Learning the tensor network model of a quantum state using a few single-qubit measurements

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea - a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct (PAC) learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a dataset which scales only linearly with the number of qubits. Here we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.Comment: 10 pages, 11 figure

Epidemiology of Hereditary Diseases in the Karachay-Cherkess Republic

Prevalence and allelic heterogeneity of hereditary diseases (HDs) could vary significantly in different human populations. Current knowledge of HDs distribution in populations is generally limited to either European data or analyses of isolated populations which were performed several decades ago. Thus, an acknowledgement of the HDs prevalence in different modern open populations is important. The study presents the results of a genetic epidemiological study of hereditary diseases (HDs) in the population of the Karachay-Cherkess Republic (KChR). Clinical screening of a population of 410,367 people for the identification of HDs was conducted. The population surveyed is represented by five major ethnic groups—Karachays, Russians, Circassians, Abazins, Nogais. The study of the populations was carried out in accordance with the proprietary protocol of genetic epidemiological examination designed to identify >3500 HDs easily diagnosed during clinical examination by qualified specialists specializing in the HDs. The protocol consists of the population genetic and medical genetic sections and is intended for comprehensive population analysis based on the data on different genetic systems, including the genes of HDs, DNA polymorphisms, demographic data collected during hospital-based survey. 8950 families (with 10,125 patients) with presumably the HDs were initially identified as a result of the survey and data collection through various sources of registration (from 1156 medical workers from 163 medical institutions). A diagnosis of hereditary pathology was established in 1849 patients (from 1295 families). Two hundred and thirty nosological forms were revealed (in 1857 patients from 1295 families). The total prevalence of HDs was 1:221. Differences between populations and ethnic groups were identified: 1:350 in Russians, 1:195 in Karachays, 1:199 in Circassians, 1:218 in Abazins, 1:135 in Nogais. Frequent diseases were determined, the presence of marked genetic heterogeneity was identified during the confirmatory DNA diagnosis. To explain the reasons for the differentiation of populations by load of HD, a correlation analysis was carried out between the FST (random inbreeding) in populations and HDs load values. This analysis showed genetic drift is probably one of the leading factors determining the differentiation of KChR populations by HDs load. For the first time, the size of the load and spectrum of HDs in the populations of the KChR are determined. We have demonstrated genetic drift to be one of the main factors of the population dynamics in studied population. A significant genetic heterogeneity of HDs, both allelic and locus, was revealed in KChR