Discussion on the Homology Theory of Lie Algebras

Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).

Quantum Computingvia Entanglement in Geometric Algebra Approach

The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

基于开源Quantum ESPRESSO软件的固体物理教学模式创新与实践

为了解决固体物理课程学习中的难点,授课时引入开源Quantum ESPRESSO软件为学生提供全面的理论学习和实践训练。实践训练分为理论学习和实际操作两个阶段,使学生在理解固体物理的难点的同时获得实际操作经验。通过自主学习、实验报告的撰写和实操演示等分层次的学习方式,学生逐渐提升对固体物理的整体理解水平。学生对这一学习方式的反应良好。Quantum ESPRESSO软件为学生提供了先进的学习工具,有效提高了固体物理课程的学习效果。

Some results on derivations of MV-algebras

In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].

Extensions of quantum enveloping algebras

In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.

(ρ, τ, σ)-Derivations of Dendriform Algebras

We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.

2D Curves in Conformal Hyperquaternion Algebras H⊗2m

The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H⊗2m in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H⊗2m is the object of this work.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

Root Systems Lie Algebras

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

Detecting the quantum phase transition from the perspective of quantum information in the Aubry–André model

We investigate the effectiveness of entropic uncertainty, entanglement and steering in discerning quantum phase transitions(QPTs). Specifically, we observe significant fluctuations in entropic uncertainty as the driving parameter traverses the phase transition point. It is observed that the entropic uncertainty, entanglement and quantum steering, based on the electron distribution probability, can serve as indicators for detecting QPTs. Notably, we reveal an intriguing anticorrelation relationship between entropic uncertainty and entanglement in the Aubry–André model. Moreover, we explore the feasibility of detecting a QPT when the period parameter is a rational number. These observations open up new and efficient avenues for probing QPTs.

N-doped graphene quantum dot-decorated N-TiO2/P-doped porous hollow g-C_(3)N_(4) nanotube composite photocatalysts for antibiotic photodegradation and H2 production

Exclusive responsiveness to ultraviolet light (~3.2 eV) and high photogenerated charge recombination rate are the two primary drawbacks of pure TiO_(2). We combined N-doped graphene quantum dots (N-GQDs), morphology regulation, and heterojunction construction strategies to synthesize N-GQD/N-doped TiO_(2)/P-doped porous hollow g-C_(3)N_(4) nanotube (PCN) composite photocatalysts (denoted as G-TPCN). The optimal sample (G-TPCN doped with 0.1wt% N-GQD, denoted as 0.1% G-TPCN) exhibits significantly enhanced photoabsorption, which is attributed to the change in bandgap caused by elemental doping (P and N), the improved light-harvesting resulting from the tube structure, and the upconversion effect of N-GQDs. In addition, the internal charge separation and transfer capability of0.1% G-TPCN are dramatically boosted, and its carrier concentration is 3.7, 2.3, and 1.9 times that of N-TiO_(2), PCN, and N-TiO_(2)/PCN(TPCN-1), respectively. This phenomenon is attributed to the formation of Z-scheme heterojunction between N-TiO_(2) and PCNs, the excellent electron conduction ability of N-GQDs, and the short transfer distance caused by the porous nanotube structure. Compared with those of N-TiO_(2), PCNs, and TPCN-1, the H2 production activity of 0.1%G-TPCN under visible light is enhanced by 12.4, 2.3, and 1.4times, respectively, and its ciprofloxacin (CIP) degradation rate is increased by 7.9, 5.7, and 2.9 times, respectively. The optimized performance benefits from excellent photoresponsiveness and improved carrier separation and migration efficiencies. Finally, the photocatalytic mechanism of 0.1% G-TPCN and five possible degradation pathways of CIP are proposed. This study clarifies the mechanism of multiple modification strategies to synergistically improve the photocatalytic performance of 0.1% G-TPCN and provides a potential strategy for rationally designing novel photocatalysts for environmental remediation and solar energy conversion.

Quantum circuit-based proxy blind signatures:A novel approach and experimental evaluation on the IBM quantum cloud platform

This paper presents a novel approach to proxy blind signatures in the realm of quantum circuits,aiming to enhance security while safeguarding sensitive information.The main objective of this research is to introduce a quantum proxy blind signature(QPBS)protocol that utilizes quantum logical gates and quantum measurement techniques.The QPBS protocol is constructed by the initial phase,proximal blinding message phase,remote authorization and signature phase,remote validation,and de-blinding phase.This innovative design ensures a secure mechanism for signing documents without revealing the content to the proxy signer,providing practical security authentication in a quantum environment under the assumption that the CNOT gates are securely implemented.Unlike existing approaches,our proposed QPBS protocol eliminates the need for quantum entanglement preparation,thus simplifying the implementation process.To assess the effectiveness and robustness of the QPBS protocol,we conduct comprehensive simulation studies in both ideal and noisy quantum environments on the IBM quantum cloud platform.The results demonstrate the superior performance of the QPBS algorithm,highlighting its resilience against repudiation and forgeability,which are key security concerns in the realm of proxy blind signatures.Furthermore,we have established authentic security thresholds(82.102%)in the presence of real noise,thereby emphasizing the practicality of our proposed solution.

Threshold-independent method for single-shot readout of spin qubits in semiconductor quantum dots

The single-shot readout data process is essential for the realization of high-fidelity qubits and fault-tolerant quantum algorithms in semiconductor quantum dots. However, the fidelity and visibility of the readout process are sensitive to the choice of the thresholds and limited by the experimental hardware. By demonstrating the linear dependence between the measured spin state probabilities and readout visibilities along with dark counts, we describe an alternative threshold-independent method for the single-shot readout of spin qubits in semiconductor quantum dots. We can obtain the extrapolated spin state probabilities of the prepared probabilities of the excited spin state through the threshold-independent method. We then analyze the corresponding errors of the method, finding that errors of the extrapolated probabilities cannot be neglected with no constraints on the readout time and threshold voltage. Therefore, by limiting the readout time and threshold voltage, we ensure the accuracy of the extrapolated probability. We then prove that the efficiency and robustness of this method are 60 times larger than those of the most commonly used method. Moreover, we discuss the influence of the electron temperature on the effective area with a fixed external magnetic field and provide a preliminary demonstration for a single-shot readout of up to 0.7K/1.5T in the future.

QBIoT:A Quantum Blockchain Framework for IoT with an Improved Proof-of-Authority Consensus Algorithm and a Public-Key Quantum Signature

The Internet of Things(IoT)is a network system that connects physical devices through the Internet,allowing them to interact.Nowadays,IoT has become an integral part of our lives,offering convenience and smart functionality.However,the growing number of IoT devices has brought about a corresponding increase in cybersecurity threats,such as device vulnerabilities,data privacy concerns,and network susceptibilities.Integrating blockchain technology with IoT has proven to be a promising approach to enhance IoT security.Nevertheless,the emergence of quantum computing poses a significant challenge to the security of traditional classical cryptography used in blockchain,potentially exposing it to quantum cyber-attacks.To support the growth of the IoT industry,mitigate quantum threats,and safeguard IoT data,this study proposes a robust blockchain solution for IoT that incorporates both classical and post-quantum security measures.Firstly,we present the Quantum-Enhanced Blockchain Architecture for IoT(QBIoT)to ensure secure data sharing and integrity protection.Secondly,we propose an improved Proof of Authority consensus algorithm called“Proof of Authority with Random Election”(PoARE),implemented within QBIoT for leader selection and new block creation.Thirdly,we develop a publickey quantum signature protocol for transaction verification in the blockchain.Finally,a comprehensive security analysis of QBIoT demonstrates its resilience against cyber threats from both classical and quantum adversaries.In summary,this research introduces an innovative quantum-enhanced blockchain solution to address quantum security concernswithin the realmof IoT.The proposedQBIoT framework contributes to the ongoing development of quantum blockchain technology and offers valuable insights for future research on IoT security.

Quantum synchronization with correlated baths

We study quantum synchronization under the nonequilibrium reservoirs.We consider a two-qubit XXZ chain coupled independently to their own reservoirs modeled by the collisional model.Two reservoir particles,initially prepared in a thermal state or a state with coherence,are correlated through a unitary transformation and afterward interact locally with the two quantum subsystems.We study the quantum effect of reservoir on synchronous dynamics of system.By preparing different reservoir initial states or manipulating the reservoir particles coupling and the temperature gradient,we find that quantum entanglement of reservoir is the key to control quantum synchronization of system qubits.

Design of a novel hybrid quantum deep neural network in INEQR images classification

We redesign the parameterized quantum circuit in the quantum deep neural network, construct a three-layer structure as the hidden layer, and then use classical optimization algorithms to train the parameterized quantum circuit, thereby propose a novel hybrid quantum deep neural network(HQDNN) used for image classification. After bilinear interpolation reduces the original image to a suitable size, an improved novel enhanced quantum representation(INEQR) is used to encode it into quantum states as the input of the HQDNN. Multi-layer parameterized quantum circuits are used as the main structure to implement feature extraction and classification. The output results of parameterized quantum circuits are converted into classical data through quantum measurements and then optimized on a classical computer. To verify the performance of the HQDNN, we conduct binary classification and three classification experiments on the MNIST(Modified National Institute of Standards and Technology) data set. In the first binary classification, the accuracy of 0 and 4 exceeds98%. Then we compare the performance of three classification with other algorithms, the results on two datasets show that the classification accuracy is higher than that of quantum deep neural network and general quantum convolutional neural network.

Quafu-RL:The cloud quantum computers based quantum reinforcement learning

With the rapid advancement of quantum computing,hybrid quantum–classical machine learning has shown numerous potential applications at the current stage,with expectations of being achievable in the noisy intermediate-scale quantum(NISQ)era.Quantum reinforcement learning,as an indispensable study,has recently demonstrated its ability to solve standard benchmark environments with formally provable theoretical advantages over classical counterparts.However,despite the progress of quantum processors and the emergence of quantum computing clouds,implementing quantum reinforcement learning algorithms utilizing parameterized quantum circuits(PQCs)on NISQ devices remains infrequent.In this work,we take the first step towards executing benchmark quantum reinforcement problems on real devices equipped with at most 136 qubits on the BAQIS Quafu quantum computing cloud.The experimental results demonstrate that the policy agents can successfully accomplish objectives under modified conditions in both the training and inference phases.Moreover,we design hardware-efficient PQC architectures in the quantum model using a multi-objective evolutionary algorithm and develop a learning algorithm that is adaptable to quantum devices.We hope that the Quafu-RL can be a guiding example to show how to realize machine learning tasks by taking advantage of quantum computers on the quantum cloud platform.

Quantum block coherence with respect to projective measurements

Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.

Single-photon scattering and quantum entanglement of two giant atoms with azimuthal angle differences in a waveguide system

We theoretically investigate coherent scattering of single photons and quantum entanglement of two giant atoms with azimuthal angle differences in a waveguide system.Using the real-space Hamiltonian,analytical expressions are derived for the transport spectra scattered by these two giant atoms with four azimuthal angles.Fano-like resonance can be exhibited in the scattering spectra by adjusting the azimuthal angle difference.High concurrence of the entangled state for two atoms can be implemented in a wide angle-difference range,and the entanglement of the atomic states can be switched on/off by modulating the additional azimuthal angle differences from the giant atoms.This suggests a novel handle to effectively control the single-photon scattering and quantum entanglement.