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Two-Qubit Geometric Gates Based on Ground-State Blockade of Rydberg Atoms
Ji-Ze Xu, Li-Na Sun, J.-F. Wei, Y.-L. Du, Ronghui Luo, Lei-Lei Yan, M. Feng, and Shi-Lei Su
Chin. Phys. Lett.    2022, 39 (9): 090301 .   DOI: 10.1088/0256-307X/39/9/090301
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We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.
Quantum Cloning of Steering
Dian Zhu, Wei-Min Shang, Fu-Lin Zhang, and Jing-Ling Chen
Chin. Phys. Lett.    2022, 39 (7): 070302 .   DOI: 10.1088/0256-307X/39/7/070302
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Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. Perfect cloning is viable if and only if the initial state is of zero discord. We also investigate the process of cloning the steered qubit of a Bell state using a universal cloning machine. Einstein–Podolsky–Rosen (EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, is observed in the two copy subsystems. This contradicts the conclusion of no-cloning of quantum steering (EPR steering) [C. Y. Chiu et al., npj Quantum Inf. 2, 16020 (2016)] based on a mutual information criterion for EPR steering.
Digital Simulation of Projective Non-Abelian Anyons with 68 Superconducting Qubits
Shibo Xu, Zheng-Zhi Sun, Ke Wang, Liang Xiang, Zehang Bao, Zitian Zhu, Fanhao Shen, Zixuan Song, Pengfei Zhang, Wenhui Ren, Xu Zhang, Hang Dong, Jinfeng Deng, Jiachen Chen, Yaozu Wu, Ziqi Tan, Yu Gao, Feitong Jin, Xuhao Zhu, Chuanyu Zhang, Ning Wang, Yiren Zou, Jiarun Zhong, Aosai Zhang, Weikang Li, Wenjie Jiang, Li-Wei Yu, Yunyan Yao, Zhen Wang, Hekang Li, Qiujiang Guo, Chao Song, H. Wang, and Dong-Ling Deng
Chin. Phys. Lett.    2023, 40 (6): 060301 .   DOI: 10.1088/0256-307X/40/6/060301
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Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather than merely a phase factor, in a space spanned by topologically degenerate wavefunctions. They are the building blocks of topological quantum computing. However, experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto, in spite of various theoretical proposals. Here, we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice. By implementing the ground states of the toric-code model with twists through quantum circuits, we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons, i.e., the Ising anyons. In particular, we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type, and can be explored to encode topological logical qubits. Furthermore, we demonstrate how to implement both single- and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits. Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons, offering a new lens into the study of such peculiar quasiparticles.
Geometric Upper Critical Dimensions of the Ising Model
Sheng Fang, Zongzheng Zhou, and Youjin Deng
Chin. Phys. Lett.    2022, 39 (8): 080502 .   DOI: 10.1088/0256-307X/39/8/080502
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The upper critical dimension of the Ising model is known to be $d_{\rm c}=4$, above which critical behavior is regarded to be trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model simultaneously exhibits two upper critical dimensions at $(d_{\rm c}=4,~d_{\rm p}=6)$, and critical clusters for $d \geq d_{\rm p}$, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs. Our findings significantly advance the understanding of the Ising model, which is a fundamental system in many branches of physics.
Measuring Quantum Geometric Tensor of Non-Abelian System in Superconducting Circuits
Wen Zheng, Jianwen Xu, Zhuang Ma, Yong Li, Yuqian Dong, Yu Zhang, Xiaohan Wang, Guozhu Sun, Peiheng Wu, Jie Zhao, Shaoxiong Li, Dong Lan, Xinsheng Tan, and Yang Yu
Chin. Phys. Lett.    2022, 39 (10): 100202 .   DOI: 10.1088/0256-307X/39/10/100202
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Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal interesting topological properties but have not been measured in non-Abelian systems. Here, we use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. By manipulating the Hamiltonian with periodic drivings, we simulate the Bernevig–Hughes–Zhang model and obtain the quantum geometric tensor from interference oscillation. In addition, we reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.
Dark Korteweg–De Vrise System and Its Higher-Dimensional Deformations
Si-Yu Zhu, De-Xing Kong, and Sen-Yue Lou
Chin. Phys. Lett.    2023, 40 (8): 080201 .   DOI: 10.1088/0256-307X/40/8/080201
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The new dimensional deformation approach is proposed to generate higher-dimensional analogues of integrable systems. An arbitrary ($K$+1)-dimensional integrable Korteweg–de Vries (KdV) system, as an example, exhibiting symmetry, is illustrated to arise from a reconstructed deformation procedure, starting with a general symmetry integrable (1+1)-dimensional dark KdV system and its conservation laws. Physically, the dark equation systems may be related to dark matter physics. To describe nonlinear physics, both linear and nonlinear dispersions should be considered. In the original lower-dimensional integrable systems, only liner or nonlinear dispersion is included. The deformation algorithm naturally makes the model also include the linear dispersion and nonlinear dispersion.
Renormalization Group Theory of Eigen Microstates
Teng Liu, Gao-Ke Hu, Jia-Qi Dong, Jing-Fang Fan, Mao-Xin Liu, and Xiao-Song Chen
Chin. Phys. Lett.    2022, 39 (8): 080503 .   DOI: 10.1088/0256-307X/39/8/080503
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We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations. A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues. Under the renormalization of a factor $b$, the largest eigenvalue $\sigma_1$ has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relation $\sigma_1^b = b^{\beta/\nu} \sigma_1$, where $\beta$ and $\nu$ are the critical exponents of order parameter and correlation length, respectively. With the Ising model in different dimensions, it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class. Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian, which is the foundation of Wilson's RG theory and is absent for most complex systems.
Theory of Critical Phenomena with Memory
Shaolong Zeng, Sue Ping Szeto, and Fan Zhong
Chin. Phys. Lett.    2022, 39 (12): 120501 .   DOI: 10.1088/0256-307X/39/12/120501
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Memory is a ubiquitous characteristic of complex systems, and critical phenomena are one of the most intriguing phenomena in nature. Here, we propose an Ising model with memory, develop a corresponding theory of critical phenomena with memory for complex systems, and discover a series of surprising novel results. We show that a naive theory of a usual Hamiltonian with a direct inclusion of a power-law decaying long-range temporal interaction violates radically a hyperscaling law for all spatial dimensions even at and below the upper critical dimension. This entails both indispensable consideration of the Hamiltonian for dynamics, rather than the usual practice of just focusing on the corresponding dynamic Lagrangian alone, and transformations that result in a correct theory in which space and time are inextricably interwoven, leading to an effective spatial dimension that repairs the hyperscaling law. The theory gives rise to a set of novel mean-field critical exponents, which are different from the usual Landau ones, as well as new universality classes. These exponents are verified by numerical simulations of the Ising model with memory in two and three spatial dimensions.
A High-Randomness and High-Stability Electronic Quantum Random Number Generator without Post Processing
Yu-Xuan Liu, Ke-Xin Huang, Yu-Ming Bai, Zhe Yang, and Jun-Lin Li
Chin. Phys. Lett.    2023, 40 (7): 070303 .   DOI: 10.1088/0256-307X/40/7/070303
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Random numbers are one of the key foundations of cryptography. This work implements a discrete quantum random number generator (QRNG) based on the tunneling effect of electrons in an avalanche photo diode. Without any post-processing and conditioning, this QRNG can output raw sequences at a rate of 100 Mbps. Remarkably, the statistical min-entropy of the 8,000,000 bits sequence reaches 0.9944 bits/bit, and the min-entropy validated by NIST SP 800-90B reaches 0.9872 bits/bit. This metric is currently the highest value we have investigated for QRNG raw sequences. Moreover, this QRNG can continuously and stably output raw sequences with high randomness over extended periods. The system produced a continuous output of 1,174 Gbits raw sequence for a duration of 11,744 s, with every 8 Mbits forming a unit to obtain a statistical min-entropy distribution with an average value of 0.9892 bits/bit. The statistical min-entropy of all data (1,174 Gbits) achieves the value of 0.9951 bits/bit. This QRNG can produce high-quality raw sequences with good randomness and stability. It has the potential to meet the high demand in cryptography for random numbers with high quality.
Higher Dimensional Camassa–Holm Equations
S. Y. Lou, Man Jia, and Xia-Zhi Hao
Chin. Phys. Lett.    2023, 40 (2): 020201 .   DOI: 10.1088/0256-307X/40/2/020201
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Utilizing some conservation laws of the (1+1)-dimensional Camassa–Holm (CH) equation and/or its reciprocal forms, some (n+1)-dimensional CH equations for $n\geq 1$ are constructed by a modified deformation algorithm. The Lax integrability can be proven by applying the same deformation algorithm to the Lax pair of the (1+1)-dimensional CH equation. A novel type of peakon solution is implicitly given and expressed by the LambertW function.
Phonon Stability of Quantum Droplets in Dipolar Bose Gases
Fan Zhang and Lan Yin
Chin. Phys. Lett.    2022, 39 (6): 060301 .   DOI: 10.1088/0256-307X/39/6/060301
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Stabilized by quantum fluctuations, dipolar Bose–Einstein condensates can form self-bound liquid-like droplets. However in the Bogoliubov theory, there are imaginary phonon energies in the long-wavelength limit, implying dynamical instability of this system. A similar instability appears in the Bogoliubov theory of a binary quantum droplet, and is removed due to higher-order quantum fluctuations as shown recently [Gu Q and Yin L 2020 Phys. Rev. B 102 220503(R)]. We study the excitation energy of a dipolar quantum droplet in the Beliaev formalism, and find that quantum fluctuations significantly enhance the phonon stability. We adopt a self-consistent approach without the problem of complex excitation energy in the Bogoliubov theory, and obtain a stable anisotropic sound velocity which is consistent with the superfluid hydrodynamic theory, but slightly different from the result of the extended Gross–Pitaevskii equation due to quantum depletion. A modified Gross–Pitaevskii equation in agreement with the Beliaev theory is proposed, which takes the effect of quantum fluctuations into account more completely.
Experimental Test of Contextuality Based on State Discrimination with a Single Qubit
Qiuxin Zhang, Chenhao Zhu, Yuxin Wang, Liangyu Ding, Tingting Shi, Xiang Zhang, Shuaining Zhang, and Wei Zhang
Chin. Phys. Lett.    2022, 39 (8): 080301 .   DOI: 10.1088/0256-307X/39/8/080301
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Exploring quantum phenomena beyond predictions of any classical model has fundamental importance to understand the boundary of classical and quantum descriptions of nature. As a typical property that a quantum system behaves distinctively from a classical counterpart, contextuality has been studied extensively and verified experimentally in systems composed of at least three levels (qutrit). Here we extend the scope of experimental test of contextuality to a minimal quantum system of only two states (qubit) by implementing the minimum error state discrimination on a single $^{171}$Yb$^+$ ion. We observe a substantial violation of a no-go inequality derived by assuming non-contextuality, and firmly conclude that the measured results of state discrimination cannot be reconciled with any non-contextual description. We also quantify the contextual advantage of state discrimination and the tolerance against quantum noises.
Geometric Thermoelectric Pump: Energy Harvesting beyond Seebeck and Pyroelectric Effects
Jie Ren
Chin. Phys. Lett.    2023, 40 (9): 090501 .   DOI: 10.1088/0256-307X/40/9/090501
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Thermal-electric conversion is crucial for smart energy control and harvesting, such as thermal sensing and waste heat recovering. So far, researchers are aware of two main ways of direct thermal-electric conversion, Seebeck and pyroelectric effects, each with different working mechanisms, conditions and limitations. Here, we report the concept of Geometric Thermoelectric Pump (GTEP), as the third way of thermal-electric conversion beyond Seebeck and pyroelectric effects. In contrast to Seebeck effect that requires spatial temperature difference, GTEP converts the time-dependent ambient temperature fluctuation into electricity. Moreover, GTEP does not require polar materials but applies to general conducting systems, and thus is also distinct from pyroelectric effect. We demonstrate that GTEP results from the temperature-fluctuation-induced charge redistribution, which has a deep connection to the topological geometric phase in non-Hermitian dynamics, as a consequence of the fundamental nonequilibrium thermodynamic geometry. The findings advance our understanding of geometric phase induced multiple-physics-coupled pump effect and provide new means of thermal-electric energy harvesting.
Stark Tuning of Telecom Single-Photon Emitters Based on a Single Er$^{3+}$
Jian-Yin Huang, Peng-Jun Liang, Liang Zheng, Pei-Yun Li, You-Zhi Ma, Duan-Chen Liu, Jing-Hui Xie, Zong-Quan Zhou, Chuan-Feng Li, and Guang-Can Guo
Chin. Phys. Lett.    2023, 40 (7): 070301 .   DOI: 10.1088/0256-307X/40/7/070301
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The implementation of scalable quantum networks requires photons at the telecom band and long-lived spin coherence. The single Er$^{3+}$ in solid-state hosts is an important candidate that fulfills these critical requirements simultaneously. However, to entangle distant Er$^{3+}$ ions through photonic connections, the emission frequency of individual Er$^{3+}$ in solid-state matrix must be the same, which is challenging because the emission frequency of Er$^{3+}$ depends on its local environment. Herein, we propose and experimentally demonstrate the Stark tuning of the emission frequency of a single Er$^{3+}$ in a Y$_2$SiO$_5$ crystal by employing electrodes interfaced with a silicon photonic crystal cavity. We obtain a Stark shift of 182.9$\pm 0.8$ MHz, which is approximately 27 times of the optical emission linewidth, demonstrating promising applications in tuning the emission frequency of independent Er$^{3+}$ into the same spectral channels. Our results provide a useful solution for construction of scalable quantum networks based on single Er$^{3+}$ and a universal tool for tuning emission of individual rare-earth ions.
Twin-Field Quantum Key Distribution Protocol Based on Wavelength-Division-Multiplexing Technology
Yanxin Han, Zhongqi Sun, Tianqi Dou, Jipeng Wang, Zhenhua Li, Yuqing Huang, Pengyun Li, and Haiqiang Ma
Chin. Phys. Lett.    2022, 39 (7): 070301 .   DOI: 10.1088/0256-307X/39/7/070301
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Quantum key distribution (QKD) generates information-theoretical secret keys between two parties based on the physical laws of quantum mechanics. Following the advancement in quantum communication networks, it becomes feasible and economical to combine QKD with classical optical communication through the same fiber using dense wavelength division multiplexing (DWDM) technology. This study proposes a detailed scheme of TF-QKD protocol with DWDM technology and analyzes its performance, considering the influence of quantum channel number and adjacent quantum crosstalk on the secret key rates. The simulation results show that the scheme further increases the secret key rate of TF-QKD and its variants. Therefore, this scheme provides a method for improving the secret key rate for practical quantum networks.
Improved Evaluation of BBR and Collisional Frequency Shifts of NIM-Sr2 with $7.2 \times 10^{-18}$ Total Uncertainty
Bing-Kun Lu, Zhen Sun, Tao Yang, Yi-Ge Lin, Qiang Wang, Ye Li, Fei Meng, Bai-Ke Lin, Tian-Chu Li, and Zhan-Jun Fang
Chin. Phys. Lett.    2022, 39 (8): 080601 .   DOI: 10.1088/0256-307X/39/8/080601
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NIM-Sr2 optical lattice clock has been developed on the Changping campus of National Institute of Metrology (NIM). Considering the limitations in NIM-Sr1, several improved parts have been designed including a differential pumping stage in the vacuum system, a permanent magnet Zeeman slower, water-cooled anti-Helmholtz coils, an extended viewport for Zeeman slower, etc. A clock laser with a short-time stability better than $3\times10^{-16}$ is realized based on a self-designed 30-cm-long ultra-low expansion cavity. The systematic frequency shift has been evaluated to an uncertainty of $7.2\times 10^{-18}$, with the uncertainty of BBR shift and the collisional frequency shift being an order of magnitude lower than the last evaluation of NIM-Sr1.
Cryo-EM Data Statistics and Theoretical Analysis of KaiC Hexamer
Xu Han, Zhaolong Wu, Tian Yang, and Qi Ouyang
Chin. Phys. Lett.    2022, 39 (7): 070501 .   DOI: 10.1088/0256-307X/39/7/070501
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Cryo-electron microscopy (cryo-EM) provides a powerful tool to resolve the structure of biological macromolecules in natural state. One advantage of cryo-EM technology is that different conformation states of a protein complex structure can be simultaneously built, and the distribution of different states can be measured. This provides a tool to push cryo-EM technology beyond just to resolve protein structures, but to obtain the thermodynamic properties of protein machines. Here, we used a deep manifold learning framework to get the conformational landscape of KaiC proteins, and further obtained the thermodynamic properties of this central oscillator component in the circadian clock by means of statistical physics.
Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions
Wen-Xiu Ma
Chin. Phys. Lett.    2022, 39 (10): 100201 .   DOI: 10.1088/0256-307X/39/10/100201
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We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz–Kaup–Newell–Segur matrix eigenvalue problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding reflectionless Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and formulate their soliton solutions via those reflectionless Riemann–Hilbert problems. Soliton solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.
Stochastic Gradient Descent and Anomaly of Variance-Flatness Relation in Artificial Neural Networks
Xia Xiong, Yong-Cong Chen, Chunxiao Shi, and Ping Ao
Chin. Phys. Lett.    2023, 40 (8): 080202 .   DOI: 10.1088/0256-307X/40/8/080202
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Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks, has attracted continuing research interests for the theoretical principles behind its success. A recent work reported an anomaly (inverse) relation between the variance of neural weights and the landscape flatness of the loss function driven under SGD [Feng Y and Tu Y Proc. Natl. Acad. Sci. USA 118 e2015617118 (2021)}]. To investigate this seeming violation of statistical physics principle, the properties of SGD near fixed points are analyzed with a dynamic decomposition method. Our approach recovers the true “energy” function under which the universal Boltzmann distribution holds. It differs from the cost function in general and resolves the paradox raised by the anomaly. The study bridges the gap between the classical statistical mechanics and the emerging discipline of artificial intelligence, with potential for better algorithms to the latter.
Characterizing Superradiant Phase of the Quantum Rabi Model
Yun-Tong Yang and Hong-Gang Luo
Chin. Phys. Lett.    2023, 40 (2): 020502 .   DOI: 10.1088/0256-307X/40/2/020502
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Recently, a superradiant phase transition first predicted theoretically in the quantum Rabi model (QRM) has been verified experimentally. This further stimulates the interest in the study of the process of phase transition and the nature of the superradiant phase since the fundamental role of the QRM in describing the interaction of light and matter, and more importantly, the QRM contains rich physics deserving further exploration despite its simplicity. Here we propose a scheme consisting of two successive diagonalizations to accurately obtain the ground-state and excited states wavefunctions of the QRM in full parameter regime ranging from weak to deep-strong couplings. Thus, one is able to see how the phase transition occurs and how the photons populate in Fock space of the superradiant phase. We characterize the photon populations by borrowing the distribution concept in random matrix theory and find that the photon population follows a Poissonian-like distribution once the phase transition takes place and further exhibits the statistics of Gaussian unitary ensemble with increasing coupling strength. More interestingly, the photons in the excited states behave even like the statistics of Gaussian orthogonal ensemble. Our results not only deepen understanding on the superradiant phase transition but also provide an insight on the nature of the superradiant phase of the QRM and related models.
Finite-Size Scaling Theory at a Self-Dual Quantum Critical Point
Long Zhang and Chengxiang Ding
Chin. Phys. Lett.    2023, 40 (1): 010501 .   DOI: 10.1088/0256-307X/40/1/010501
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The nondivergence of the generalized Grüneisen ratio (GR) at a quantum critical point (QCP) has been proposed to be a universal thermodynamic signature of self-duality. We study how the Kramers–Wannier-type self-duality manifests itself in the finite-size scaling behavior of thermodynamic quantities in the quantum critical regime. While the self-duality cannot be realized as a unitary transformation in the total Hilbert space for the Hamiltonian with the periodic boundary condition, it can be implemented in certain symmetry sectors with proper boundary conditions. Therefore, the GR and the transverse magnetization of the one-dimensional transverse-field Ising model exhibit different finite-size scaling behaviors in different sectors. This implies that the numerical diagnosis of self-dual QCP requires identification of the proper symmetry sectors.
Exploring Explicit Coarse-Grained Structure in Artificial Neural Networks
Xi-Ci Yang, Z. Y. Xie, and Xiao-Tao Yang
Chin. Phys. Lett.    2023, 40 (2): 020501 .   DOI: 10.1088/0256-307X/40/2/020501
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We propose to employ a hierarchical coarse-grained structure in artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network called TaylorNet, which aims to approximate the general mapping from input data to output result in terms of Taylor series directly, without resorting to any magic nonlinear activations. The other is a new setup for data distillation, which can perform multi-level abstraction of the input dataset and generate new data that possesses the relevant features of the original dataset and can be used as references for classification. In both the cases, the coarse-grained structure plays an important role in simplifying the network and improving both the interpretability and efficiency. The validity has been demonstrated on MNIST and CIFAR-10 datasets. Further improvement and some open questions related are also discussed.
Semi-Measurement-Device-Independent Quantum State Tomography
Jian Li, Jia-Li Zhu, Jiang Gao, Zhi-Guang Pang, and Qin Wang
Chin. Phys. Lett.    2022, 39 (7): 070303 .   DOI: 10.1088/0256-307X/39/7/070303
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As a fundamental tool in the quantum information field, quantum state tomography can be used to reconstruct any unknown state. Generally, it needs a tomographically complete set of measurements, such that all measurements are fully characterized. Here, we propose a semi-measurement-device-independent quantum state tomography protocol, which only needs one characterized measurement and a trusted ancillary system. Furthermore, we perform corresponding experiments using linear optics. Our results show that the average state fidelity is as high as 0.973, verifying the effectiveness of the scheme.
Logarithmic Quantum Time Crystal
Haipeng Xue, Lingchii Kong, and Biao Wu
Chin. Phys. Lett.    2022, 39 (8): 080501 .   DOI: 10.1088/0256-307X/39/8/080501
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We investigate a time-independent many-boson system, whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit. Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles, that is, $T\sim \log N$. This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit. The logarithmic dependence of its period on the total particle number $N$ makes it observable experimentally even for systems with very large number of particles. Possible experimental proposals are discussed.
Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations
Sheng-Chen Bai, Yi-Cheng Tang, and Shi-Ju Ran
Chin. Phys. Lett.    2022, 39 (10): 100701 .   DOI: 10.1088/0256-307X/39/10/100701
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Given an image of a white shoe drawn on a blackboard, how are the white pixels deemed (say by human minds) to be informative for recognizing the shoe without any labeling information on the pixels? Here we investigate such a “white shoe” recognition problem from the perspective of tensor network (TN) machine learning and quantum entanglement. Utilizing a generative TN that captures the probability distribution of the features as quantum amplitudes, we propose an unsupervised recognition scheme of informative features with variations of entanglement entropy (EE) caused by designed measurements. In this way, a given sample, where the values of its features are statistically meaningless, is mapped to the variations of EE that statistically characterize the gain of information. We show that the EE variations identify the features that are critical to recognize this specific sample, and the EE itself reveals the information distribution of the probabilities represented by the TN model. The signs of the variations further reveal the entanglement structures among the features. We test the validity of our scheme on a toy dataset of strip images, the MNIST dataset of hand-drawn digits, the fashion-MNIST dataset of the pictures of fashion articles, and the images of nerve cord. Our scheme opens the avenue to the quantum-inspired and interpreted unsupervised learning, which can be applied to, e.g., image segmentation and object detection.
Multi-Mode Bus Coupling Architecture of Superconducting Quantum Processor
Changhao Zhao, Yongcheng He, Xiao Geng, Kaiyong He, Genting Dai, Jianshe Liu, and Wei Chen
Chin. Phys. Lett.    2023, 40 (1): 010301 .   DOI: 10.1088/0256-307X/40/1/010301
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Resonators in circuit quantum electrodynamics systems naturally carry multiple modes, which may have non-negligible influence on qubit parameters and device performance. While new theories and techniques are under investigation to deal with the multi-mode effects in circuit quantum electrodynamics systems, researchers have proposed novel engineering designs featuring multi-mode resonators to achieve enhanced functionalities of superconducting quantum processors. Here, we propose multi-mode bus coupling architecture, in which superconducting qubits are coupled to multiple bus resonators to gain larger coupling strength. Applications of multi-mode bus couplers can be helpful for improving iSWAP gate fidelity and gate speed beyond the limit of single-mode scenario. The proposed multi-mode bus coupling architecture is compatible with a scalable variation of the traditional bus coupling architecture. It opens up new possibilities for realization of scalable superconducting quantum computation with circuit quantum electrodynamics systems.
Engineering Knill–Laflamme–Milburn Entanglement via Dissipation and Coherent Population Trapping in Rydberg Atoms
Rui Li, Shuang He, Zhi-Jun Meng, Zhao Jin, and Wei-Jiang Gong
Chin. Phys. Lett.    2023, 40 (6): 060302 .   DOI: 10.1088/0256-307X/40/6/060302
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We present a scheme for dissipatively preparing bipartite Knill–Laflamme–Milburn (KLM) entangled state in a neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the coherent population trapping, is actively exploited to engineer a steady KLM state from an arbitrary initial state. Instead of commonly used antiblockade dynamics of two Rydberg atoms, we particularly utilize the Rydberg–Rydberg interaction as the pumping source to drive the undesired states so that it is unnecessary to satisfy a certain relation with laser detuning. The numerical simulation of the master equation signifies that both the fidelity and the purity above 98$\%$ is available with the current feasible parameters, and the corresponding steady-state fidelity is robust to the variations of the dynamical parameters.
Quench Dynamics of Bose–Einstein Condensates in Boxlike Traps
Rong Du, Jian-Chong Xing, Bo Xiong, Jun-Hui Zheng, and Tao Yang
Chin. Phys. Lett.    2022, 39 (7): 070304 .   DOI: 10.1088/0256-307X/39/7/070304
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By quenching the interatomic interactions, we investigate the nonequilibrium dynamics of two-dimensional Bose–Einstein condensates in boxlike traps with power-law potential boundaries. We show that ring dark solitons can be excited during the quench dynamics for both concave and convex potentials. The quench's modulation strength and the steepness of the boundary are two major factors influencing the system's evolution. In terms of the number of ring dark solitons excited in the condensate, five dynamic regimes have been identified. The condensate undergoes damped radius oscillation in the absence of ring dark soliton excitations. When it comes to the appearance of ring dark solitons, their decay produces interesting structures. The excitation patterns for the concave potential show a nested structure of vortex-antivortex pairs. The dynamic excitation patterns for the convex potential, on the other hand, show richer structures with multiple transport behaviors.
Bounding Free Energy Difference with Flow Matching
Lu Zhao and Lei Wang
Chin. Phys. Lett.    2023, 40 (12): 120201 .   DOI: 10.1088/0256-307X/40/12/120201
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We introduce a method for computing the Helmholtz free energy using the flow matching technique. Unlike previous work that utilized flow-based models for variational free energy calculations, this method provides bounds for free energy estimation based on targeted free energy perturbation by performing calculations on samples from both ends of the mapping. We demonstrate applications of the present method by estimating the free energy of a classical Coulomb gas in a harmonic trap.
A Hierarchy in Majorana Non-Abelian Tests and Hidden Variable Models
Peng Qian and Dong E. Liu
Chin. Phys. Lett.    2023, 40 (10): 100501 .   DOI: 10.1088/0256-307X/40/10/100501
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The recent progress of the Majorana experiments paves a way for the future tests of non-Abelian braiding statistics and topologically protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary so as to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-Abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity.
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