scholarly journals Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multiqubit controlled low-rank counterparts

2022 ◽  
Vol 105 (1) ◽  
Author(s):  
Luogen Xu ◽  
Joseph T. Lee ◽  
J. K. Freericks
Keyword(s):  
Low Rank ◽  
2013 ◽  
Vol 6 (4) ◽  
pp. 1053-1060 ◽  
Author(s):  
W. Lin ◽  
M. Portabella ◽  
A. Stoffelen ◽  
A. Verhoef

Abstract. The inversion of the Advanced Scatterometer (ASCAT) backscatter measurement triplets generally leads to two wind ambiguities with similar wind speed values and opposite wind directions. However, for up-, down- and crosswind (with respect to the mid-beam azimuth direction) cases, the inversion often leads to three or four wind solutions. In most of such cases, the inversion residuals or maximum likelihood estimators (MLEs) of the third and fourth solutions (i.e. high-rank solutions) are substantially higher than those of the first two (low-rank) ambiguities. This indicates a low probability for the high-rank solutions and thus essentially dual ambiguity. This paper investigates the characteristics of ASCAT high-rank wind solutions under different conditions with the objective of developing a method for rejecting the spurious high-rank solutions. The implementation of this rejection procedure improves the effectiveness of the ASCAT wind quality control (QC) and ambiguity removal procedures.


2016 ◽  
Vol 28 (2) ◽  
pp. 286-304 ◽  
Author(s):  
Asunur Cezar ◽  
Hulisi Ögüt

Purpose – The aim of this paper is to examine the impact of three main technologies on converting browsers into customers: impact of review rating (location rating and service rating), recommendation and search listings. Design/methodology/approach – This paper estimates conversion rate model parameters using a quasi-likelihood method with the Bernoulli log-likelihood function and parametric regression model based on the beta distribution. Findings – The results show that a high rank in search listings, a high number of recommendations and location rating have a significant and positive impact on conversion rates. However, service rating and star rating do not have a significant effect on conversion rate. Furthermore, room price and hotel size are negatively associated with conversion rate. It was also found that a high rank in search listings, a high number of recommendations and location rating increase online hotel bookings. Furthermore, it was found that a high number of recommendations increase the conversion rate of hotels with low ranks. Practical implications – The findings show that hotels’ location ratings are more important than both star and service ratings for the conversion of visitors into customers. Thus, hotels that are located in convenient locations can charge higher prices. The results may also help entrepreneurs who are planning to open new hotels to forecast the conversion rates and demand for specific locations. It was found that a high number of recommendations help to increase the conversion rate of hotels with low ranks. This result suggests that a high numbers of recommendations mitigate the adverse effect of a low rank in search listings on the conversion rate. Originality/value – This paper contributes to the understanding of the drivers of conversion rates in online channels for the successful implementation of hotel marketing.


2021 ◽  
Vol 13 (16) ◽  
pp. 8969
Author(s):  
Noureen Fatima ◽  
Asif Jamal ◽  
Zaixing Huang ◽  
Rabia Liaquat ◽  
Bashir Ahamad ◽  
...  

Currently, conversion of coal into alternative fuel and non-fuel valuable products is in demand and growing interest. In the present study, humic acid was extracted from two different ranks of coal, i.e., low rank and high rank (lignite and bituminous), through chemical pretreatment by nitric acid. Samples of lignite and bituminous coal were subjected to nitric acid oxidation followed by extraction using KOH and NaOH gravimetric technique. The chemical pretreatment of both types of coal led to enhanced yield of humic acid from 21.15% to 57.8% for lignite low-rank coal and 11.6% to 49.6% bituminous high rank coal. The derived humic acid from native coal and nitric acid treated coal was analyzed using elemental analysis, E4/E6 ratio of absorbance at 465 nm and 665 nm using UV-Visible spectrophotometry and Fourier transformed infrared spectroscopy FTIR. The chemical characteristics of coal treated with nitric acid have shown increased molecular weight and improved aromaticity with more oxygen and nitrogen and lower C, H, and sulphur content. The E4/E6 ratio of nitric acid-treated low and high ranks of coal were high. The FTIR spectroscopic data of nitric acid-treated lignite coal indicates an intensive peak of carboxyl group at 2981.84 cm, while bituminous coal was shown in cooperation of N-H group at 2923.04 cm. SEM was performed to detect the morphological changes that happen after producing humic acid from HNO3 treatment and native coal. The humic acid produced from HNO3 treated coal had shown clear morphological changes and some deformations on the surface. SEM-EDS detected the major elements, such as nitrogen, in treated humic acid that were absent in raw coal humic acid. Hence, the produced humic acid through HNO3 oxidation showed a more significant number of humic materials with improved efficiency as compared to native coal. This obtained humic acid can be made bioactive for agriculture purposes, i.e., for soil enrichment and improvement in growth conditions of plants and development of green energy solution.


2021 ◽  
Vol 2021 (1) ◽  
pp. 11601
Author(s):  
Merrick Osborne ◽  
Elizabeth Trinh ◽  
Melissa Valentine ◽  
Jieying Xu ◽  
Min Yu
Keyword(s):  

2012 ◽  
Vol 134 (2) ◽  
pp. 561-579 ◽  
Author(s):  
Hal Schenck ◽  
Mike Stillman
Keyword(s):  
Low Rank ◽  

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Mario Motta ◽  
Erika Ye ◽  
Jarrod R. McClean ◽  
Zhendong Li ◽  
Austin J. Minnich ◽  
...  

AbstractThe quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $${\mathcal{O}}({N}^{4})$$ O ( N 4 ) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity in small simulations, which reduces to $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) depth on a linearly connected array, an improvement over the $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 105 non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.


Author(s):  
Yuchen Guo ◽  
Guiguang Ding ◽  
Jungong Han ◽  
Hang Shao ◽  
Xin Lou ◽  
...  

Zero-shot learning (ZSL) is a recently emerging research topic which aims to build classification models for unseen classes with knowledge from auxiliary seen classes. Though many ZSL works have shown promising results on small-scale datasets by utilizing a bilinear compatibility function, the ZSL performance on large-scale datasets with many classes (say, ImageNet) is still unsatisfactory. We argue that the bilinear compatibility function is a low-rank approximation of the true compatibility function such that it is not expressive enough especially when there are a large number of classes because of the rank limitation. To address this issue, we propose a novel approach, termed as High-rank Deep Embedding Networks (GREEN), for ZSL with many classes. In particular, we propose a feature-dependent mixture of softmaxes as the image-class compatibility function, which is a simple extension of the bilinear compatibility function, but yields much better results. It utilizes a mixture of non-linear transformations with feature-dependent latent variables to approximate the true function in a high-rank way, which makes GREEN more expressive. Experiments on several datasets including ImageNet demonstrate GREEN significantly outperforms the state-of-the-art approaches.


2021 ◽  
Author(s):  
Chiara Zuffetti ◽  
Riccardo Bersezio

<p>In active foreland basins, stratigraphic unconformities develop on the flanks and crests of the uplifting thrust-related structures and correspond to correlative conformities in the adjacent depocenters. The geometrical, morphological, stratigraphic, sedimentological, and petrographic attributes of unconformities and associated sediments are highly variable from the uplifting to the subsiding basin sectors. In Quaternary continental foreland basins, landscape evolution, sedimentation, and the nature of the geological boundaries are controlled by the competing turnovers of climate (i.e. glacial advances and retreats) and tectonics (i.e. steady-state uplift/subsidence vs. unsteady deformation increments).</p><p>In order to recognize the fingerprints of tectonic and climatic factors on the nature of the stratigraphic unconformities, we studied the Pleistocene shallow marine (Calabrian) to alluvial and glacio-fluvial sediments (Calabrian-Latest Pleistocene) associated to the active external arc of the N-Apennine thrusts in the Quaternary Po basin of Lombardy (N-Italy).</p><p>A set of intra-basin reliefs corresponding to ramp-folds was the key-site to describe the nature and attributes of the exposed Pleistocene unconformities and stratigraphy. We integrated different-scale geological, sedimentological, stratigraphic, geo-pedological, geomorphological, and structural field surveys, constrained by C14 and OSL age determinations, to down-trace the stratigraphic boundaries to the subsurface and to assist correlation of borehole logs and geophysical images. The surface facies associations of the stratigraphic units were compared to the litho-textural associations of their subsurface equivalents to draw the best fitting surface-subsurface model, which was constrained to the geological evolution and chronostratigraphy. A hierarchic 3D geological model was computed by the potential field method, which includes the 4D attributes of the stratigraphic boundaries and unconformities organized into three hierarchic orders. Among them, five Quaternary high-rank, and seven intermediate-rank unconformities were recognized.</p><p>The high-rank unconformities (Gelasian, intra-Calabrian, Early-Middle Pleistocene, Late Pleistocene and Latest Pleistocene-Holocene unconformities) are erosional, angular (high angle), composite, diachronous surfaces. They originated in front of and above the uplifting ramp-folds, where the discrete, polyphase, and unsteady propagation stages of the blind outermost Apennines arc directly controlled sedimentation, erosion, and accommodation patterns. The intermediate- and low-rank stratigraphic boundaries are either: (i) stratigraphic surfaces of erosion and deposition, occasionally with low-angle unconformity; (ii) stratigraphic surfaces of aggradation (covered by late Pleistocene loess units at places); (iii) morphological surfaces of stabilization marked by (paleo-) soils. These attributes and the 3D relations with the high-rank unconformities show that these surfaces formed during steady uplift/subsidence increments and/or at times or sites of tectonic quiescence. In these cases, the development of erosion surfaces, facies and provenance changes are not associated to tectonic-induced angles, wedging or fanning of sedimentary units. Chronological constraints link these changes to the regional advances and retreats of the Pleistocene alpine glaciers, suggesting that the intermediate-rank surfaces are mostly dependent on the major climate changes, while the low-rank ones relate to depositional unsteadiness, either autocyclic or short-term allocyclic. </p>


2020 ◽  
Vol 23 (2) ◽  
pp. 105-115
Author(s):  
Datin Umar ◽  
◽  
Suganal Suganal ◽  
Ika Monika ◽  
Gandhi Hudaya ◽  
...  

Steam drying process of the Low Rank Coals (LRCs) has been conducted to produce coal which is comparable with the High Rank Coal (HRC). Characterization of the raw and dried coals was carried out through proximate, ultimate, calorific value, Fourier Transform Infrared (FTIR) spectroscopy and Thermo Gravimetry-Differential Thermal Analysis (TG-DTA) to study the combustion behavior of the coals. This study used Indonesian low rank coals coming from Tabang (TKK coal) and Samurangau (SP coal), East Kalimantan. The results indicate that the calorific value of the dried coals increases significantly due to the decrease in moisture content of the coal. The FTIR spectrums show that the methylene-ethylene (RCH3/CH2) and aromaticity-aliphaticity ratios (Rar/al) of the dried coals increased while the ratio of RCO/ar decreased which reflect that the rank of the coals increased equivalent to the high rank coal (bituminous). Meanwhile, the TG-DTA indicates that the ignition temperature (Tig) and combustion rate (Rmax) of the dried coals increased. This analysis expresses that the dried coals produced by steam drying process have better combustion behavior due to the higher calorific value than those of the raw coals.


2012 ◽  
Vol 5 (6) ◽  
pp. 8839-8857 ◽  
Author(s):  
W. Lin ◽  
M. Portabella ◽  
A. Stoffelen ◽  
A. Verhoef

Abstract. The inversion of the Advanced Scatterometer (ASCAT) backscatter measurement triplets generally leads to two wind ambiguities with similar wind speed values and opposite wind directions. However, for up-, down- and cross-wind (with respect to the mid beam azimuth direction) cases, the inversion often leads to three or four wind solutions. In most of such cases, the inversion residual or maximum likelihood estimator (MLE) of the 3rd and 4th solutions (i.e. high-rank solutions) are substantially higher than those of the first two (low rank) ambiguities, indicating a low probability of the former and thus essentially dual ambiguity. This paper investigates the characteristics of ASCAT high-rank wind solutions under different conditions with the objective to develop a method for rejecting the spurious high-rank solutions. The implementation of this rejection procedure improves the effectiveness of the ASCAT wind quality control (QC) and ambiguity removal procedures.


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