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Solving quantum rotor model with different Monte Carlo techniques

Weilun Jiang(姜伟伦), Gaopei Pan(潘高培), Yuzhi Liu(刘毓智), and Zi-Yang Meng(孟子杨)

Chin. Phys. B, 2022, 31 (4): 040504. DOI: 10.1088/1674-1056/ac4f52

Abstract （779）

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We systematically test the performance of several Monte Carlo update schemes for the (2+1)d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) schemes, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z₂ topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.

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LnCu₃(OH)₆Cl₃ (Ln = Gd, Tb, Dy): Heavy lanthanides on spin-1/2 kagome magnets

Ying Fu(付盈), Lianglong Huang(黄良龙), Xuefeng Zhou(周雪峰), Jian Chen(陈见), Xinyuan Zhang(张馨元), Pengyun Chen(陈鹏允), Shanmin Wang(王善民), Cai Liu(刘才), Dapeng Yu(俞大鹏), Hai-Feng Li(李海峰), Le Wang(王乐), and Jia-Wei Mei(梅佳伟)

Chin. Phys. B, 2021, 30 (10): 100601. DOI: 10.1088/1674-1056/ac1e20

Abstract （731）

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The spin-1/2 kagome antiferromagnets are key prototype materials for studying frustrated magnetism. Three isostructural kagome antiferromagnets LnCu₃(OH)₆Cl₃ (Ln = Gd, Tb, Dy) have been successfully synthesized by the hydrothermal method. LnCu₃(OH)₆Cl₃ adopts space group P3m1 and features the layered Cu-kagome lattice with lanthanide Ln³⁺ cations sitting at the center of the hexagons. Although heavy lanthanides (Ln = Gd, Tb, Dy) in LnCu₃(OH)₆Cl₃ provide a large effective magnetic moment and ferromagnetic-like spin correlations compared to light-lanthanides (Nd, Sm, Eu) analogues, Cu-kagome holds an antiferromagnetically ordered state at around 17 K like YCu₃(OH)₆Cl₃.

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Quantum algorithm for neighborhood preserving embedding

Shi-Jie Pan(潘世杰), Lin-Chun Wan(万林春), Hai-Ling Liu(刘海玲), Yu-Sen Wu(吴宇森), Su-Juan Qin(秦素娟), Qiao-Yan Wen(温巧燕), and Fei Gao(高飞)

Chin. Phys. B, 2022, 31 (6): 060304. DOI: 10.1088/1674-1056/ac523a

Abstract （588）

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Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (i) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (ii) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve a significant speedup compared to Liang et al.'s algorithm even without considering the complexity of the VQA.

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Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

Kaiyuan Cao(曹凯源), Ming Zhong(钟鸣), and Peiqing Tong(童培庆)

Chin. Phys. B, 2022, 31 (6): 060505. DOI: 10.1088/1674-1056/ac4a6e

Abstract （576）

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We study the dynamical quantum phase transitions (DQPTs) in the $XY$ chains with the Dzyaloshinskii-Moriya interaction and the $XZY$-$YZX$ type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form $H=\sum_{k}ǎrepsilon_{k}(\eta^{†}_{k}\eta_{k}-\frac{1}{2})$, where the quasiparticle excitation spectra $ǎrepsilon_{k}$ may be smaller than 0 for some $k$ and are asymmetrical ($ǎrepsilon_{k}\neqǎrepsilon_{-k}$). It is found that the factors of Loschmidt echo equal 1 for some $k$ corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying $ǎrepsilon_{k}\cdotǎrepsilon_{-k}<0$, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general $XY$ chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.

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Adaptive synchronization of chaotic systems with less measurement and actuation

Shun-Jie Li(李顺杰), Ya-Wen Wu(吴雅文), and Gang Zheng(郑刚)

Chin. Phys. B, 2021, 30 (10): 100503. DOI: 10.1088/1674-1056/abec33

Abstract （542）

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We investigate the synchronization problem between identical chaotic systems only when necessary measurement (output) and actuation (input) are needed to be implemented by the adaptive controllers. A sufficient condition is derived based on the Lyapunov stability theory and Schur complementary lemma. Moreover, the theoretic result is applied to the Rikitake system and the hyperchaotic Liu system to show its effectiveness and correctness. Numerical simulations are presented to verify the results.

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Hardware for multi-superconducting qubit control and readout

Zhan Wang(王战), Hai Yu(于海), Rongli Liu(刘荣利), Xiao Ma(马骁), Xueyi Guo(郭学仪), Zhongcheng Xiang(相忠诚), Pengtao Song(宋鹏涛), Luhong Su(苏鹭红), Yirong Jin(金贻荣), and Dongning Zheng(郑东宁)

Chin. Phys. B, 2021, 30 (11): 110305. DOI: 10.1088/1674-1056/ac0425

Abstract （527）

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We have developed an electronic hardware system for the control and readout of multi-superconducting qubit devices. The hardware system is based on the design ideas of good scalability, high synchronization and low latency. The system, housed inside a VPX-6U chassis, includes multiple arbitrary-waveform generator (AWG) channels, analog-digital-converter (ADC) channels as well as direct current source channels. The system can be used for the control and readout of up to twelve superconducting transmon qubits in one chassis, and control and readout of more and more qubit can be carried out by interconnecting the chassis. By using field programmable gate array (FPGA) processors, the system incorporates three features that are specifically useful for superconducting qubit research. Firstly, qubit signals can be processed using the on-board FPGA after being acquired by ADCs, significantly reducing data processing time and data amount for storage and transmission. Secondly, different output modes, such as direct output and sequential output modes, of AWG can be implemented with pre-encoded FPGA. Thirdly, with data acquisition ADCs and control AWGs jointly controlled by the same FPGA, the feedback latency can be reduced, and in our test a 178.4 ns latency time is realized. This is very useful for future quantum feedback experiments. Finally, we demonstrate the functionality of the system by applying the system to the control and readout of a 10 qubit superconducting quantum processor.

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Real-space parallel density matrix renormalization group with adaptive boundaries

Fu-Zhou Chen(陈富州), Chen Cheng(程晨), and Hong-Gang Luo(罗洪刚)

Chin. Phys. B, 2021, 30 (8): 080202. DOI: 10.1088/1674-1056/abeb08

Abstract （525）

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We propose an improved real-space parallel strategy for the density matrix renormalization group (DMRG) method, where boundaries of separate regions are adaptively distributed during DMRG sweeps. Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks, compared with the original real-space parallel DMRG with fixed boundaries. We implement our new strategy based on the message passing interface (MPI), and dynamically control the number of kept states according to the truncation error in each DMRG step. We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule. The maximum parallel efficiencies for these two models are 91% and 76% in 4 nodes, which are much higher than the real-space parallel DMRG with fixed boundaries.

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Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients

Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫)

Chin. Phys. B, 2021, 30 (11): 110202. DOI: 10.1088/1674-1056/abff31

Abstract （520）

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The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics, physics, biological fluid mechanics, oceanography, etc. Using the reductive perturbation theory and long wave approximation, the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrödinger (NLS) equations with variable coefficients. The third-order nonlinear Schrödinger equation is degenerated into a completely integrable Sasa-Satsuma equation (SSE) whose solutions can be used to approximately simulate the real rogue waves in the vessels. For the first time, we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves. Based on the traveling wave solutions of the fourth-order nonlinear Schrödinger equation, we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall. Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube. The high-order nonlinear and dispersion terms lead to the distortion of the wave, while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.

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Stabilization strategy of a car-following model with multiple time delays of the drivers

Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞)

Chin. Phys. B, 2021, 30 (12): 120506. DOI: 10.1088/1674-1056/abfcc9

Abstract （517）

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An extended car-following model with multiple delays is constructed to describe driver's driving behavior. Through stability analysis, the stability condition of this uncontrolled model is given. To dampen the negative impact of the driver's multiple delays (i.e., stability condition is not satisfied), a novel control strategy is proposed to assist the driver in adjusting vehicle operation. The control strategy consists of two parts:the design of control term as well as the design of the parameters in the term. Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms. In the course of the design of parameters in the control term, we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation, which can determine the appropriate parameters in the control terms more quickly. Finally, in the case study, we validate the control strategy by utilizing measured data and configuring scenario, which is closer to the actual traffic. The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver's delays.

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Realization of simultaneous balanced multi-outputs for multi-protocols QKD decoding based onsilica-based planar lightwave circuit

Jin You(游金), Yue Wang(王玥), and Jun-Ming An(安俊明)

Chin. Phys. B, 2021, 30 (8): 080302. DOI: 10.1088/1674-1056/abe2ff

Abstract （504）

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Silica-based planar lightwave circuit (PLC) devices can reduce transmission loss and cost in a quantum key distribution (QKD) system, and have potential applications in integration and production. A PLC-based quantum decoding integrated chip for multi-protocols is designed and fabricated, which is composed of variable optical splitters (VOSs), asymmetric Mach-Zehnder interferometers (AMZIs), and variable directional couplers (VDCs). Balanced pulse-pairs of four outputs are obtained simultaneously with measured delay times of 405 ps and 402 ps, respectively. The chip has advantages in achieving high interference visibility and low quantum bit error rate (QBER).

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Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map

Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦)

Chin. Phys. B, 2022, 31 (8): 080504. DOI: 10.1088/1674-1056/ac5a43

Abstract （492）

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We present a new cosine chaotic mapping proved by chaos theory test and analysis such that the system has good cryptography properties, wide chaos range, simple structure, and good sensitivity to initial value, and the mapping can meet the needs of chaotic image encryption. Based on the cosine chaotic system, we propose a new encryption method. First, according to the cyclic characteristics of the mapping, the cyclic information wave is simulated. Second, the quasi-Doppler effect is used to synchronously scramble and diffuse the image to obfuscate the original pixel. Finally, the XOR diffusion of image pixels is carried out by information wave to further enhance the encryption effect. Simulation experiment and security analysis show that the algorithm has good security, can resist the common attack mode, and has good efficiency.

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A sign-function receiving scheme for sine signals enhanced by stochastic resonance

Zhao-Rui Li(李召瑞), Bo-Hang Chen(陈博航), Hui-Xian Sun(孙慧贤), Guang-Kai Liu(刘广凯), and Shi-Lei Zhu(朱世磊)

Chin. Phys. B, 2021, 30 (8): 080502. DOI: 10.1088/1674-1056/abfccc

Abstract （472）

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To address the problem that it is difficult to detect an intermediate frequency (IF) signal at the receiving end of a communication system under extremely low signal-to-noise ratio (SNR) conditions, we propose a stochastic resonance (SR)-enhanced sine-signal detection method based on the sign function. By analyzing the SR mechanism of the sine signal and combining it with the characteristics of a dual-sequence frequency-hopping (DSFH) receiver, a periodic stationary solution of the Fokker-Planck equation (FPE) with a time parameter is obtained. The extreme point of the sine signal is selected as the decision time, and the force law of the electromagnetic particles is analyzed. A receiving structure based on the sign function is proposed to maximize the output difference of the system, and the value condition of the sign function is determined. In order to further improve the detection performance, in combination with the central-limit theorem, the sampling points are averaged N times, and the signal-detection problem is transformed into a hypothesis-testing problem under a Gaussian distribution. The theoretical analysis and simulation experiment results confirm that when N is 100 and the SNR is greater than 20 dB, the bit-error ratio (BER) is less than 1.5×10^-2 under conditions in which the signal conforms to the optimal SR parameters.

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Determination of quantum toric error correction code threshold using convolutional neural network decoders

Hao-Wen Wang(王浩文), Yun-Jia Xue(薛韵佳), Yu-Lin Ma(马玉林), Nan Hua(华南), and Hong-Yang Ma(马鸿洋)

Chin. Phys. B, 2022, 31 (1): 010303. DOI: 10.1088/1674-1056/ac11e3

Abstract （472）

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Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers. In order to find the best syndrome of the stabilizer code in quantum error correction, we need to find a fast and close to the optimal threshold decoder. In this work, we build a convolutional neural network (CNN) decoder to correct errors in the toric code based on the system research of machine learning. We analyze and optimize various conditions that affect CNN, and use the RestNet network architecture to reduce the running time. It is shortened by 30%-40%, and we finally design an optimized algorithm for CNN decoder. In this way, the threshold accuracy of the neural network decoder is made to reach 10.8%, which is closer to the optimal threshold of about 11%. The previous threshold of 8.9%-10.3% has been slightly improved, and there is no need to verify the basic noise.

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Memristor-based multi-synaptic spiking neuron circuit for spiking neural network

Wenwu Jiang(蒋文武), Jie Li(李杰), Hongbo Liu(刘洪波), Xicong Qian(钱曦聪), Yuan Ge(葛源), Lidan Wang(王丽丹), and Shukai Duan(段书凯)

Chin. Phys. B, 2022, 31 (4): 040702. DOI: 10.1088/1674-1056/ac380b

Abstract （472）

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Spiking neural networks (SNNs) are widely used in many fields because they work closer to biological neurons. However, due to its computational complexity, many SNNs implementations are limited to computer programs. First, this paper proposes a multi-synaptic circuit (MSC) based on memristor, which realizes the multi-synapse connection between neurons and the multi-delay transmission of pulse signals. The synapse circuit participates in the calculation of the network while transmitting the pulse signal, and completes the complex calculations on the software with hardware. Secondly, a new spiking neuron circuit based on the leaky integrate-and-fire (LIF) model is designed in this paper. The amplitude and width of the pulse emitted by the spiking neuron circuit can be adjusted as required. The combination of spiking neuron circuit and MSC forms the multi-synaptic spiking neuron (MSSN). The MSSN was simulated in PSPICE and the expected result was obtained, which verified the feasibility of the circuit. Finally, a small SNN was designed based on the mathematical model of MSSN. After the SNN is trained and optimized, it obtains a good accuracy in the classification of the IRIS-dataset, which verifies the practicability of the design in the network.

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Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves

Ping Liu(刘萍), Bing Huang(黄兵), Bo Ren(任博), and Jian-Rong Yang(杨建荣)

Chin. Phys. B, 2021, 30 (8): 080203. DOI: 10.1088/1674-1056/ac052a

Abstract （469）

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We study a forced variable-coefficient extended Korteweg-de Vries (KdV) equation in fluid dynamics with respect to internal solitary wave. Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevé expansion. When the variable coefficients are time-periodic, the wave function evolves periodically over time. Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations. One-parameter group transformations and one-parameter subgroup invariant solutions are presented. Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method. The consistent Riccati expansion (CRE) solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE. Interaction phenomenon between cnoidal waves and solitary waves can be observed. Besides, the interaction waveform changes with the parameters. When the variable parameters are functions of time, the interaction waveform will be not regular and smooth.

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Heterogeneous dual memristive circuit: Multistability, symmetry, and FPGA implementation

Yi-Zi Cheng(承亦梓), Fu-Hong Min(闵富红), Zhi Rui(芮智), and Lei Zhang(张雷)

Chin. Phys. B, 2021, 30 (12): 120502. DOI: 10.1088/1674-1056/abfa03

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An improved heterogeneous dual memristive circuit (DMC) is proposed based on Chua's circuit, which shows good symmetry and multistablility. For the difficulty in controlling the initial conditions, which restricts the engineering applications, the 3rd-order model (3OM) in flux-charge domain is derived from the 5th-order model (5OM) in volt-ampere domain by using the flux-charge analysis method (FCAM). The consistence of symmetry and multistability before and after dimensionality decreasing is meticulously investigated via bifurcation diagram, Lyapunov exponents, and especially attraction basins. The comparative analysis validates the effectiveness of reduction model and improves the controllability of the circuit. To avoid the noise in the analog circuit, a field-programmable gate array (FPGA) is utilized to realize the reduction model, which is rarely reported and valuable for relevant research and application.

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Reference-frame-independent quantum key distribution of wavelength division multiplexing with multiple quantum channels

Zhongqi Sun(孙钟齐), Yanxin Han(韩雁鑫), Tianqi Dou(窦天琦), Jipeng Wang(王吉鹏), Zhenhua Li(李振华), Fen Zhou(周芬), Yuqing Huang(黄雨晴), and Haiqiang Ma(马海强)

Chin. Phys. B, 2021, 30 (11): 110303. DOI: 10.1088/1674-1056/abf350

Abstract （466）

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Reference-frame-independent quantum key distribution (RFI-QKD) can allow a quantum key distribution system to obtain the ideal key rate and transmission distance without reference system calibration, which has attracted much attention. Here, we propose an RFI-QKD protocol based on wavelength division multiplexing (WDM) considering finite-key analysis and crosstalk. The finite-key bound for RFI-QKD with decoy states is derived under the crosstalk of WDM. The resulting secret key rate of RFI-QKD, which is more rigorous, is obtained. Simulation results reveal that the secret key rate of RFI-QKD based on WDM is affected by the multiplexing channel number, as well as crosstalk between adjacent channels.

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Darboux transformation and soliton solutions of a nonlocal Hirota equation

Yarong Xia(夏亚荣), Ruoxia Yao(姚若侠), and Xiangpeng Xin(辛祥鹏)

Chin. Phys. B, 2022, 31 (2): 020401. DOI: 10.1088/1674-1056/ac11e9

Abstract （465）

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Starting from local coupled Hirota equations, we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz-Kaup-Newell-Segur scattering problem. The Lax integrability of the nonlocal Hirota equation is also guaranteed by existence of the Lax pair. By Lax pair, an n-fold Darboux transformation is constructed for the nonlocal Hirota equation by which some types of exact solutions are found. The solutions with specific properties are distinct from those of the local Hirota equation. In order to further describe the properties and the dynamic features of the solutions explicitly, several kinds of graphs are depicted.

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Stability analysis of multiple-lattice self-anticipative density integration effect based on lattice hydrodynamic model in V2V environment

Geng Zhang(张埂) and Da-Dong Tian(田大东)

Chin. Phys. B, 2021, 30 (12): 120201. DOI: 10.1088/1674-1056/ac05b4

Abstract （455）

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Under the environment of vehicle-to-vehicle (V2V) communication, the traffic information on a large scale can be obtained and used to coordinate the operation of road traffic system. In this paper, a new traffic lattice hydrodynamic model is proposed which considers the influence of multiple-lattice self-anticipative density integration on traffic flow in the V2V environment. Through theoretical analysis, the linear stability condition of the new model is derived and the stable condition can be enhanced when more-preceding-lattice self-anticipative density integration effect is taken into account. The property of the unstable traffic density wave in the unstable region is also studied according to the nonlinear analysis. It is shown that the unstable traffic density wave can be described by solving the modified Korteweg-de-Vries (mKdV) equation. Finally, the simulation results demonstrate the validity of the theoretical results. Both theoretical analysis and numerical simulations demonstrate that multiple-lattice self-anticipative density integration effect can enhance the stability of traffic flow system in the V2V environment.

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Numerical investigation on threading dislocation bending with InAs/GaAs quantum dots

Guo-Feng Wu(武国峰), Jun Wang(王俊), Wei-Rong Chen(陈维荣), Li-Na Zhu(祝丽娜), Yuan-Qing Yang(杨苑青), Jia-Chen Li(李家琛), Chun-Yang Xiao(肖春阳), Yong-Qing Huang(黄永清), Xiao-Min Ren(任晓敏), Hai-Ming Ji(季海铭), and Shuai Luo(罗帅)

Chin. Phys. B, 2021, 30 (11): 110201. DOI: 10.1088/1674-1056/abfd9f

Abstract （450）

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The threading dislocations (TDs) in GaAs/Si epitaxial layers due to the lattice mismatch seriously degrade the performance of the lasers grown on silicon. The insertion of InAs quantum dots (QDs) acting as dislocation filters is a pretty good alternative to solving this problem. In this paper, a finite element method (FEM) is proposed to calculate the critical condition for InAs/GaAs QDs bending TDs into interfacial misfit dislocations (MDs). Making a comparison of elastic strain energy between the two isolated systems, a reasonable result is obtained. The effect of the cap layer thickness and the base width of QDs on TD bending are studied, and the results show that the bending area ratio of single QD (the bending area divided by the area of the QD base) is evidently affected by the two factors. Moreover, we present a method to evaluate the bending capability of single-layer QDs and multi-layer QDs. For the QD with 24-nm base width and 5-nm cap layer thickness, taking the QD density of 10¹¹ cm^-2 into account, the bending area ratio of single-layer QDs (the area of bending TD divided by the area of QD layer) is about 38.71%. With inserting five-layer InAs QDs, the TD density decreases by 91.35%. The results offer the guidelines for designing the QD dislocation filters and provide an important step towards realizing the photonic integration circuits on silicon.

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