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In the NISQ era, achieving large-scale quantum computing demands compact circuits to mitigate decoherence and gate error accumulation. Quantum operations with diverse degrees of freedom hold promise for circuit compression, but conventional approaches encounter challenges in simultaneously adjusting multiple parameters. Here, we propose a transition composite gate (TCG) scheme grounded on state-selective transition path engineering, enabling more expressive conditional operations. We experimentally validate a controlled unitary (CU) gate as an example, with independent and continuous parameters. By adjusting the parameters of $\rm X^{12}$ gate, we obtain the CU family with a fidelity range of 95.2% to 99.0% leveraging quantum process tomography (QPT). To demonstrate the capability of circuit compression, we use TCG scheme to prepare 3-qubit Greenberger-Horne-Zeilinger (GHZ) and W states, with the fidelity of 96.77% and 95.72%. TCG can achieve the reduction in circuit depth of about 40% and 44% compared with the use of CZ gates only. Moreover, we show that short-path TCG (SPTCG) can further reduce the state-preparation circuit time cost. The TCG scheme exhibits advantages in certain quantum circuits and shows significant potential for large-scale quantum algorithms., Comment: 21 pages, 12 figures

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method "Iterative-QLS" that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than $0.2\%$, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum-classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science., Comment: 31 pages, 10 figures

The 2-distance coloring of a graph $G$ is equivalent to the proper coloring of its square graph $G^2$, it is a special distance labeling problem. DP-coloring (or "Correspondence coloring") was introduced by Dvo\v{r}\'ak and Postle in 2018, to answer a conjecture of list coloring proposed by Borodin. In recent years, many researches pay attention to the DP-coloring of planar graphs with some restriction in cycles. We study the DP-coloring of the square of subcubic graphs in terms of maximum average degree $\rm{mad}(G)$, and by the discharging method, we showed that: for a subcubic graph $G$, if $\rm{mad}(G)<9/4$, then $G^2$ is DP-5-colorable; if $\rm{mad}(G)<12/5$, then $G^2$ is DP-6-colorable. And the bound in the first result is sharp., Comment: 7 pages, 3 figures

Quantum Convolutional Layer (QCL) is considered as one of the core of Quantum Convolutional Neural Networks (QCNNs) due to its efficient data feature extraction capability. However, the current principle of QCL is not as mathematically understandable as Classical Convolutional Layer (CCL) due to its black-box structure. Moreover, classical data mapping in many QCLs is inefficient. To this end, firstly, the Quantum Adjoint Convolution Operation (QACO) consisting of a quantum amplitude encoding and its inverse is theoretically shown to be equivalent to the quantum normalization of the convolution operation based on the Frobenius inner product while achieving an efficient characterization of the data. Subsequently, QACO is extended into a Quantum Adjoint Convolutional Layer (QACL) by Quantum Phase Estimation (QPE) to compute all Frobenius inner products in parallel. At last, comparative simulation experiments are carried out on PennyLane and TensorFlow platforms, mainly for the two cases of kernel fixed and unfixed in QACL. The results demonstrate that QACL with the insight of special quantum properties for the same images, provides higher training accuracy in MNIST and Fashion MNIST classification experiments, but sacrifices the learning performance to some extent. Predictably, our research lays the foundation for the development of efficient and interpretable quantum convolutional networks and also advances the field of quantum machine vision.

Numerous current Quantum Machine Learning (QML) models exhibit an inadequacy in discerning the significance of quantum data, resulting in diminished efficacy when handling extensive quantum datasets. Hard Attention Mechanism (HAM), anticipated to efficiently tackle the above QML bottlenecks, encounters the substantial challenge of non-differentiability, consequently constraining its extensive applicability. In response to the dilemma of HAM and QML, a Grover-inspired Quantum Hard Attention Mechanism (GQHAM) consisting of a Flexible Oracle (FO) and an Adaptive Diffusion Operator (ADO) is proposed. Notably, the FO is designed to surmount the non-differentiable issue by executing the activation or masking of Discrete Primitives (DPs) with Flexible Control (FC) to weave various discrete destinies. Based on this, such discrete choice can be visualized with a specially defined Quantum Hard Attention Score (QHAS). Furthermore, a trainable ADO is devised to boost the generality and flexibility of GQHAM. At last, a Grover-inspired Quantum Hard Attention Network (GQHAN) based on QGHAM is constructed on PennyLane platform for Fashion MNIST binary classification. Experimental findings demonstrate that GQHAN adeptly surmounts the non-differentiability hurdle, surpassing the efficacy of extant quantum soft self-attention mechanisms in accuracies and learning ability. In noise experiments, GQHAN is robuster to bit-flip noise in accuracy and amplitude damping noise in learning performance. Predictably, the proposal of GQHAN enriches the Quantum Attention Mechanism (QAM), lays the foundation for future quantum computers to process large-scale data, and promotes the development of quantum computer vision.

Self-Attention Mechanism (SAM) excels at distilling important information from the interior of data to improve the computational efficiency of models. Nevertheless, many Quantum Machine Learning (QML) models lack the ability to distinguish the intrinsic connections of information like SAM, which limits their effectiveness on massive high-dimensional quantum data. To tackle the above issue, a Quantum Kernel Self-Attention Mechanism (QKSAM) is introduced to combine the data representation merit of Quantum Kernel Methods (QKM) with the efficient information extraction capability of SAM. Further, a Quantum Kernel Self-Attention Network (QKSAN) framework is proposed based on QKSAM, which ingeniously incorporates the Deferred Measurement Principle (DMP) and conditional measurement techniques to release half of quantum resources by mid-circuit measurement, thereby bolstering both feasibility and adaptability. Simultaneously, the Quantum Kernel Self-Attention Score (QKSAS) with an exponentially large characterization space is spawned to accommodate more information and determine the measurement conditions. Eventually, four QKSAN sub-models are deployed on PennyLane and IBM Qiskit platforms to perform binary classification on MNIST and Fashion MNIST, where the QKSAS tests and correlation assessments between noise immunity and learning ability are executed on the best-performing sub-model. The paramount experimental finding is that a potential learning advantage is revealed in partial QKSAN subclasses that acquire an impressive more than 98.05% high accuracy with very few parameters that are much less in aggregate than classical machine learning models. Predictably, QKSAN lays the foundation for future quantum computers to perform machine learning on massive amounts of data while driving advances in areas such as quantum computer vision.

Self-Attention Mechanism (SAM) is good at capturing the internal connections of features and greatly improves the performance of machine learning models, espeacially requiring efficient characterization and feature extraction of high-dimensional data. A novel Quantum Self-Attention Network (QSAN) is proposed for image classification tasks on near-term quantum devices. First, a Quantum Self-Attention Mechanism (QSAM) including Quantum Logic Similarity (QLS) and Quantum Bit Self-Attention Score Matrix (QBSASM) is explored as the theoretical basis of QSAN to enhance the data representation of SAM. QLS is employed to prevent measurements from obtaining inner products to allow QSAN to be fully implemented on quantum computers, and QBSASM as a result of the evolution of QSAN to produce a density matrix that effectively reflects the attention distribution of the output. Then, the framework for one-step realization and quantum circuits of QSAN are designed for fully considering the compression of the measurement times to acquire QBSASM in the intermediate process, in which a quantum coordinate prototype is introduced as well in the quantum circuit for describing the mathematical relation between the output and control bits to facilitate programming. Ultimately, the method comparision and binary classification experiments on MNIST with the pennylane platform demonstrate that QSAN converges about 1.7x and 2.3x faster than hardware-efficient ansatz and QAOA ansatz respevtively with similar parameter configurations and 100% prediction accuracy, which indicates it has a better learning capability. QSAN is quite suitable for fast and in-depth analysis of the primary and secondary relationships of image and other data, which has great potential for applications of quantum computer vision from the perspective of enhancing the information extraction ability of models.

Since the black hole and cosmological horizons in the de Sitter (dS) spacetime with the Reissner-Nordstrom (RN) black hole are not independent to each other, which is caused by the gravitational effect, the interplay between two horizons should be considered. Based on this, by introducing the interactive entropy the RN-dS spacetime is analogous to a thermodynamic system with various thermodynamic quantities, in which the thermodynamic laws still hold on. In our work, the thermodynamic properties of the RN-dS spacetime are mapped out in the induced phase space, which are similar to that in AdS black holes. The phase transition of the RN-dS spacetime between the high-potential and the low-potential black hole phases is observed. Compared with an ordinary thermodynamic system, the similar behaviors about the Joule-Thomson expansion and the critical exponents are also checked out. Finally, the scalar curvature of two existent phases are presented to reveal the underlying microstructure and nature of phase transition in the RN-dS spacetime, which opens a new window to investigate the dS spacetime with black holes from a observational perspective.

Non-linear interaction between the electromagnetic fields (EMF) are occurred when vacuum polarization in quantum electrodynamics (QED) happens. The field of non-linear electrodynamics which may be resulting from this interaction could have important effects on black hole physics. In this work, we investigate the relationship between the observable quantity, the shadow radius and the first-order phase transition for the non-linear charged AdS black hole in the frame of the Einstein-power-Yang-Mills (EPYM) gravity. Through the analysis, we find with a certain condition there exist the non-monotonic behaviors between the shadow radius, the horizon radius, and temperature (or pressure). And from the viewpoint of the shadow radius, the phase transition temperature is higher than that from the viewpoint of the horizon radius with the same condition. These indicate that the shadow radius can be regarded a probe to reveal the thermodynamic phase transition information of black holes. When the system is undergoing the phase transition in two cases of the different non-linear YM charge parameter values: $\gamma=1,~1.5$, the thermal profiles of the coexistent big and small black hole phases with the temperature are presented. Furthermore, the effects of non-linear YM charge parameter on the shadow radius and the thermal profile are also investigated., Comment: arXiv admin note: substantial text overlap with arXiv:2204.01007; text overlap with arXiv:1507.04217 by other authors

Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity. We investigate the condition and latent heat of phase transition for non-linear charged AdS black holes using the Maxwell's equal-area law, and analysis the boundary and curve of the two-phase coexistence area in the expanded phase space. We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature ($T

The basic equations of the thermodynamic system give the relationship between the internal energy, entropy and volume of two neighboring equilibrium states. By using the functional relationship between the state parameters in the basic equation, we give the differential equation satisfied by the entropy of spacetime. We can obtain the expression of the entropy by solving the differential equationy. This expression is the sum of entropy corresponding to the two event horizons and the interaction term. The interaction term is a function of the ratio of the locations of the black hole horizon and the cosmological horizon. The entropic force, which is strikingly similar to the Lennard-Jones force between particles, varies with the ratio of the two event horizons. The discovery of this phenomenon makes us realize that the entropic force between the two horizons may be one of the candidates to promote the expansion of the universe., Comment: 16 pages,3 figures

Previously, the Maxwell equal-area law has been used to discuss the conditions satisfied by the phase transition of charged AdS black holes with cloud of string and quintessence, and it was concluded that black holes have phase transition similar to that of vdW system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On the basis of this result, we study the relation between the latent heat of the phase transition and the parameter of dark energy, and use the Landau continuous phase transition theory to discuss the critical phenomenon of the black hole with quintessence and give the critical exponent. By introducing the number density of the black hole molecules, some properties of the microstructure of black holes are studied in terms of a phase transition. It is found that the electric charge of the black hole and the normalization parameter related to the density of quintessence field play a key role in phase transition. By constructing the binary fluid model of the black hole molecules, we also discuss the microstructure of charged AdS black holes with a cloud of strings and quintessence., Comment: 25 pages,4 figures,added refs. arXiv admin note: text overlap with arXiv:1901.04703