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2022 Vol. 52, No. 8

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2022-8 Contents
2022, 52(8): 1-2.
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2022-8 Abstract
2022, 52(8): 1-2.
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Physics
Pure state tomography with adaptive Pauli measurements
Xiangrui Meng, Minggen He, Zhensheng Yuan
2022, 52(8): 1. doi: 10.52396/JUSTC-2022-0037
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Quantum state tomography provides a key tool for validating and fully exploiting quantum resources. However, current protocols of pure-state informationally-complete (PS-IC) measurement settings generally involve various multi-qubit gates or complex quantum algorithms, which are not practical for large systems. In this study, we present an adaptive approach to $N$-qubit pure-state tomography with Pauli measurements. First, projective measurements on each qubit in the Z-direction were implemented to determine the amplitude of each base of the target state. Then, a set of Pauli measurement settings was recursively deduced by the Z-measurement results, which can be used to determine the phase of each base. The number of required measurement settings is $O(N)$ for certain quantum states, including cluster and W states. Finally, we numerically verified the feasibility of our strategy by reconstructing a 1-D chain state using a neural network algorithm.
Non-Hermitian skin effect in a spin-orbit-coupled Bose-Einstein condensate
Haowei Li, Xiaoling Cui, Wei Yi
2022, 52(8): 2. doi: 10.52396/JUSTC-2022-0003
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We study a Bose-Einstein condensate of ultracold atoms subject to a non-Hermitian spin-orbit coupling, where the system acquires the non-Hermitian skin effect under the interplay of spin-orbit coupling and laser-induced atom loss. The presence of the non-Hermitian skin effect is confirmed through its key signatures in terms of the spectral winding under the periodic boundary condition, the accumulation of eigen wavefunctions at boundaries under an open boundary condition, and bulk dynamics signaled by a directional flow. We show that bulk dynamics, in particular, serves as a convenient signal for experimental detection. The impact of interaction and trapping potentials is also discussed based on the non-Hermitian Gross-Pitaevskii equations. Our work demonstrates that the non-Hermitian skin effect and its rich implications in topology, dynamics, and beyond are well within the reach of current cold-atom experiments.
Mathematics
Intersection complex via residues
Xiaojin Lin
2022, 52(8): 3. doi: 10.52396/JUSTC-2021-0263
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We provide an intrinsic algebraic definition of the intersection complex for a variety.
Sparse linear discriminant analysis via ℓ0 constraint
Qi Yin, Lei Shu
2022, 52(8): 4. doi: 10.52396/JUSTC-2022-0045
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We consider the problem of interpretable classification in a high-dimensional setting, where the number of features is extremely large and the number of observations is limited. This setting has been extensively studied in the chemometric literature and has recently become pervasive in the biological and medical literature. Linear discriminant analysis (LDA) is a canonical approach for solving this problem. However, in the case of high dimensions, LDA is unsuitable for two reasons. First, the standard estimate of the within-class covariance matrix is singular; therefore, the usual discriminant rule cannot be applied. Second, when $p$ is large, it is difficult to interpret the classification rules obtained from LDA because $p$ features are involved. In this setting, motivated by the success of the primal-dual active set algorithm for best subset selection, we propose a method for sparse linear discriminant analysis via $\ell_0$ constraint, which imposes a sparsity criterion when performing linear discriminant analysis, allowing classification and feature selection to be performed simultaneously. Numerical results on synthetic and real data suggest that our method obtains competitive results compared with existing alternative methods.
Chemistry
Boosting photocatalytic Suzuki coupling reaction over Pd nanoparticles by regulating Pd/MOF interfacial electron transfer
Zi-Xuan Sun, Hai-Long Jiang
2022, 52(8): 5. doi: 10.52396/JUSTC-2022-0063
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Palladium-catalyzed C-C coupling reactions are of significant importance, but they often require harsh conditions. Herein, we report an interface-regulated photocatalytic Suzuki coupling reaction over Pd nanoparticles supported on a metal-organic framework (MOF), ZIF-8. Two Pd/MOFs were synthesized, PdPVP/ZIF-8 and Pd/ZIF-8, which have similar Pd sizes and loading amounts, except that the former contains poly(vinylpyrrolidone) (PVP) as a surfactant. The diffuse-reflectance infrared Fourier transform of CO adsorption (CO-DRIFT) indicates that Pd/ZIF-8 represents a more negative electronic state of Pd than PdPVP/ZIF-8. In the photocatalytic Suzuki coupling reaction between iodobenzene and phenylboronic acid, Pd/ZIF-8 exhibits excellent performance (99.1% yield), much better than that of PdPVP/ZIF-8 (57.9% yield). Moreover, Pd/ZIF-8 is highly stable and shows broad substrate scope for this reaction. The superior activity of Pd/ZIF-8 can be attributed to sufficient electron transfer between the MOFs and Pd nanoparticles in the absence of an interfacial surfactant. This work provides new insights into a Pd-catalyzed C-C coupling reaction involving photocatalysis and interfacial electron transfer.
Three-dimensional tubular carbon aerogel for supercapacitors
Qiguo Shang, Jie Xu, Jianwei Liu
2022, 52(8): 6. doi: 10.52396/JUSTC-2022-0065
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A three-dimensional elastic carbon nanotube aerogel is fabricated via a simple solution-based strategy using Te nanowires as templates, which can be recycled. The pipe diameter and wall thickness of the carbon nanotube are strongly dependent on the diameter of the Te nanowires and carbon source. The obtained free-standing carbon nanotube aerogel with a large specific surface area (up to 1865 m2∙g-1) is promising as an electrode material for supercapacitors. After combination with MnO2, the capacitor exhibits a specific capacitance of 360.4 F∙g-1 at a current of 1 A∙g-1 and retention of 97% after 2000 cycles. The high power capabilities and good stability make it a promising candidate as an electrode for supercapacitors.
Management
An advance selling strategy with a trade-in program
Jie Wu, Junjie Huang, Xiang Ji, Zhixin Chen
2022, 52(8): 7. doi: 10.52396/JUSTC-2021-0250
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Recently, advance selling and trade-in programs have become increasingly popular in many industries. While previous studies have examined these two strategies individually, the combination of both strategies has not been studied. Inspired by business practices, we investigate an emerging advance selling strategy (hereinafter, the AT strategy) that utilizes the trade-in concept as a reward or discount for participating in the advance selling program. This study explores a seller’s optimal pricing decision and profit when using the AT strategy, traditional advance selling (AS), and traditional trade-in (TN) strategies. We find that, compared to AT strategy, it is better for the seller to adopt the AS strategy when the salvage value of used products is sufficiently low and the product cost is not too small. In addition, compared to TN, when the salvage value and product cost are relatively low, the seller should adopt the AT strategy under most circumstances. Furthermore, we demonstrate that sellers can still gain profits when the product price is extremely high under the AT strategy. Even if consumer utility is negative during the advance selling period, consumers are willing to participate in AT programs because the total consumer surplus from buying two generations of products is positive.
The optimization and selection of venture capital incentive policies under uncertain condition
Wenjun Yan, Jiaqi Zhang, Jianing Xu, Haonan He, Shanyong Wang
2022, 52(8): 8. doi: 10.52396/JUSTC-2022-0011
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Venture capital is crucial innovation capital. A venture capital option game model is constructed to obtain an incentive strategy that drives venture capital to actively allocate resources to support innovation based on risk subsidies and tax incentives. Moreover, the implementation effect of venture capital incentive policies under the value-uncertain condition of the entrepreneurial enterprise is studied. The results illustrate that when the uncertainty of the value of the entrepreneurial enterprise is less than the threshold, the tax preference policy is more effective in accelerating the investment decision-making of venture capital institutions. In contrast, the two policies have identical effects. When the uncertainty of the value of the entrepreneurial enterprise is less than the threshold, the risk subsidy policy has a better effect on increasing the investment scale of venture capital institutions, while the two policies have the same effect.

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