Estimating expectation values using approximate quantum states

We introduce an approximate description of an N-qubit state, which contains sufficient information to estimate the expectation value of any observable to a precision that is upper bounded by the ratio of a suitably-defined seminorm of the observable to the square root of the number of the system's identical preparations M, with no explicit dependence on N. We describe an operational procedure for constructing the approximate description of the state that requires, besides the quantum state preparation, only single-qubit rotations followed by single-qubit measurements. We show that following this procedure, the cardinality of the resulting description of the state grows as 3MN. We test the proposed method on Rigetti's quantum processor unit with 12, 16 and 25 qubits for random states and random observables, and find an excellent agreement with the theory, despite experimental errors.

КОНЦЕПТ-КАРТА ЯК ДІЄВИЙ ЗАСІБ НАВЧАННЯ ІНОЗЕМНОЇ МОВИ

The article reveals the concept of conceptual mapping in the process of learning a foreign language. It is stated that a concept map is a diagram that shows the relationships between notions. Such maps are graphical tools for organizing and presenting knowledge. It is emphasized that the most useful form of a concept map for teaching and learning is one that is placed in a hierarchical organization, where more general and comprehensive notions are at the top of the map and more specific at the bottom. The difference between concert cards and mind maps is given. It is emphasized that despite a similarity of mind maps and concept maps, these two methods differ in many respects, in particular, concept maps are characterized by clear links between the described ideas and are more structured than mind maps, as a formally approximate description, which places ideas in some sequence and organizes them hierarchically by levels of importance.

Approximate and Limited Description of Natural Phenomena

This chapter discusses what it means to “understand” a phenomenon in Science. It anticipates that the only knowledge of phenomena accessible to scientists is the approximate description of material reality, limited to a finite set of phenomena that share some characteristics.

Development of fiber laser optic system for laser polishing of parts

The possibility of an approximate description of a multimode beam of a fiber laser in the Zemax modeling system for the development of an optic system of a laser head is shown. There are developed and manufactured optic units of a laser head taking into account characteristic peculiarities of radiation of high-power fiber lasers. The possibilities are shown the developed optic system in the technology of laser polishing by the remelting of a sample surface made of stainless steel of type 1540-00.