On character table of Clifford groups

Based on a presentation of $\mathcal{C}_n$ and the help of [GAP], we construct the character table of the Clifford group $\mathcal{C}_n$ for $n=1,2,3$. As an application, we can efficiently decompose the (higher power of) tensor product of the matrix representation in those cases. Our results recover some known results in [HWW, WF] and reveal some new phenomena. We prove that the trivial character is the only linear character for $\mathcal{C}_n$ and hence $\mathcal{C}_n$ equals to its commutator subgroup when $n\geq 3$. A few conjectures about $\mathcal{C}_n$ for general $n$ are proposed.Comment: 13 pages; comments and suggestions are welcom

The design of a prospective, randomized, open-labeled study to compare the efficacy of lercanidipine with amlodipine on renal function in hypertensive patients aged at least 55 years (LEADER study)

AbstractBackgroundAlthough all classes of antihypertensive treatment can successfully reduce morbidity and mortality of cardiac pathology, prevention of target organ damages is of great importance beyond blood pressure lowering. Unlike most dihydropyridines, lercanidipine dilates both afferent and the efferent arterioles of nephrons, so it may provide renoprotective effects, which other CCBs may not have. The main purpose of this study is to compare the renoprotective effect of lercanidipine and amlodipine among hypertensive people aged 55years and older with newly diagnosed hypertension or those who were treatment-naïve for one month.MethodsThe study is a prospective, open-labelled, randomized, controlled trial to enrol 232 hypertensive patients aged ≥55 years. Subjects will be randomized into lercanidipine arm (10–20mg/day) and amlodipine arm (5–10mg/day) by 1:1 ratio. The dosage can be up-titrated to 20mg/day (lercanidipine group) and 10mg/day (amlodipine group), respectively, at week 4 or any following visit thereafter. Efficacy and safety data will be collected at week 4, 12 and 24 by evaluating the blood pressure lowering, estimated glomerular filtration rate, creatinine clearance, and urine albumin-creatinine ratio.ConclusionsThe reno-protective effects of new generation of CCBs such as lercanidipine administered to patients with hypertension are not investigated well. After all, this study will bring benefit to older patients who need drugs with both excellent anti-hypertensive and reno-protective efficacy. And the results will be provided for future treatment guideline of elder population in Taiwan

Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits

Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum and classical computing have become the main paradigm for exhibiting NISQ applications, where low-depth quantum circuits are repeatedly applied. In order to further scale up the problem size solvable by the NISQ devices, it is also possible to reduce the number of physical qubits by "cutting" the quantum circuit into different pieces. In this work, we experimentally demonstrated a circuit-cutting method for simulating quantum circuits involving many logical qubits, using only a few physical superconducting qubits. By exploiting the symmetry of linear-cluster states, we can estimate the effectiveness of circuit-cutting for simulating up to 33-qubit linear-cluster states, using at most 4 physical qubits for each subcircuit. Specifically, for the 12-qubit linear-cluster state, we found that the experimental fidelity bound can reach as much as 0.734, which is about 19\% higher than a direct simulation {on the same} 12-qubit superconducting processor. Our results indicate that circuit-cutting represents a feasible approach of simulating quantum circuits using much fewer qubits, while achieving a much higher circuit fidelity

6-Shogaol Induces Apoptosis in Human Hepatocellular Carcinoma Cells and Exhibits Anti-Tumor Activity In Vivo through Endoplasmic Reticulum Stress

6-Shogaol is an active compound isolated from Ginger (Zingiber officinale Rosc). In this work, we demonstrated that 6-shogaol induces apoptosis in human hepatocellular carcinoma cells in relation to caspase activation and endoplasmic reticulum (ER) stress signaling. Proteomic analysis revealed that ER stress was accompanied by 6-shogaol-induced apoptosis in hepatocellular carcinoma cells. 6-shogaol affected the ER stress signaling by regulating unfolded protein response (UPR) sensor PERK and its downstream target eIF2α. However, the effect on the other two UPR sensors IRE1 and ATF6 was not obvious. In prolonged ER stress, 6-shogaol inhibited the phosphorylation of eIF2α and triggered apoptosis in SMMC-7721 cells. Salubrinal, an activator of the PERK/eIF2α pathway, strikingly enhanced the phosphorylation of eIF2α in SMMC-7721 cells with no toxicity. However, combined treatment with 6-shogaol and salubrinal resulted in significantly increase of apoptosis and dephosphorylation of eIF2α. Overexpression of eIF2α prevented 6-shogaol-mediated apoptosis in SMMC-7721 cells, whereas inhibition of eIF2α by small interfering RNA markedly enhanced 6-shogaol-mediated cell death. Furthermore, 6-shogaol-mediated inhibition of tumor growth of mouse SMMC-7721 xenograft was associated with induction of apoptosis, activation of caspase-3, and inactivation of eIF2α. Altogether our results indicate that the PERK/eIF2α pathway plays an important role in 6-shogaol-mediated ER stress and apoptosis in SMMC-7721 cells in vitro and in vivo