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.

翻译：揭示量子计算能力的来源一直是量子信息科学领域的主要目标。近年来，量子资源理论（QRT）已被建立用于刻画各种量子资源，但这些资源在量子计算任务中的作用仍需探究。所谓的通用量子计算模型（UQCM），例如电路模型，一直是指导量子算法设计、构建实际量子计算机等任务的主要框架。在本工作中，我们将QRT的研究与UQCM相结合。我们发现，一方面，利用QRT可以对UQCM进行资源理论刻画，揭示模型之间的关系并激发新模型；另一方面，利用UQCM为资源的应用、资源间关系的探究及资源分类提供了框架。我们发展了UQCM框架下的通用资源理论，并发现了丰富的UQCM谱系及其对应的通用资源。基于资源理论的层级结构，我们发现模型可按族分类。本工作详细研究了三个自然族的UQCM：振幅族、准概率族和哈密顿量族。这些族中包含一些知名模型（如基于测量的模型和绝热模型），也启发了新模型（如我们提出的语境模型）。每个族至少包含一个三元组模型，这种简洁的UQCM族结构为资源研究和模型设计提供了统一视角，也为解决诸如纠缠与干涉的作用等难题提供了严格框架，并揭示了量子算法的资源理论特征。