Universal resources for quantum computing

Unravelling the source of quantum computing power has been a major goal in the field of quantum information science. In recent years, the quantum resource theory (QRT) has been established to characterize various quantum resources, yet their roles in quantum computing tasks still require investigation. The so-called universal quantum computing model (UQCM), e.g., the circuit model, has been the main framework to guide the design of quantum algorithms, creation of real quantum computers etc. In this work, we combine the study of UQCM together with QRT. We find on one hand, using QRT can provide a resource-theoretic characterization of a UQCM, the relation among models and inspire new ones, and on the other hand, using UQCM offers a framework to apply resources, study relation among resources and classify them. We develop the theory of universal resources in the setting of UQCM, and find a rich spectrum of UQCMs and the corresponding universal resources. Depending on a hierarchical structure of resource theories, we find models can be classified into families. In this work, we study three natural families of UQCMs in details: the amplitude family, the quasi-probability family, and the Hamiltonian family. They include some well known models, like the measurement-based model and adiabatic model, and also inspire new models such as the contextual model we introduce. Each family contains at least a triplet of models, and such a succinct structure of families of UQCMs offers a unifying picture to investigate resources and design models. It also provides a rigorous framework to resolve puzzles, such as the role of entanglement vs. interference, and unravel resource-theoretic features of quantum algorithms.

A comparative study of universal quantum computing models: towards a physical unification

Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCM), which lie at the foundation of quantum computing and have tight connections with fundamental physics. Although being developed decades ago, a physically concise principle or picture to formalize and understand UQCM is still lacking. This is challenging given the diversity of still-emerging models, but important to understand the difference between classical and quantum computing. In this work, we carried out a primary attempt to unify UQCM by classifying a few of them as two categories, hence making a table of models. With such a table, some known models or schemes appear as hybridization or combination of models, and more importantly, it leads to new schemes that have not been explored yet. Our study of UQCM also leads to some insights into quantum algorithms. This work reveals the importance and feasibility of systematic study of computing models.