Investigating Topological Order using Recurrent Neural Networks

Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. Here, we employ 2D RNNs to investigate two prototypical quantum many-body Hamiltonians exhibiting topological order. Specifically, we demonstrate that RNN wave functions can effectively capture the topological order of the toric code and a Bose-Hubbard spin liquid on the kagome lattice by estimating their topological entanglement entropies. We also find that RNNs favor coherent superpositions of minimally-entangled states over minimally-entangled states themselves. Overall, our findings demonstrate that RNN wave functions constitute a powerful tool to study phases of matter beyond Landau's symmetry-breaking paradigm.Comment: 14 pages, 7 figures, 1 table. A version with new correction

Genomic and phenotypic analysis of Vavilov's historic landraces reveals the impact of environment and genomic islands of agronomic traits.

The Vavilov Institute of Plant Genetic Resources (VIR), in St. Petersburg, Russia, houses a unique genebank, with historical collections of landraces. When they were collected, the geographical distribution and genetic diversity of most crops closely reflected their historical patterns of cultivation established over the preceding millennia. We employed a combination of genomics, computational biology and phenotyping to characterize VIR's 147 chickpea accessions from Turkey and Ethiopia, representing chickpea's center of origin and a major location of secondary diversity. Genotyping by sequencing identified 14,059 segregating polymorphisms and genome-wide association studies revealed 28 GWAS hits in potential candidate genes likely to affect traits of agricultural importance. The proportion of polymorphisms shared among accessions is a strong predictor of phenotypic resemblance, and of environmental similarity between historical sampling sites. We found that 20 out of 28 polymorphisms, associated with multiple traits, including days to maturity, plant phenology, and yield-related traits such as pod number, localized to chromosome 4. We hypothesize that selection and introgression via inadvertent hybridization between more and less advanced morphotypes might have resulted in agricultural improvement genes being aggregated to genomic 'agro islands', and in genotype-to-phenotype relationships resembling widespread pleiotropy

Predicting Many Properties of a Quantum System from Very Few Measurements

Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order log(M) measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods