Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCMs), 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.
Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCMs), 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.
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. There is still no systematic method 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.
Abstract 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 these 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 detail: 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 that 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 versus interference, and unravel resource-theoretic features of quantum algorithms.
"This breakthrough volume touts having dissolved the remaining barriers to implementing Bulk Universal Quantum Computing (UQC), and as such most likely describes the most advanced QC development platform. Numerous books, 100s of patents, 1,000s of papers and a Googolplex of considerations fill the pantheon of QC R&D. Of late QC mathemagicians claim QCs already exist; but by what chimeric definition. Does flipping a few qubits in a logic gate without an algorithm qualify as quantum computing? In physics, theory bears little weight without rigorous experimental confirmation, less if new, radical or a paradigm shift. This volume develops quantum computing based on '3rd regime' physics of Unified Field Mechanics (UFM). What distinguishes this work from myriad other avenues to UQC under study? Virtually all R&D paths struggle with technology and decoherence. If highly favored room-sized cryogenically cooled QCs ever become successful, they would be reminiscent of the city block-sized Eniac computer of 1946. The QC prototype proposed herein is room temperature and tabletop. It is dramatically different in that it is not confined to the limitations of quantum mechanics; since it is based on principles of UFM the Uncertainty Principle and Decoherence no longer apply. Thus this QC model could be implemented on any other quantum platform!"...
Quantum computing represents a transformative approach to computation that exploits the principles of quantum mechanics to process information in fundamentally different ways from classical computers. Over the past few decades, the field has evolved from a primarily theoretical discipline into an active area of research spanning computer science, mathematics, physics, information theory, and engineering. As quantum technologies continue to develop, understanding the fundamental computational principles underlying quantum algorithms has become increasingly important. Foundations of Quantum Computing: The Query Model Perspective presents a systematic introduction to quantum computing with particular emphasis on the query model, a powerful framework for studying the computational complexity of quantum algorithms. The query model provides a clean and mathematically tractable setting in which the number of queries made to an unknown function or oracle can be used as the primary measure of computational cost. This perspective offers valuable insights into the capabilities and limitations of quantum computation and provides a natural foundation for understanding quantum speedups. The book introduces the fundamental concepts required to study quantum computation, including quantum states, quantum gates, quantum circuits, measurement, superposition, entanglement, and quantum algorithms. These concepts are developed alongside the query-complexity framework, enabling readers to understand how quantum algorithms exploit interference and other quantum phenomena to reduce the number of queries required to solve computational problems. Particular attention is given to important quantum query algorithms and complexity results. Classical and quantum query complexities are discussed comparatively to illustrate the sources and significance of quantum advantages. Well-known examples such as the Deutsch–Jozsa algorithm, Grover's search algorithm, and related oracle-based problems provide concrete illustrations of how quantum procedures can outperform their classical counterparts. The discussion also introduces lower-bound techniques and fundamental principles that help establish the limitations of quantum query algorithms. The query model is not only useful for understanding individual algorithms but also serves as an important bridge between quantum algorithms and computational complexity theory. By focusing on query complexity, many problems can be examined independently of the details of a particular physical implementation. This abstraction makes the framework especially useful for developing rigorous proofs, comparing computational resources, and identifying the fundamental sources of quantum advantage. This book is intended for students, researchers, educators, and professionals interested in quantum computing and theoretical computer science. It can serve as an introductory reference for readers with a background in discrete mathematics, linear algebra, algorithms, or theoretical computer science, while also providing a foundation for readers who wish to pursue more advanced studies in quantum complexity theory and quantum algorithms. The chapters have been organized to progress from foundational concepts toward more advanced aspects of the quantum query model. Mathematical formulations are accompanied by explanations and examples to help readers connect abstract theoretical ideas with computational intuition. The broader objective is to provide readers with the tools necessary not only to understand existing quantum algorithms but also to reason about new problems from a query-complexity perspective. As quantum computing continues to mature, the ability to distinguish genuine computational advantages from implementation-specific effects will become increasingly significant. The query model provides one of the clearest theoretical environments for making this distinction. By studying quantum computation through this lens, readers can develop a deeper appreciation of both the power and the limitations of quantum algorithms It is hoped that Foundations of Quantum Computing: The Query Model Perspective will serve as a useful resource for learning, teaching, and research, and will encourage further exploration into the rapidly evolving landscape of quantum computation and quantum complexity theory.
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics and nanotechnology. Understanding and simulating quantum operations on a classical computer has different approaches and is modeled in different ways. However, the most repute ways are Quantum Turing Machine, Network Model or circuit model of connected gates and Quantum Programming Language. Many simulators do exist that varies in many features such as implementation languages, target platforms, paradigms, visuality, and applied quantum algorithms. There was a developmental trade-off between the simplicity and the functionality of the simulator. The goals and research activities are outlined as follows: First, surveying the quantum computing world, its characteristics, issues, problems, and challenges. Second, surveying the existing quantum simulators, illustrating representative simulators of major approaches, their features, and functionalities. Third, introducing a framework to provide the power of quantum computing , while insisting the simplicity and high usability. Finally, providing a case study for a new quantum algorithm based on the introduced framework.