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TCAS-PINN: Physics-informed neural networks with a novel temporal causality-based adaptive sampling method

Jia Guo, Haifeng Wang, Shilin Gu, and Chenping Hou

Chin. Phys. B, 2024, 33 (5): 050701. DOI: 10.1088/1674-1056/ad21f3

Abstract （3）

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Physics-informed neural networks (PINNs) have become an attractive machine learning framework for obtaining solutions to partial differential equations (PDEs). PINNs embed initial, boundary, and PDE constraints into the loss function. The performance of PINNs is generally affected by both training and sampling. Specifically, training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs, and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished. However, a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category, namely, time-dependent PDEs, where temporal information plays a key role in the algorithms used. There is one method, called Causal PINN, that considers temporal causality at the training level but not special temporal utilization at the sampling level. Incorporating temporal knowledge into sampling remains to be studied. To fill this gap, we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality. By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain, we provide a practical solution by incorporating temporal information into sampling. Numerical experiments of several nonlinear time-dependent PDEs, including the Cahn-Hilliard, Korteweg-de Vries, Allen-Cahn and wave equations, show that our proposed sampling method can improve the performance. We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods, especially when points are limited.

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Quantum control based on three forms of Lyapunov functions

Guo-Hui Yu(俞国慧) and Hong-Li Yang(杨洪礼)

Chin. Phys. B, 2024, 33 (4): 040201. DOI: 10.1088/1674-1056/ad11e6

Abstract （36）

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This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors. In this paper, the specific control laws under the three forms are given. Stability is analyzed by the LaSalle invariance principle and the numerical simulation is carried out in a 2D test system. The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm. Finally, a unified form of the control laws under the three forms is given.

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Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton

Qiao-Hong Han(韩巧红) and Man Jia(贾曼)

Chin. Phys. B, 2024, 33 (4): 040202. DOI: 10.1088/1674-1056/ad1822

Abstract （43）

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Integrable systems play a crucial role in physics and mathematics. In particular, the traditional (1+1)-dimensional and (2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions. Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from (1+1)-dimensional integrable systems by using a deformation algorithm. Here we establish a new (2+1)-dimensional Chen—Lee—Liu (C—L—L) equation using the deformation algorithm from the (1+1)-dimensional C—L—L equation. The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the (1+1)-dimension. It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C—L—L equation and its reciprocal transformation. The traveling wave solutions are derived in implicit function expression, and some asymmetry peakon solutions are found.

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Thermal-contact capacity of one-dimensional attractive Gaudin—Yang model

Xiao-Min Zhang(张小敏), Song Cheng(程颂), and Yang-Yang Chen(陈洋洋)

Chin. Phys. B, 2024, 33 (4): 040203. DOI: 10.1088/1674-1056/ad21f4

Abstract （27）

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Tan's contact $\mathcal{C}$ is an important quantity measuring the two-body correlations at short distances in a dilute system. Here we make use of the technique of exactly solved models to study the thermal-contact capacity $\mathcal{K}_{\scriptscriptstyle{\rm T}}$, i.e., the derivative of $\mathcal{C}$ with respect to temperature in the attractive Gaudin—Yang model. It is found that $\mathcal{K}_{\scriptscriptstyle{\rm T}}$ is useful in identifying the low temperature phase diagram, and using the obtained analytical expression of $\mathcal{K}_{\scriptscriptstyle{\rm T}}$, we study its critical behavior and the scaling law. Especially, we show $\mathcal{K}_{\scriptscriptstyle{\rm T}}$ versus temperature and thus the non-monotonic tendency of $\mathcal{C}$ in a tiny interval, for both spin-balanced and imbalanced phases. Such a phenomenon is merely observed in multi-component systems such as $SU(2)$ Fermi gases and spinor bosons, indicating the crossover from the Tomonaga—Luttinger liquid to the spin-coherent liquid.

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Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

Wenying Mu(穆文英), Bo Zhuang(庄波), and Fang Qiu(邱芳)

Chin. Phys. B, 2024, 33 (4): 040204. DOI: 10.1088/1674-1056/ad1a8c

Abstract （29）

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We develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network. It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network. For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed. In an event-triggered system, when an error signal exceeds a specified time-varying threshold, it indicates the occurrence of a typical event. The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed. Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs. A simulation example is finally used to verify that the effectiveness of such a control strategy can enhance the system performance.

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Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

Yayong Wu(吴亚勇), Xinwei Wang(王欣伟), and Guo-Ping Jiang(蒋国平)

Chin. Phys. B, 2024, 33 (4): 040205. DOI: 10.1088/1674-1056/ad20d7

Abstract （27）

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In many engineering networks, only a part of target state variables are required to be estimated. On the other hand, multi-layer complex network exists widely in practical situations. In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied. A suitable functional state observer is constructed with the limited measurement. The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem. Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained. Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states. Thus, it can greatly reduce the placement of observers and computational cost. Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.

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Cryptanalysis of efficient semi-quantum secret sharing protocol using single particles

Gan Gao(高甘)

Chin. Phys. B, 2024, 33 (4): 040301. DOI: 10.1088/1674-1056/ad2bee

Abstract （23）

PDF （405KB）（6）

In paper [Chin. Phys. B 32 070308 (2023)], Xing et al. proposed a semi-quantum secret sharing protocol by using single particles. We study the security of the proposed protocol and find that it is not secure, that is, the three dishonest agents, Bob, Charlie and Emily can collude to obtain Alice's secret without the help of David.

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Integer multiple quantum image scaling based on NEQR and bicubic interpolation

Shuo Cai(蔡硕), Ri-Gui Zhou(周日贵), Jia Luo(罗佳), and Si-Zhe Chen(陈思哲)

Chin. Phys. B, 2024, 33 (4): 040302. DOI: 10.1088/1674-1056/ad1b40

Abstract （35）

PDF （1951KB）（9）

As a branch of quantum image processing, quantum image scaling has been widely studied. However, most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation, the quantum version of bicubic interpolation has not yet been studied. In this work, we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation (NEQR). Our scheme can realize synchronous enlargement and reduction of the image with the size of 2ⁿ×2ⁿ by integral multiple. Firstly, the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules. Then, 16 neighborhood pixels are obtained by quantum operation circuits, and the corresponding weights of these pixels are calculated by quantum arithmetic modules. Finally, a quantum matrix operation, instead of a classical convolution operation, is used to realize the sum of convolution of these pixels. Through simulation experiments and complexity analysis, we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm, and has better effect than the quantum version of bilinear interpolation.

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Analysis of learnability of a novel hybrid quantum—classical convolutional neural network in image classification

Tao Cheng(程涛), Run-Sheng Zhao(赵润盛), Shuang Wang(王爽), Rui Wang(王睿), and Hong-Yang Ma(马鸿洋)

Chin. Phys. B, 2024, 33 (4): 040303. DOI: 10.1088/1674-1056/ad1926

Abstract （42）

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We design a new hybrid quantum—classical convolutional neural network (HQCCNN) model based on parameter quantum circuits. In this model, we use parameterized quantum circuits (PQCs) to redesign the convolutional layer in classical convolutional neural networks, forming a new quantum convolutional layer to achieve unitary transformation of quantum states, enabling the model to more accurately extract hidden information from images. At the same time, we combine the classical fully connected layer with PQCs to form a new hybrid quantum—classical fully connected layer to further improve the accuracy of classification. Finally, we use the MNIST dataset to test the potential of the HQCCNN. The results indicate that the HQCCNN has good performance in solving classification problems. In binary classification tasks, the classification accuracy of numbers 5 and 7 is as high as 99.71%. In multivariate classification, the accuracy rate also reaches 98.51%. Finally, we compare the performance of the HQCCNN with other models and find that the HQCCNN has better classification performance and convergence speed.

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Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism

Run-Sheng Zhao(赵润盛), Hong-Yang Ma(马鸿洋), Tao Cheng(程涛), Shuang Wang(王爽), and Xing-Kui Fan(范兴奎)

Chin. Phys. B, 2024, 33 (4): 040304. DOI: 10.1088/1674-1056/ad02e7

Abstract （59）

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Readout errors caused by measurement noise are a significant source of errors in quantum circuits, which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum (NISQ) computing. In this paper, we use the bit-flip averaging (BFA) method to mitigate frequent readout errors in quantum generative adversarial networks (QGAN) for image generation, which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance, successfully solving problems with high cost of measurement for traditional error mitigation methods. Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method, the Kullback—Leibler (KL) divergence of the generated images converges to 0.04, 0.05, and 0.1 for readout error probabilities of p=0.01, p=0.05, and p=0.1, respectively. Additionally, by evaluating the fidelity of the quantum states representing the images, we observe average fidelity values of 0.97, 0.96, and 0.95 for the three readout error probabilities, respectively. These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models.

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Coherence of nonlinear Bloch dynamics of Bose—Einstein condensates in deep optical lattices

Ai-Xia Zhang(张爱霞), Wei Zhang(张薇), Jie Wang(王杰), Xiao-Wen Hu(胡潇文), Lai-Lai Mi(米来来), and Ju-Kui Xue(薛具奎)

Chin. Phys. B, 2024, 33 (4): 040305. DOI: 10.1088/1674-1056/ad1b46

Abstract （24）

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Atomic interaction leads to dephasing and damping of Bloch oscillations (BOs) in optical lattices, which limits observation and applications of BOs. How to obtain persistent BOs is particularly important. Here, the nonlinear Bloch dynamics of the Bose—Einstein condensate with two-body and three-body interactions in deep optical lattices is studied. The damping rate induced by interactions is obtained. The damping induced by two-body interaction plays a dominant role, while the damping induced by three-body interaction is weak. However, when the two-body and three-body interactions satisfy a threshold, long-lived coherent BOs are observed. Furthermore, the Bloch dynamics with periodical modulation of linear force is studied. The frequencies of linear force corresponding to resonance and pseudoresonance are obtained, and rich dynamical phenomena, i.e., stable and strong BOs, drifting and dispersion of wave packet, are predicted. The controllable Bloch dynamics is provided with the periodic modulation of the linear force.

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Double quantum images encryption scheme based on chaotic system

She-Xiang Jiang(蒋社想), Yang Li(李杨), Jin Shi(石锦), and Ru Zhang(张茹)

Chin. Phys. B, 2024, 33 (4): 040306. DOI: 10.1088/1674-1056/ad1174

Abstract （22）

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This paper explores a double quantum images representation (DNEQR) model that allows for simultaneous storage of two digital images in a quantum superposition state. Additionally, a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated, offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps. Based on the DNEQR model and the hyperchaotic system, a double quantum images encryption algorithm is proposed. Firstly, two classical plaintext images are transformed into quantum states using the DNEQR model. Then, the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences. These chaotic sequences are utilized to perform pixel value and position operations on the quantum image, resulting in changes to both pixel values and positions. Finally, the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences. The corresponding quantum circuits are also given. Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission, improves the encryption efficiency, and enhances anti-interference and anti-attack capabilities.

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Recurrent neural network decoding of rotated surface codes based on distributed strategy

Fan Li(李帆), Ao-Qing Li(李熬庆), Qi-Di Gan(甘启迪), and Hong-Yang Ma(马鸿洋)

Chin. Phys. B, 2024, 33 (4): 040307. DOI: 10.1088/1674-1056/ad2bef

Abstract （31）

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Quantum error correction is a crucial technology for realizing quantum computers. These computers achieve fault-tolerant quantum computing by detecting and correcting errors using decoding algorithms. Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models. In this paper, we use a distributed decoding strategy, which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases. Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder. The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy. Then we test the decoding performance of our distributed strategy decoder, recurrent neural network decoder, and the classic minimum weight perfect matching (MWPM) decoder for rotated surface codes with different code distances under the circuit noise model, the thresholds of these three decoders are about 0.0052, 0.0051, and 0.0049, respectively. Our results demonstrate that the distributed strategy decoder outperforms the other two decoders, achieving approximately a 5 % improvement in decoding efficiency compared to the MWPM decoder and approximately a 2 % improvement compared to the recurrent neural network decoder.

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Non-Gaussian quantum states generated via quantum catalysis and their statistical properties

Xiao-Yan Zhang(张晓燕), Chun-Yan Yang(杨春燕), Ji-Suo Wang(王继锁), and Xiang-Guo Meng(孟祥国)

Chin. Phys. B, 2024, 33 (4): 040308. DOI: 10.1088/1674-1056/ad2a74

Abstract （21）

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A new kind of non-Gaussian quantum catalyzed state is proposed via multiphoton measurements and two-mode squeezing as an input of thermal state. The characteristics of the generated multiphoton catalysis output state depends on the thermal parameter, catalyzed photon number and squeezing parameter. We then analyze the nonclassical properties by examining the photon number distribution, photocount distribution and partial negativity of the Wigner function. Our findings indicate that nonclassicality can be achieved through the implementation of multiphoton catalysis operations and modulated by the thermal parameter, catalyzed photon number and squeezing parameter.

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Harmonic balance simulation of the influence of component uniformity and reliability on the performance of a Josephson traveling wave parametric amplifier

Yuzhen Zheng(郑煜臻), Kanglin Xiong(熊康林), Jiagui Feng(冯加贵), and Hui Yang(杨辉)

Chin. Phys. B, 2024, 33 (4): 040401. DOI: 10.1088/1674-1056/ad0624

Abstract （31）

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A Josephson traveling wave parametric amplifier (JTWPA), which is a quantum-limited amplifier with high gain and large bandwidth, is the core device of large-scale measurement and control systems for quantum computing. A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching. Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics, the fabrication of a JTWPA typically necessitates precise processing equipment. To guide the fabrication process and further improve the design for manufacturability, it is necessary to understand how each electronic component affects the amplifier. In this paper, we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA. The results provide insightful and scientific guidance for device design and fabrication processes.

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Thermodynamics in a quantum corrected Reissner—Nordström—AdS black hole and its GUP-corrections

Jian-Jun Song(宋建君) and Cheng-Zhou Liu(刘成周)

Chin. Phys. B, 2024, 33 (4): 040402. DOI: 10.1088/1674-1056/ad1a8a

Abstract （27）

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We calculate the thermodynamic quantities in the quantum corrected Reissner—Nordström—AdS (RN-AdS) black hole, and examine their quantum corrections. By analyzing the mass and heat capacity, we give the critical state and the remnant state, respectively, and discuss their consistency. Then, we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method, and charged massive boson W^± and fermions by using the Hamilton—Jacob method. It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods. Next, by using the generalized uncertainty principle (GUP), we study the quantum corrections to the tunneling and the temperature. Then the logarithmic correction to the black hole entropy is obtained.

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View of thermodynamic phase transition of the charged Gauss—Bonnet AdS black hole via the shadow

Ke-Jian He(何柯腱), Sen Guo(郭森), Zhi Luo(罗智), and Guo-Ping Li(李国平)

Chin. Phys. B, 2024, 33 (4): 040403. DOI: 10.1088/1674-1056/ad225d

Abstract （20）

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We examine thermodynamic phase transition (PT) of the charged Gauss—Bonnet AdS black hole (BH) by utilizing the shadow radius. In this system, we rescale the corresponding Gauss—Bonnet coefficient α by a factor of 1/(D-4), and ensure that α is positive to avoid any singularity problems. The equation derived for the shadow radius indicates that it increases as the event horizon radius increases, making it an independent variable for determining BH temperature. By investigating the PT curve in relation to shadows, we can observe that the shadow radius can be used as an alternative to the event horizon radius in explaining the phenomenon of BH PT. Furthermore, the results indicate that an increase in the parameter α corresponds to a decrease in the temperature of the BH. By utilizing the relationship between the temperature and the shadow radius, it is possible to obtain the thermal profile of the Gauss—Bonnet AdS BH. It is evident that there is an N-type variation in temperature for pressures P<P_c. Additionally, as the parameter α increases, the region covered by shadow expands while the temperature decreases. The utilization of BH shadows as a probe holds immense significance in gaining a deeper understanding of BH thermodynamic behavior.

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Computing large deviation prefactors of stochastic dynamical systems based on machine learning

Yang Li(李扬), Shenglan Yuan(袁胜兰), Linghongzhi Lu(陆凌宏志), and Xianbin Liu(刘先斌)

Chin. Phys. B, 2024, 33 (4): 040501. DOI: 10.1088/1674-1056/ad12a8

Abstract （29）

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We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise. We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning. More specifically, we design a neural network framework to compute quasipotential, most probable paths and prefactors based on the orthogonal decomposition of a vector field. We corroborate the higher effectiveness and accuracy of our algorithm with two toy models. Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.

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Influencer identification of dynamical networks based on an information entropy dimension reduction method

Dong-Li Duan(段东立), Si-Yuan Ji(纪思源), and Zi-Wei Yuan(袁紫薇)

Chin. Phys. B, 2024, 33 (4): 040502. DOI: 10.1088/1674-1056/ad102e

Abstract （31）

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Identifying critical nodes or sets in large-scale networks is a fundamental scientific problem and one of the key research directions in the fields of data mining and network science when implementing network attacks, defense, repair and control. Traditional methods usually begin from the centrality, node location or the impact on the largest connected component after node destruction, mainly based on the network structure. However, these algorithms do not consider network state changes. We applied a model that combines a random connectivity matrix and minimal low-dimensional structures to represent network connectivity. By using mean field theory and information entropy to calculate node activity, we calculated the overlap between the random parts and fixed low-dimensional parts to quantify the influence of node impact on network state changes and ranked them by importance. We applied this algorithm and the proposed importance algorithm to the overall analysis and stratified analysis of the C. elegans neural network. We observed a change in the critical entropy of the network state and by utilizing the proposed method we can calculate the nodes that indirectly affect muscle cells through neural layers.

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Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

Heyang Ma(马赫阳), Wanzhou Zhang(张万舟), Yanting Tian(田彦婷), Chengxiang Ding(丁成祥), and Youjin Deng(邓友金)

Chin. Phys. B, 2024, 33 (4): 040503. DOI: 10.1088/1674-1056/ad1d4d

Abstract （30）

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The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.

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