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）的建立旨在刻画各类量子资源，但这些资源在量子计算任务中的作用仍需深入研究。所谓通用量子计算模型（UQCM），例如电路模型，一直是指导量子算法设计、构建真实量子计算机等工作的主要框架。本研究将UQCM研究与QRT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，揭示模型间的关系并启发新模型；另一方面，利用UQCM为资源应用、关系研究和分类提供了框架。我们在UQCM框架下发展了通用资源理论，发现了丰富的UQCM谱系及其对应的通用资源。基于资源理论的层次结构，我们发现模型可归为不同家族。本研究详细探讨了三类自然UQCM家族：振幅家族、拟概率家族和哈密顿量家族。这些家族包含一些著名模型（如基于测量的模型和绝热模型），同时也启发新模型（如本文提出的上下文模型）。每个家族至少包含三重模型，这种简洁的UQCM家族结构为研究资源和设计模型提供了统一视角，也为解决纠缠与干涉作用等难题、揭示量子算法的资源理论特征提供了严格框架。