Majorana stellar representation for mixed-spin (s,12)(s,\frac{1}{2}) systems

By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, Majorana's stellar representation provides an intuitive geometric perspective to comprehend a quantum system with high-dimensional Hilbert space. However, the problem of the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet. Here, we present a practical method to resolve the problem for the mixed-spin $(s, 1/2)$ system. The system can be decomposed into two spins: spin-$(s+1/2)$ and spin-$(s-1/2)$ at the coupling bases, which can be regarded as independent spins. Besides, we may write any pure state as a superposition of two orthonormal states with one spin-$(s+1/2)$ state and the other spin-$(s-1/2)$ state. Thus, the whole state can be regarded as a state of a pseudo spin-$1/2$. In this way, the mixed spin decomposes into three spins. Therefore, we can represent the state by $(2s+1)+(2s-1)+1=4s+1$ sets of stars on a Bloch sphere. Finally, to demonstrate our theory, we give some examples that indeed show laconic and symmetric patterns on the Bloch sphere, and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on a Bloch sphere

Exponentially Improved Efficient Machine Learning for Quantum Many-body States with Provable Guarantees

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error $\varepsilon$, provided that a sample set (of size $N$) of the states can be efficiently prepared and measured. In a recent work [Huang et al., Science 377, eabk3333 (2022)], a rigorous guarantee for such an generalization was proved. Unfortunately, an exponential scaling, $N = m^{ {\cal{O}} \left(\frac{1}{\varepsilon} \right) }$, was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative scenario, where $m$ is a finite, not necessarily large constant while the scaling with the prediction error becomes the central concern. By exploiting physical constraints and positive good kernels for predicting the density matrix, we rigorously obtain an exponentially improved sample complexity, $N = \mathrm{poly} \left(\varepsilon^{-1}, n, \log \frac{1}{\delta}\right)$, where $\mathrm{poly}$ denotes a polynomial function; $n$ is the number of qubits in the system, and ($1-\delta$) is the probability of success. Moreover, if restricted to learning ground-state properties with strong locality assumptions, the number of samples can be further reduced to $N = \mathrm{poly} \left(\varepsilon^{-1}, \log \frac{n}{\delta}\right)$. This provably rigorous result represents a significant improvement and an indispensable extension of the existing work.Comment: 8 + 10 pages, 1 + 1 figures; With supplemental materia

Exotic superfluidity and pairing phenomena in atomic Fermi gases in mixed dimensions

Abstract Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction, while one component is confined on a one-dimensional (1D) optical lattice whereas the other is in a homogeneous 3D continuum. We study the phase diagram and the pseudogap phenomena throughout the entire BCS-BEC crossover, using a pairing fluctuation theory. We find that the effective dimensionality of the non-interacting lattice component can evolve from quasi-3D to quasi-1D, leading to strong Fermi surface mismatch. Upon pairing, the system becomes effectively quasi-two dimensional in the BEC regime. The behavior of T c bears similarity to that of a regular 3D population imbalanced Fermi gas, but with a more drastic departure from the regular 3D balanced case, featuring both intermediate temperature superfluidity and possible pair density wave ground state. Unlike a simple 1D optical lattice case, T c in the mixed dimensions has a constant BEC asymptote

Estimated intraoperative blood loss correlates with postoperative cardiopulmonary complications and length of stay in patients undergoing video-assisted thoracoscopic lung cancer lobectomy: a retrospective cohort study

Abstract Background The purpose of our study was to estimate the influence of estimated intraoperative blood loss (EIBL) on postoperative cardiopulmonary complications (PCCs) in patients undergoing video-assisted thoracoscopic surgery (VATS) lobectomy for non-small-cell lung cancer (NSCLC). Methods We conducted a single-center retrospective analysis on the clinical data of consecutive patients in our institution between April 2015 and February 2016. Demographic differences between PCC group and non-PCC group were initially assessed. Receiver operating characteristic (ROC) analysis was performed to determine the threshold value of EIBL for the prediction of PCCs. Demographic differences in the PCC rates and length of stay between two groups of patients divided by this cutoff were further evaluated. A multivariable logistic-regression model involving the clinicopathological parameters with P-value< 0.05 was finally established to identify independent risk factors for PCCs. Results A total of 429 patients with operable NSCLC were included and 80 of them developed PCCs (rate = 18.6%). The mean EIBL in PCC group was significantly higher than that in non-PCC group (133.3 ± 191.3 vs. 79.1 ± 107.1 mL; P < 0.001). The ROC analysis showed an EIBL of 100 mL as the threshold value at which the joint sensitivity (50.0%) and specificity (73.4%) was maximal. The PCC rate in patients with EIBL≥100 mL was significantly higher than that in patients with EIBL< 100 mL (30.1 vs. 13.5%; P < 0.001). Both the length of stay and chest tube duration were significantly prolonged in the patients with EIBL≥100 mL. Finally, EIBL≥100 mL was identified to be predictive of PCCs by multivariable logistic-regression analysis (odds ratio = 3.01; 95% confidence interval = 1.47–6.16; P = 0.003). Conclusions EIBL serves as a significant categorical predictor for cardiopulmonary complications following VATS lobectomy for NSCLC. Thoracic surgeons should minimize the EIBL and strive for the ‘bloodless’ goal to optimize surgical outcomes

Status of core competencies of wound, ostomy and continence nurses and their influence on career success: a cross-sectional study

Objectives The wound, ostomy and continence nursing practice has its own scope and standards, and each standard requires relevant competency. However, the core competencies of wound, ostomy and continence nurses that contribute to the career success are poorly known. To identify associations between career success and core competencies of wound, ostomy and continence nurses in China.Design A cross-sectional survey with a convenience sample.Setting Participants were recruited from 108 hospitals in 28 provinces.Participants A total of 123 wound, ostomy and continence nurses were surveyed.Measures Career success, core competencies and demographic characteristics of wound, ostomy and continence nurses, were measured in this study.Methods A survey was distributed to 123 wound, ostomy and continence nurses were recruited from 108 hospitals in 28 provinces. Multivariate logistic regression was undertaken to explore associations between career success outcomes and core competency scores of wound ostomy and continence nurses and their demographic characteristics.Results The career success and core competency of wound, ostomy and continence nurses were both above average. Nurses who had higher total scores of core competency were more likely to have higher career success, including total score (OR=4.90), career satisfaction (OR=5.58) and perceived internal (OR=4.55)/external (OR=3.42) organisation competitiveness. Higher competency in interpersonal communication (OR=7.70) and more time for wound care per month (OR=8.80) predicted higher career satisfaction. Additionally, nurses with higher professional development were more likely to score higher in perceived internal organisation competitiveness of career success (OR=4.36) and the overall career success (OR=5.96).Conclusions The career success and core competency of the wound, ostomy and continence nurses in China were at an above average level. The associations between career success and core competency of the wound, ostomy and continence nurses were positive, suggesting that competency enhancement could improve nurses’ career success