Efficient quantum measurement of Pauli operators in the presence of finite sampling error

Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed computational basis. One common solution splits the operator into a weighted sum of Pauli operators and measures each separately, at the cost of many measurements. An improved version collects mutually commuting Pauli operators together before measuring all operators within a collection simultaneously. The effectiveness of doing this depends on two factors. Firstly, we must understand the improvement offered by a given arrangement of Paulis in collections. In our work, we propose two natural metrics for quantifying this, operating under the assumption that measurements are distributed optimally among collections so as to minimise the overall finite sampling error. Motivated by the mathematical form of these metrics, we introduce SORTED INSERTION, a collecting strategy that exploits the weighting of each Pauli operator in the overall sum. Secondly, to measure all Pauli operators within a collection simultaneously, a circuit is required to rotate them to the computational basis. In our work, we present two efficient circuit constructions that suitably rotate any collection of $k$ independent commuting $n$-qubit Pauli operators using at most $kn-k(k+1)/2$ and $O(kn/\log k)$ two-qubit gates respectively. Our methods are numerically illustrated in the context of the Variational Quantum Eigensolver, where the operators in question are molecular Hamiltonians. As measured by our metrics, SORTED INSERTION outperforms four conventional greedy colouring algorithms that seek the minimum number of collections.Comment: 19 pages, journal versio

The African surgical outcomes-2 (Asos-2) pilot trial, a mixed-methods implementation study

Funding Information: The ASOS-2 Pilot Trial was supported by a grant (OPP#1161108) from the Bill & Melinda Gates Foundation.Peer reviewe

Disturbed oscillatory brain dynamics in subcortical ischemic vascular dementia

<p>Abstract</p> <p>Background</p> <p>White matter hyperintensities (WMH) can lead to dementia but the underlying physiological mechanisms are unclear. We compared relative oscillatory power from electroencephalographic studies (EEGs) of 17 patients with subcortical ischemic vascular dementia, based on extensive white matter hyperintensities (SIVD-WMH) with 17 controls to investigate physiological changes underlying this diagnosis.</p> <p>Results</p> <p>Differences between the groups were large, with a decrease of relative power of fast activity in patients (alpha power 0.25 ± 0.12 versus 0.38 ± 0.13, p = 0.01; beta power 0.08 ± 0.04 versus 0.19 ± 0.07; p<0.001) and an increase in relative powers of slow activity in patients (theta power 0.32 ± 0.11 versus 0.14 ± 0.09; p<0.001 and delta power 0.31 ± 0.14 versus 0.23 ± 0.09; p<0.05). Lower relative beta power was related to worse cognitive performance in a linear regression analysis (standardized beta = 0.67, p<0.01).</p> <p>Conclusions</p> <p>This pattern of disturbance in oscillatory brain activity indicate loss of connections between neurons, providing a first step in the understanding of cognitive dysfunction in SIVD-WMH.</p

Protecting tropical forests from the rapid expansion of rubber using carbon payments

Expansion of Hevea brasiliensis rubber plantations is a resurgent driver of deforestation, carbon emissions, and biodiversity loss in Southeast Asia. Southeast Asian rubber extent is massive, equivalent to 67% of oil palm, with rapid further expansion predicted. Results-based carbon finance could dis-incentivise forest conversion to rubber, but efficacy will be limited unless payments match, or at least approach, the costs of avoided deforestation. These include opportunity costs (timber and rubber profits), plus carbon finance scheme setup (transaction) and implementation costs. Using comprehensive Cambodian forest data, exploring scenarios of selective logging and conversion, and assuming land-use choice is based on net present value, we find that carbon prices of $30-$51 per tCO2are needed to break even against costs, higher than those currently paid on carbon markets or through carbon funds. To defend forests from rubber, either carbon prices must be increased, or other strategies are needed, such as corporate zero-deforestation pledges, and governmental regulation and enforcement of forest protection

Accretion, Outflows, and Winds of Magnetized Stars

Many types of stars have strong magnetic fields that can dynamically influence the flow of circumstellar matter. In stars with accretion disks, the stellar magnetic field can truncate the inner disk and determine the paths that matter can take to flow onto the star. These paths are different in stars with different magnetospheres and periods of rotation. External field lines of the magnetosphere may inflate and produce favorable conditions for outflows from the disk-magnetosphere boundary. Outflows can be particularly strong in the propeller regime, wherein a star rotates more rapidly than the inner disk. Outflows may also form at the disk-magnetosphere boundary of slowly rotating stars, if the magnetosphere is compressed by the accreting matter. In isolated, strongly magnetized stars, the magnetic field can influence formation and/or propagation of stellar wind outflows. Winds from low-mass, solar-type stars may be either thermally or magnetically driven, while winds from massive, luminous O and B type stars are radiatively driven. In all of these cases, the magnetic field influences matter flow from the stars and determines many observational properties. In this chapter we review recent studies of accretion, outflows, and winds of magnetized stars with a focus on three main topics: (1) accretion onto magnetized stars; (2) outflows from the disk-magnetosphere boundary; and (3) winds from isolated massive magnetized stars. We show results obtained from global magnetohydrodynamic simulations and, in a number of cases compare global simulations with observations.Comment: 60 pages, 44 figure

Altered fibroblast proteoglycan production in COPD

<p>Abstract</p> <p>Background</p> <p>Airway remodeling in COPD includes reorganization of the extracellular matrix. Proteoglycans play a crucial role in this process as regulators of the integrity of the extracellular matrix. Altered proteoglycan immunostaining has been demonstrated in COPD lungs and this has been suggested to contribute to the pathogenesis. The major cell type responsible for production and maintenance of ECM constituents, such as proteoglycans, are fibroblasts. Interestingly, it has been proposed that central airways and alveolar lung parenchyma contain distinct fibroblast populations. This study explores the hypothesis that altered depositions of proteoglycans in COPD lungs, and in particular versican and perlecan, is a result of dysregulated fibroblast proteoglycan production.</p> <p>Methods</p> <p>Proliferation, proteoglycan production and the response to TGF-β₁were examined <it>in vitro </it>in centrally and distally derived fibroblasts isolated from COPD patients (GOLD stage IV) and from control subjects.</p> <p>Results</p> <p>Phenotypically different fibroblast populations were identified in central airways and in the lung parenchyma. Versican production was higher in distal fibroblasts from COPD patients than from control subjects (p < 0.01). In addition, perlecan production was lower in centrally derived fibroblasts from COPD patients than from control subjects (p < 0.01). TGF-β₁triggered similar increases in proteoglycan production in distally derived fibroblasts from COPD patients and control subjects. In contrast, centrally derived fibroblasts from COPD patients were less responsive to TGF-β₁than those from control subjects.</p> <p>Conclusions</p> <p>The results show that fibroblasts from COPD patients have alterations in proteoglycan production that may contribute to disease development. Distally derived fibroblasts from COPD patients have enhanced production of versican that may have a negative influence on the elastic recoil. In addition, a lower perlecan production in centrally derived fibroblasts from COPD patients may indicate alterations in bronchial basement membrane integrity in severe COPD.</p

Can current moisture responses predict soil CO2 efflux under altered precipitation regimes? A synthesis of manipulation experiments.

As a key component of the carbon cycle, soil CO2 efflux (SCE) is being increasingly studied to improve our mechanistic understanding of this important carbon flux. Predicting ecosystem responses to climate change often depends on extrapolation of current relationships between ecosystem processes and their climatic drivers to conditions not yet experienced by the ecosystem. This raises the question of to what extent these relationships remain unaltered beyond the current climatic window for which observations are available to constrain the relationships. Here, we evaluate whether current responses of SCE to fluctuations in soil temperature and soil water content can be used to predict SCE under altered rainfall patterns. Of the 58 experiments for which we gathered SCE data, 20 were discarded because either too few data were available or inconsistencies precluded their incorporation in the analyses. The 38 remaining experiments were used to test the hypothesis that a model parameterized with data from the control plots (using soil temperature and water content as predictor variables) could adequately predict SCE measured in the manipulated treatment. Only for 7 of these 38 experiments was this hypothesis rejected. Importantly, these were the experiments with the most reliable data sets, i.e., those providing high-frequency measurements of SCE. Regression tree analysis demonstrated that our hypothesis could be rejected only for experiments with measurement intervals of less than 11 days, and was not rejected for any of the 24 experiments with larger measurement intervals. This highlights the importance of high-frequency measurements when studying effects of altered precipitation on SCE, probably because infrequent measurement schemes have insufficient capacity to detect shifts in the climate dependencies of SCE. Hence, the most justified answer to the question of whether current moisture responses of SCE can be extrapolated to predict SCE under altered precipitation regimes is ?no? ? as based on the most reliable data sets available. We strongly recommend that future experiments focus more strongly on establishing response functions across a broader range of precipitation regimes and soil moisture conditions. Such experiments should make accurate measurements of water availability, should conduct high-frequency SCE measurements, and should consider both instantaneous responses and the potential legacy effects of climate extremes. This is important, because with the novel approach presented here, we demonstrated that, at least for some ecosystems, current moisture responses could not be extrapolated to predict SCE under altered rainfall conditions