Simulation of quantum algorithms for classification of their complexity (original) (raw)

2015, Simulation of quantum algorithms for classification of their complexity

This article examines the quantum computational complexity in three fundamental aspects: quantum computations feasible in polynomial time, effective verification of the quantum proofs, as well as quantum interactive proof systems. On the basis of these concepts are defined the classes of quantum complexity, such as BQP, QMA and QIP, which contain computational issues of varying difficulty. The relationships between these classes and the classical complexity classes are presented. Since these concepts and the complexity classes are usually defined within the model of the quantum circuit, this article includes a section, which focuses on the basic properties of the quantum circuits, which are important when determining the quantum complexity. Two different, but closely related areas of study, are not discussed in this article: complexity of the quantum requests and the quantum communication complexity. These discussions are intended only to highlight the aspects of these topics, which are non-standard, require clarification, or have a relative importance for the quantum computational complexity.