Extension of exactly-solvable Hamiltonians using symmetries of Lie algebras

Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki approximations of the evolution operator for the quantum phase estimation algorithm, or in the quantum measurement problem for the variational quantum eigensolver. One of the typical forms of exactly solvable Hamiltonians is a linear combination of operators forming a modest size Lie algebra. Very frequently such linear combinations represent non-interacting Hamiltonians and thus are of limited interest for describing interacting cases. Here we propose the extension where coefficients in these combinations are substituted by polynomials of the Lie algebra symmetries. This substitution results in a more general class of solvable Hamiltonians and for qubit algebras is related to the recently proposed non-contextual Pauli Hamiltonians. In fermionic problems, this substitution leads to Hamiltonians with eigenstates that are single Slater determinants but with different sets of single-particle states for different eigenstates. The new class of solvable Hamiltonians can be measured efficiently using quantum circuits with gates that depend on the result of a mid-circuit measurement of the symmetries

Distributions of highly branched isoprenoid alkenes and other algal lipids in surface waters from East Antarctica: Further insights for biomarker-based paleo sea-ice reconstruction

The occurrence and variable abundance of certain di- and tri-unsaturated C₂₅ highly branched isoprenoid (HBI) biomarkers in Antarctic marine sediments has previously been proposed as a possible proxy measure of paleo sea-ice extent in the Southern Ocean. In the current study, we obtained 47 near-surface (ca. 0-10 m) water samples taken from locations in East Antarctica with different sea ice settings and analysed them for their HBI, sterol and fatty acid content. Sampling locations ranged from the permanently open-ocean zone (POOZ), with no seasonal sea-ice cover, the near-shore summer sea ice zone (SIZ), where sea ice remains long into the summer melt season, and the marginal ice zone (MIZ), located between the POOZ and the SIZ, and with a highly variable latitudinal sea-ice edge throughout the season. A di-unsaturated C₂₅ HBI (diene II) was only identified in surface waters from the MIZ and the SIZ, consistent with a sea-ice diatom origin for this biomarker. In contrast, a tri-unsaturated C₂₅ HBI (triene III) was detected in all samples from the POOZ, the MIZ and the SIZ, and with a stable isotopic composition (δ¹³C = -35 ± 1.5‰) consistent with a phytoplankton source. The highest concentrations of diene II and triene III were in samples from the SIZ and the MIZ, respectively, thus providing further insights into the sea-ice conditions likely favourable for their production and how their relative abundances (the II/III ratio) in underlying sediments might be better interpreted for paleo sea-ice reconstruction. In this respect, relatively high II/III might be a good indicator of extended (into summer) seasonal sea-ice cover, while lower II/III may provide a better indicator of the MIZ. However, the observation of highly variable II/III within the polynya setting of the SIZ may also have significant impacts on sedimentary values. Distributions of diatom sterols and fatty acids were also variable between the three sampling zones, but these were not as distinctive as those observed for the HBIs.10 page(s

EIMS Fragmentation and detection of autoxidation products of 2,6,10,14‐tetramethyl‐7‐(3‐methylpent‐4‐enyl)‐pentadec‐5‐ene in Arctic sediments

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Autoxidation of the sea ice biomarker proxy IPSO <inf>25</inf> in the near-surface oxic layers of Arctic and Antarctic sediments

© 2019 Over the last decade or so, the mono- and di-unsaturated highly branched isoprenoid (HBI) lipids IP 25 (Ice Proxy with 25 carbon atoms) and IPSO 25 (Ice Proxy for the Southern Ocean with 25 carbon atoms) have emerged as useful proxies for sea ice in the Arctic and Antarctic, respectively. A more complete understanding of their respective proxy signatures, however, requires more detailed knowledge of their stability in the water column and in sediments. In the current study, we focused on the autoxidation of IPSO 25 , first by performing laboratory-based oxidation reactions on a purified sample and characterizing products based on detailed mass spectral analysis. We then analysed for the same oxidation products in near-surface sediments retrieved from the Arctic and the Antarctic, and some suspended organic matter from the Antarctic. Our data show that IPSO 25 is susceptible to partial autoxidation within the oxic layers of Arctic and Antarctic sediments, while the same processes appear not to be so important in the water column. Although the number of primary autoxidation reactions identified in sediments was not as large as in laboratory experiments, there was evidence for their subsequent modification by biotic degradation. Quantifying the extent of degradation of IPSO 25 and IP 25 in sediments, and thus the impact of such process on the use of these biomarkers as paleo sea ice proxies, remains challenging at this stage, since most of the primary oxidation products do not accumulate, likely due to secondary biodegradation reactions. Some interesting differences in reactivity were also observed between IPSO 25 and IP 25 present in the same Arctic sediments. This suggests that factors other than environmental control may influence the IPSO 25 /IP 25 ratio (i.e. DIP 25 ) in Arctic sediments

A novel biomarker-based proxy for the spring phytoplankton bloom in Arctic and sub-arctic settings – HBI T25

Source at https://doi.org/10.1016/j.epsl.2019.06.038. The spring phytoplankton bloom is a characteristic feature of mid-high latitudes in modern times, but can be challenging to identify in palaeo records. In the current study, we investigated the absolute and relative distributions of two diatom-derived tri-unsaturated highly branched isoprenoid (HBI) lipids, at least one of which has previously been suggested to be a possible proxy for the productive region of the marginal ice zone (MIZ) in the Polar Regions. Based on a comparison of their distributions in surface sediments from the Barents Sea and neighbouring regions with a range of oceanographic parameters, we identify, via principal component analysis, a strong association between the relative proportion of the two HBIs and satellite-derived spring chlorophyll a (chl a) concentration. Further, based on agglomerative hierarchical clustering, we identify two clusters of HBI biomarker ratios and spring chl a together with a potential threshold biomarker ratio (termed HBI TR25) for the spring phytoplankton bloom. A modified version of HBI TR25 (i.e. HBI T25) provides a potentially more straightforward binary measure of the spring phytoplankton bloom. Analysis of HBI TR25 and HBI T25 values in a series of short (spanning recent centuries) and long (Holocene) sediment cores from the region provides an initial evaluation of the applicability of this novel proxy in the palaeo record. Outcomes are mainly consistent with the findings from the surface sediments and with other proxy-based reconstructions, including estimates of past sea ice cover, which is well-known to influence primary production in the region. Indeed, we suggest that the new HBI T25 phytoplankton bloom proxy may also represent an important new tool for characterising the MIZ in palaeo records, especially when used alongside well-established sea ice proxies, such as IP25 and PIP25. Despite the largely empirical nature of the study, we also provide a possible explanation for the observed biomarker ratio-chl a relationship. Thus, a previous laboratory investigation showed that the distributions of the same two HBIs analysed herein in their likely source (viz. Rhizosolenia setigera) was strongly influenced by culture temperature and growth rate. Confirmation of the generality of our findings and of the causal relationship between HBI T25 and the spring phytoplankton bloom will, however, require further laboratory- and field-based studies in the futur

Ocean surface and bottom water conditions, iceberg drift and sediment transport on the North Iceland margin during MIS 3 and MIS 2

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