On Quantum Computation In The Perspective Of Philosophy Of Science

As the combination of quantum mechanics and computer science, Quantum computation has important significance both in elucidating the nature of computation and analysising of basic questions of quantum mechanics. Although quantum mechanics and computer science has already attracted the attentions of philosophers of science for long time, but philosophical research on quantum computation is still few. A comprehensive philosophical analysis is made in this thesis, on those questions quantum computation involves, including the logic foundation of quantum computation, computability, computational complexity, and the interpretation of quantum mechanics, for revealing the nature of quantum computation.This paper consists of the introduction, four systematic chapters discusses and the conclusion.Chapter 1, an overview of the historical development and the representation of quantum computation. This chapter introduces the historical background and the physical basis of quantum computation; carries on the syntax and semantic analysis for the theory of quantum computation, explains that the specific performance of quantum speed-up is quantum parallel computation; simple discusses how the appearance of quantum computation affects the theory of logic, computability theory, computational complexity theory and the interpretations of quantum mechanics.Chapter 2, the logical implication of quantum computation. This chapter mainly discusses the logical basis of quantum computation. This chapter first introduces the theory of classical logic, and based on it, analysis the syntax structure of quantum logic, then examines in detail the logic rules represented by the quantum logic gates, and shows that logic based quantum computation is a new quantum computational logic, rather than quantum logic; based on the comparison of these two non-classical logics, points out that although they are both based on the logic of quantum mechanics, but in fact their logic rules of and semantic rules are different.Chapter 3, computability and computational complexity about Quantum Computation. This chapter first analyses the phenomenon that the meaning and the form of Church-Turing Thesis is constantly changing with transformations of computational contexts, and points out that during the transformation of contexts, the Church-Turing Thesis which is a thesis describing the abstract mathematical calculation concept originally, has converted to be a experiential thesis revealing the essence of the evolution of real nature of system. Then this chapter discusses the issue if quantum computation can realize hypercomputation i.e. can compute beyond Turing computability, here we point out that both the quantum circuit computation and the quantum adiabatic computation cannot be used as that theoretical model computation, and we consider that the negative answer illustrates that the Church-Turing Thesis includeing its physical version indeed found the boundary of human’s understanding. Finally this chapter analyses if the quantum computation can break through the classical computational complexity, and we pointed out that the huge integer factorization question quantum shor algorithm solved does belong to NP problem, but doesn’t belong to NP-complete problem. Only a quantum algorithm is found can solve the NP-complete problem, we can say, it breaks through the classical computational complexity, but so far this kind of quantum algorithm has yet not appears.Chapter 4, quantum computation and the interpretations of quantum mechanics. This chapter mainly discusses three novel interpretations of quantum mechanics which are closely related to quantum computation, and they are the Neo-Everett Interpretation, the Many Computations Interpretation and the Information Interpretation. This chapter firstly analyse the Neo-Everett Interpretation of quantum mechanics, by re-examining the relationship between quantum computation and classical computation, considers quantum computation as the basic model of computation, and the classic computation as its special case, in this sense we extends the concept of computation. Then I applies the computationlism epistemology to quantum mechanics, explains the measurement problem by using the Many Computations Interpretation, and points out that it can avoid the inconsistency between the spontaneous linear evolution of quantum world and the collapse caused by conscious observers, accordingly solves the "dualism" problem in quantum mechanics. Finally, by analysing the viewpoints of Zeilinger et al. that quantum mechanics can be rebuilt as a theory about information, I points out that quantum mechanics could be understood as a principle theory.As a conclusion, I points out that the quantum computation has important philosophical significances in affirming methodological position of new computation modes, understanding the concept of computation as "natural mechanism plus algorithms", generalizing the creeds of computationalism, and providing the better interpretations of quantum mechanics.