The Bravyi-Kitaev transformation for quantum computation of electronic structure

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu. Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure

Long non-coding RNA SNHG8 drives stress granule formation in tauopathies

Tauopathies are a heterogenous group of neurodegenerative disorders characterized by tau aggregation in the brain. In a subset of tauopathies, rare mutations in the MAPT gene, which encodes the tau protein, are sufficient to cause disease; however, the events downstream of MAPT mutations are poorly understood. Here, we investigate the role of long non-coding RNAs (lncRNAs), transcripts \u3e200 nucleotides with low/no coding potential that regulate transcription and translation, and their role in tauopathy. Using stem cell derived neurons from patients carrying a MAPT p.P301L, IVS10 + 16, or p.R406W mutation and CRISPR-corrected isogenic controls, we identified transcriptomic changes that occur as a function of the MAPT mutant allele. We identified 15 lncRNAs that were commonly differentially expressed across the three MAPT mutations. The commonly differentially expressed lncRNAs interact with RNA-binding proteins that regulate stress granule formation. Among these lncRNAs, SNHG8 was significantly reduced in a mouse model of tauopathy and in FTLD-tau, progressive supranuclear palsy, and Alzheimer\u27s disease brains. We show that SNHG8 interacts with tau and stress granule-associated RNA-binding protein TIA1. Overexpression of mutant tau in vitro is sufficient to reduce SNHG8 expression and induce stress granule formation. Rescuing SNHG8 expression leads to reduced stress granule formation and reduced TIA1 levels in immortalized cells and in MAPT mutant neurons, suggesting that dysregulation of this non-coding RNA is a causal factor driving stress granule formation via TIA1 in tauopathies

A Comprehensive Resource for Induced Pluripotent Stem Cells from Patients with Primary Tauopathies.

Primary tauopathies are characterized neuropathologically by inclusions containing abnormal forms of the microtubule-associated protein tau (MAPT) and clinically by diverse neuropsychiatric, cognitive, and motor impairments. Autosomal dominant mutations in the MAPT gene cause heterogeneous forms of frontotemporal lobar degeneration with tauopathy (FTLD-Tau). Common and rare variants in the MAPT gene increase the risk for sporadic FTLD-Tau, including progressive supranuclear palsy (PSP) and corticobasal degeneration (CBD). We generated a collection of fibroblasts from 140 MAPT mutation/risk variant carriers, PSP, CBD, and cognitively normal controls; 31 induced pluripotent stem cell (iPSC) lines from MAPT mutation carriers, non-carrier family members, and autopsy-confirmed PSP patients; 33 genome engineered iPSCs that were corrected or mutagenized; and forebrain neural progenitor cells (NPCs). Here, we present a resource of fibroblasts, iPSCs, and NPCs with comprehensive clinical histories that can be accessed by the scientific community for disease modeling and development of novel therapeutics for tauopathies

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.Comment: See journal reference for teh final published versio

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

Convection, Radiation, and Climate: Fundamental Mechanisms and Impacts of a Changing Atmosphere

A hierarchy of models is used to connect fundamental mechanisms to impacts in a changing atmosphere. On the subject of forcings, an intermediate-complexity model for the radiative forcing of carbon dioxide is developed. This model is used to provide simple explanations for well-known properties of carbon dioxide (CO2) forcing such as its magnitude, dependence on atmospheric conditions, and logarithmic scaling. In the realm of impacts, climate models are used to investigate the impact of global warming on the kind of severe thunderstorms that produce hail and damaging winds. The results suggest that severe thunderstorms will become more damaging in the future, and that increases in Convective Available Potential Energy (CAPE) are the culprit. This motivates the subsequent use of cloud-resolving simulations to develop of a theory of CAPE and its dependence on temperature, which highlights the importance of the atmospheric saturation deficit. Another result of that theory for CAPE is an explanation for why cloud buoyancy and updraft strength are largest in the upper troposphere, a property that has traditionally been attributed to the release of the latent heat of fusion above the melting line. It is shown that this ice-based explanation is a fallacy: cloud buoyancy and updraft strength are the same in a world with or without ice. Finally, on the topic of feedbacks, the relationship between high clouds and the tropopause is investigated in cloud-resolving simulations. The results support the existence of a Fixed Tropopause Temperature (FiTT) rather than a Fixed Anvil Temperature (FAT), which implies a decoupling of anvil clouds from the tropopause. This decoupling motivates further investigation into the formation mechanisms of anvil clouds; it is found that anvil clouds do not result from enhanced detrainment below the tropopause, as is the traditional view, but from the slow evaporation of cloudy air in the cold upper troposphere