable systems

Doctoral thesis, 2024

In our ever-connected world, information technology has woven itself into the fabric of our daily life. But as we peer into the horizon of the digital age, the landscape of computing is on the brink of a monumental shift.
Unprecedented advances in the ability to control and harness genuine quantum effects opened the possibility to use quantum phenomena in technology.
Quantum computing employs quantum effects to open doors to solutions previously deemed impossible.


At its core, quantum computing operates on two paradigms: discrete variables and continuous variables. In the discrete realm, information is encoded into qudits, which are just quantum mechanical $d$-level systems, the quantum analogy of $d$-level classical bits. Meanwhile, continuous-variable quantum computing explores the infinite-dimensional spaces of harmonic oscillators, showing great noise resilience due to the inherent redundancy.
Both promise to unlock unprecedented computational power, from cracking cryptographic codes to revolutionizing material science.

Quantum systems are notoriously delicate, prone to errors and disruptions from their noisy environments necessitating the development of fault-tolerant architectures and error correction codes. Physical real world implementations of such architectures have limitations on what operations can be performed in an error resilient way.
Here, the concept of resource theories becomes a guiding light in understanding and harnessing the fundamental building blocks of quantum computation.

In this thesis, we delve into the fascinating world of non-Gaussianity and magic, two fundamental resources that underpin the power of quantum computing.
We investigate the conversion of resourceful states in the realm of continuous variables and uncover the intricate connection between resources for discrete and continuous-variable quantum computing.