A construction of Combinatorial NLTS

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity (with complexity measured by the quantum circuit depth preparing the state). Here, we prove a weaker version called the combinatorial NLTS, where a quantum circuit lower bound is shown against states that violate a (small) constant fraction of local terms. This generalizes the prior NLETS results (Eldar and Harrow [2017]; Nirkhe, Vazirani and Yuen [2018]). Our construction is obtained by combining tensor networks with expander codes (Sipser and Spielman [1996]). The Hamiltonian is the parent Hamiltonian of a perturbed tensor network, inspired by the `uncle Hamiltonian' of Fernandez-Gonzalez et. al. [2015]. Thus, we deviate from the quantum CSS code Hamiltonians considered in most prior works.Comment: 14 pages, 4 figures, added funding information and some discussio

NLTS Hamiltonians from good quantum codes

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). We prove this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians.Comment: 12 pages, 1 figure, added funding information and discussion

Unveiling Novel insights in healthcare through exploring knowledge, Attitude, and practice (KAP) toward Covid-19: A Cross sectional study among Nepalese College students

Purpose: The goal of this study was to evaluate the COVID-19 knowledge, attitude, and practise of college students in Lalitpur, Nepal, and to investigate how these factors relate to sociodemo graphic factors. Design/Methodology/Approach: College students were surveyed through questionnaire to learn more about their understanding, attitudes, and COVID-19-related behaviours. Binary logistic regression was used to examine the association between these variables. Findings: The survey found that a fair amount of people had a general understanding of COVID-19 symptoms (29.32%), whereas a smaller number had a good understanding of preventive actions (16.42%). It was discovered that students' knowledge of COVID-19 was highly influenced by income, education, and age. The majority of those surveyed (82.11%) thought that following preventive guidelines was very helpful in limiting the spread of the virus. Students' perceptions towards COVID-19 were found to be highly influenced by their age, education, and income. A considerable percentage of the students avoided large gatherings in practise (88.26%), showing the influence of age, education, income, and occupation on preventive practises. However, there was no discernible connection between marital status and COVID-19 preventive strategies. Originality/Value: This study advances knowledge of college students' beliefs, practises, and knowledge of COVID-19. In order to effectively stop the virus from spreading among college students, it emphasises the significance of focused interventions and educational campaigns that emphasise knowledge enhancement, the promotion of preventative measures, and consideration of socio-demographic factors

Circuit-to-Hamiltonian from tensor networks and fault tolerance

We define a map from an arbitrary quantum circuit to a local Hamiltonian whose ground state encodes the quantum computation. All previous maps relied on the Feynman-Kitaev construction, which introduces an ancillary `clock register' to track the computational steps. Our construction, on the other hand, relies on injective tensor networks with associated parent Hamiltonians, avoiding the introduction of a clock register. This comes at the cost of the ground state containing only a noisy version of the quantum computation, with independent stochastic noise. We can remedy this - making our construction robust - by using quantum fault tolerance. In addition to the stochastic noise, we show that any state with energy density exponentially small in the circuit depth encodes a noisy version of the quantum computation with adversarial noise. We also show that any `combinatorial state' with energy density polynomially small in depth encodes the quantum computation with adversarial noise. This serves as evidence that any state with energy density polynomially small in depth has a similar property. As an application, we show that contracting injective tensor networks to additive error is BQP-hard. We also discuss the implication of our construction to the quantum PCP conjecture, combining with an observation that QMA verification can be done in logarithmic depth

B cell responses to a peptide epitope. VII. Antigen-dependent modulation of the germinal center reaction

Germinal center responses to two analogous peptides, PS1CT3 and G32CT3, that differ in sequence only at one position within the B cell epitopic region were examined. In comparison with peptide PS1CT3, peptide G32CT3 elicited a poor germinal center response. By demonstrating equal facility of immune complexes with IgM and IgG Ab isotypes to seed germinal centers, we excluded differences in isotype profiles of early primary anti-PS1CT3 and anti-G32CT3 Ig as the probable cause. Quantitative differences in germinal center responses to the two peptides were also not due to either qualitative/quantitative differences in T cell priming or variation in the frequency of the early Ag-activated B cells induced. Rather, they resulted from qualitative differences in the nature of B cells primed. Analysis of early primary anti-PS1CT3 and anti-G32CT3 IgMs revealed that the latter population was of a distinctly lower affinity, implying the existence of an Ag affinity threshold that restricts germinal center recruitment of G32CT3-specific B cells. The impediment in anti-G32CT3 germinal center initiation could be overcome by making available an excess of Ag-activated Th cells at the time of immunization. This resulted in the appearance of a higher affinity population of G32CT3-specific B cells that, presumably, are now capable of seeding germinal centers. These data suggest that the strength of a germinal center reaction generated is Ag dependent. At least one regulatory parameter represents the quality of B cells that are initially primed

B cell responses to a peptide epitope. VIII. Immune complex-mediated regulation of memory B cell generation within germinal centers

Using an in vivo reconstitution assay, we examine here the role of immune complexes in both formation of germinal centers (GC) and processes that occur subsequently within. The presence of Ag, as immune complexes, was found not to constitute a limiting requirement for the initiation of GC formation. No detrimental effect either on numbers or sizes of the resulting GC was observed when Ag-containing immune complexes were omitted during reconstitution. Thus, both recruitment and proliferation of Ag-activated B cells within GC appear not to be limited by Ag concentrations. In contrast, the presence of immune complexes was observed to be obligatory for the generation of Ag-specific memory B cells. This optimally required immune complexes to be constituted by IgG-class Abs with epitope specificities that were homologous to those of the GC B cells. The GC reaction was also found to be characterized by an enhancement of Ab specificity for the homologous epitope. Although some improvement in specificity was noted in recall responses from immune complex-deficient GC, the presence of appropriate immune complexes served to further optimize the outcome. Here again, isotype and epitope-specificity of the Ab constituent in immune complexes proved to be important

Ytterbium triflate (and trimethylsilyl triflate) catalyzed isomerization of glycidic esters to α-hydroxy-β,γ-unsaturated esters and their conversion into cyclopentanoids using Johnson-Claisen rearrangement

A variety of glycidic esters undergo smooth isomerization to the corresponding α-hydroxy-β, γ-unsaturated esters upon reaction with Yb(OTf)3 or TMSOTf. These α-hydroxy-β, γ-unsaturated esters undergo Johnson-Claisen rearrangement to appropriately substituted diesters, some of which are converted into cyclopentanoids

Clinicopathological study of benign and malignant ovarian tumours and the role of HER2/neu and ER expression in these tumours

Background: Ovarian cancers represent the 6th most common cancer among females and are the most common cause of death from gynaecological cancers in the world. The aim is to do clinicopathologic study of ovarian tumours along with evaluation of the expression of estrogen receptor (ER) and human epidermal growth factor receptor (HER2/neu).Methods: A total of 85 cases of ovarian tumors were studied and immunohistochemistry was performed with specific antibodies against ER and HER2/neu as per standard protocol.Results: In present study, surface epithelial tumours were the commonest type comprising 64 cases (75.2%), followed by Germ cell tumours, 17cases (20%) and sex cord stromal tumours, 04 cases (4.8%).Among the surface epithelial tumours , ER‑positive cases were higher in malignant (71.4%) tumours as compared to borderline tumours (33.3%) and benign tumours (7.7%) while Her2/neu positive cases were higher in borderline (66.7%) tumours as compared to malignant tumours (42.9%) and benign tumours (15.3%).Among the germ cell tumours, ER expression was positive in 62.5% cases of mature teratoma while HER2/neu expression was positive in only 12.5% cases of mature teratoma. None of the sex cord stromal tumours showed positive expression of ER and HER2/neu.Conclusions: Positive expression of estrogen receptors is seen predominantly in surface epithelial malignancies and in mature teratoma. It proves the mitogenic role of estrogen in ovarian tumours. Her-2 neu was expressed mainly in malignant tumours. This suggests their carcinogenic role. This also helps in differentiating borderline and malignant tumours