Number system is a basic tool to describe computation. The traditional binary system has placed a pivotal position in the development of classic computers. However, it is a quite a riddle to find a proper numeral system for the new-fashioned quantum computation. The present paper analyses the dilemma of numeral system for quantum computation from the ancient Chinese trinity theory represented by TaiXuan. The essential difference of Quantum computation from classical computation is quanta entanglement, which reflects not only but also the indescribable True-false value in logic. The paper concludes with the dilemma that we caneither describe quantum computation by the classic number system at the cost of losing the essence of quanta entanglement or we can’t find a number system to describe the quantum Hehe nature altogether.
Number system is a basic tool to describe computation. The traditional binary system has placed a pivotal position in the development of classic computers. However, it is a quite a riddle to find a proper numeral system for the new-fashioned quantum computation. The present paper analyses the dilemma of numeral system for quantum computation from the ancient Chinese trinity theory represented by TaiXuan. The essential difference of Quantum computation from classical computation is quanta entanglement, which reflects not only but also the indescribable True-false value in logic. The paper concludes with the dilemma that we caneither describe quantum computation by the classic number system at the cost of losing the essence of quanta entanglement or we can’t find a number system to describe the quantum Hehe nature altogether.
The rapid development of computing hardware has been driven by an ever-emerging need for high throughput, scalable performance, and computation capabilities to be able to address increasingly complex problems. The paradigm of classical computing, centered on deterministic binary logic and the von Neumann architecture, has long favored modern information processing and still supports a wide range of applications. However, physical limits in scaling transistors, power dissipation, and slowing down Moore's Law have stimulated the consideration of alternative computing paradigms. Quantum computing is now an emerging means that exploits the basic principles of quantum mechanics-such as superposition, entanglement, and quantum interference-to enable new forms of computation. This review study discusses a comparison between the classical and quantum computing systems in operational paradigms, architecture structures, performance characteristics, and application domains. This work is supported by a systematic review of the established theories, currently realized hardware implementations, and representative algorithms. The analysis underlines that classical systems remain very reliable, scalable, and efficient in general-purpose and deterministic workloads, while quantum systems ensure essential advantages in specified problem classes, such as cryptography, quantum chemistry, combinatorial optimization, and selected machine learning tasks. The study concludes that classical and quantum computing are best viewed as complementary technologies. Future high-performance computing platforms will most likely be based on hybrid-classical–quantum architectures in which quantum processors serve as specialized accelerators to help classical systems solve new computational challenges.
Quantum computation is based on quantum physics and different from classical computation based on classical physics.It has non-classical characteristics such as quantum superposition principle, uncertainty principle, and no-cloning theorem and has been mainly studied by original methodology.However, it does not mean we cannot investigate quantum computation using traditional methods that have been studied in non-quantum area.We believe that quite a lot of methods are useful to investigate quantum computation and it is important to find such methods.When they are found, they will accelerate the research of quantum computation using the knowledge about them.Moreover, due to their classical nature, they will naturally help us to analyse quantum computation using classical computers.In order to support the idea, we show two classical methodologies, abstract interpretation and classical public-key cryptography, enhance analysis in two topics of quantum computation, entanglement in quantum programming languages and blind quantum computation protocols.The behaviour of entangled quantum system is counterintuitive.Therefore, it is important to know how entangled states are in quantum programs without executing them.In order to statistically analyse the problem, it was proposed to apply the abstract interpretation technique to the analysis.However, the proposed method does not store information about entangled states and ignores the fact that an operator on multiple qubits may undo entanglements, and hence the method only gives a rough approximation.We combine the method with the stabiliser formalism.We show abstract interpretation can be used to efficiently analyse the existence of entanglement in quantum programs with higher precision.Blind quantum computation protocols give users having no powerful quantum devices a method to delegate their quantum computation to remote quantum servers without leaking any crucial information about their computation.Some protocols enable users to verify whether the quantum servers honestly do the delegated computation, but no protocols give third parties ways to analyse the computation.We propose a new blind quantum computation protocol using a classical public-key encryption scheme.Our protocol is based on an existing protocol, but third parties, who have only classical computers and check the classical message between users and quantum servers, can analyse the computation and verify whether users obtain the correct outcomes or not.These results show classical methodology, which achieves a development outside the area of quantum computation, may be useful for investigation of quantum computation.
A well-known model in game theory, the Volunteer's Dilemma describes a group of n players who decide whether to volunteer for a collective benefit at a personal cost, or to abstain and risk forfeiting the benefit altogether. A quantum version of this dilemma, developed within the Eisert-Wilkens-Lewenstein framework, allows each player to manipulate one qubit of a shared entangled state, leading to symmetric Nash equilibria with higher expected payoffs than in the classical game. Existing analyses, however, assume maximal entanglement, which is experimentally demanding for hardware-constrained quantum systems. Within the same framework, we introduce a generalized Quantum Volunteer's Dilemma with a tunable entanglement parameter γ and study the extent to which equilibrium behavior depends on the level of entanglement. We derive explicit conditions relating γ, the number of players, and the players' strategies under which symmetric Nash equilibria exist, focusing on two canonical strategy profiles: one for 2≤n≤9, and one for even n. We find that maximal entanglement is not required to sustain symmetric equilibria. Instead, equilibrium behavior persists above a threshold value, which we compute analytically in both cases. We also demonstrate that the threshold value directly depends on system size.
Despite the significant technological advancements, the amount of data to be processed remains enormous, and certain problems remain unsolved or take millions of years to be solved. The advent of quantum computing, with its unique properties, represents a pivotal point in the technological world. Although quantum computers are still under development in the laboratories, research is progressing in parallel with the aim of creating a good basis for any contribution in order to be ready for the commercialization of the first computer. This article clarifies the essential basics required before entering the quantum realm. We present the basic properties of quantum computing based on four fondations and their differences from classical computing.
Quantum mechanics has proven its position as the primary theory for accurately describing microscopic domains. Numerous fields in physics utilize quantum mechanics to great effects, with one prominent application being quantum computing. Quantum computing extends the field of quantum mechanics to information theory, striving to perform computational tasks utilizing quantum phenomena with notably greater efficiency compared to classical alternatives. In this thesis, I will go through the basics required in the field of quantum computing. To understand quantum computing demands adapting a new type of matrix mechanical view. This involves considering Hilbert spaces, which are linear vector space having a well defined inner product. Hilbert spaces contain state vectors describing quantum states, as well as operators for altering and measuring these states. The dynamics of quantum systems are governed by three quantum postulates. These specify Hilbert spaces and state vectors as the fundamental components of quantum systems, Hermitian operators as providing the physical manifestation of these systems, and finally, the Schrödinger's equation to describe the time evolution of such systems. These notions are required in producing quantum computing. Quantum computing uses qubits as the computational basis, analogous to classical bits but with the added capability of quantum superposition. Qubits are represented as two-state vectors, and can be physically realized with any quantum-behaving binary-valued system, like the electron spins. Qubits can be combined into higher dimensional states with the use of tensor products, causing the system's Hilbert space to expand as 2^n with n being the number of qubits, allowing for exponential computational speedup. Computational logic can be constructed by acting on the qubits using unitary operators, known as quantum gates. The combinations of qubits and quantum gates can be visualized as quantum circuits, depicted using specialized circuit diagram notations. An essential part of quantum computing, and the phenomena enabling exponential computational speedup, is quantum entanglement. Entanglement arises in interacting qubits, intertwining them so that the individual states become correlated. Entanglement can be characterized by being unable to reduce a combined state into its pure constituents. The amount of entanglement in a system can be measured using von Neumann entropy, analogous to Shannon entropy in classical information theory. Entanglement serves various purposes in quantum computing and is a defining feature distinguishing it from the classical domain. In this thesis, the entanglement properties of a periodic four-qubit circuit with alternating quantum gates were simulated. The simulation was performed computationally, and measured entanglement entropy as a function of the amount of circuit periods. The results demonstrated different characteristics of entanglement depending on the parameters used for the quantum gates, with the entanglement either being periodic, non-occurring or chaotic in nature.