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在近几十年，量子信息物理极大地促进了量子理论的现代发展，并在通信、计算、计量等方面展现了巨大的应用前景。其理论基础之一是通用量子计算模型理论，用于描述量子信息的演化特别是其大规模的应用，也是算法和纠错码等设计的基础。本文着重从物理的角度介绍近期在通用量子计算模型上的研究，结合量子资源理论对量子信息的刻画，发展了能统一描述不同计算模型的理论框架。研究发现，结合通用性和容错性的要求，可以构建模型的分类表，它包含上百种不同的通用量子计算方案，其中多数尚未得到深入研究。本文重点讨论了在通用性方面即针对信息不同表示形式的四个家族的模型，其中一类模型是近期提出的量子冯诺依曼架构，它可以绕开在量子程序存储和量子控制单元上的不可能定理，从而构建可量子编程的计算机体系.本文也探讨了量子芯片与算法设计、量子资源与优势等问题。本研究展现了通用量子计算模型研究的丰富性和复杂性，也为量子计算机的建造和量子信息的应用提供了更多的可能。Quantum computing has been proven to be powerful, however, there are still great challenges for building real quantum computers due to the requirements of both fault-tolerance and universality. People still lack a systematic way to design fast quantum algorithms and identify the key quantum resources. In this work, we develop a resource-theoretic approach to characterize universal quantum computing models and the universal resources for quantum computing.
Our theory combines the framework of universal quantum computing model (UQCM) and the quantum resource theory (QRT). The former has played major roles in quantum computing, while the later was developed mainly for quantum information theory. Putting them together proves to be 'win-win': 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.
In quantum theory, we mainly study states, evolution, observable, and probability from measurements, and this motivates the introduction of different families of UQCMs. A family also includes generations depending on a hierarchical structure of resource theories. We introduce a table of UQCMs by first classifying two categories of models: one referring to the format of information, and one referring to the logical evolution of information requiring quantum error-correction codes. Each category contains a few families of models, leading to more than one hundred of them in total. Such a rich spectrum of models include some well-known ones that people use, such as the circuit model, the adiabatic model, but many of them are relatively new and worthy of more study in the future. Among them are the models of quantum von Neumann architectures established recently. This type of architecture or model circumvents the no-go theorems on both the quantum program storage and quantum control unit, enabling the construction of more complete quantum computer systems and high-level programming.
Correspondingly, each model is captured by a unique quantum resource. For instance, in the state family, the universal resource for the circuit model is coherence, for the local quantum Turing machine is bipartite entanglement, and for the cluster-state based, also known as measurement-based model is a specific type of entanglement relevant to symmetry-protected topological order. As program-storage is a central feature of the quantum von Neumann architecture, we find the quantum resources for it are quantum memories, which are dynamical resources closely related to entanglement. In other words, our classification of UQCMs also serves as a computational classification of quantum resources. This can be used to resolve the dispute over the computing power of resources, such as interference, entanglement, or contextuality. In all, we believe our theory lays down a solid framework to study computing models, resources, and design algorithms. -
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