Complex networks have been a prominent topic of research for several years,spanning a wide range of fields from mathematics to computer science and also to social and biological sciences.The eigenvalues of the Seidel ...Complex networks have been a prominent topic of research for several years,spanning a wide range of fields from mathematics to computer science and also to social and biological sciences.The eigenvalues of the Seidel matrix,Seidel Signless Laplacian matrix,Seidel energy,Seidel Signless Laplacian energy,Maximum and Minimum energy,Degree Sum energy and Distance Degree energy of the Unitary Cayley graphs[UCG]have been calculated.Low-power devices must be able to transfer data across long distances with low delay and reliability.To overcome this drawback a small-world network depending on the unitary Cayley graph is proposed to decrease the delay and increase the reliability and is also used to create and analyze network communication.Small-world networks based on the Cayley graph have a basic construction and are highly adaptable.The simulation result shows that the small-world network based on unitary Cayley graphs has a shorter delay and is more reliable.Furthermore,the maximum delay is lowered by 40%.展开更多
In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuti...In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.展开更多
Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems.Quantum information processing can be used to red...Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems.Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems.We speak of pseudo-telepathy when it is able to completely eliminate the need for communication.Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game,quantum players are almost certain to make errors even though they use a winning strategy.After introducing a model for pseudotelepathy games,we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game.The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.展开更多
We examine critically how tightly the density dependence of nuclear symmetry energy E_(sym)(q) is constrained by the universal equation of state of the unitary Fermi gas EUG(q) considering currently known uncertaintie...We examine critically how tightly the density dependence of nuclear symmetry energy E_(sym)(q) is constrained by the universal equation of state of the unitary Fermi gas EUG(q) considering currently known uncertainties of higher order parameters describing the density dependence of the equation of state of isospin asymmetric nuclear matter. We found that E_(UG)(q) does provide a useful lower boundary for the E_(sym)(q). However, it doesnot tightly constrain the correlation between the magnitude E_(sym)(q_0) and slope L unless the curvature K_(sym)of the symmetry energy at saturation density q_0 is more precisely known. The large uncertainty in the skewness parameters affects the E_(sym)(q_0) versus L correlation by the same almost as significantly as the uncertainty in K_(sym).展开更多
The supersymmetric partner system of Hulthen system in the s state is obtained by using a semi-unitary transformation.The physical foundation of applications of semi-unitary transformation to supersymmetric quantum me...The supersymmetric partner system of Hulthen system in the s state is obtained by using a semi-unitary transformation.The physical foundation of applications of semi-unitary transformation to supersymmetric quantum mechanics is explored.展开更多
We propose a method to estimate the average fidelity using the unitary 2t-design of a twirled noisy channel, which is suitable for large-scale quantum circuits. Compared with the unitary 2-design in randomized benchma...We propose a method to estimate the average fidelity using the unitary 2t-design of a twirled noisy channel, which is suitable for large-scale quantum circuits. Compared with the unitary 2-design in randomized benchmarking, the unitary2t-design for the twirling of noisy channels is more flexible in construction and can provide more information. In addition,we prove that the proposed method provides an efficient and reliable estimation of the average fidelity in benchmarking multistage quantum gates and estimating the weakly gate-and time-dependent noise. For time-dependent noise, we provide a scheme of moment superoperator to analyze the noise in different experiments. In particular, we give a lower bound on the average fidelity of a channel with imperfect implementation of benchmarking and state preparation and measurement errors(SPAM).展开更多
Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any fo...Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates,and time evolution of state vector are obtained.展开更多
We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of trans...We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.展开更多
It is well-known that the multi-valued CDMA spreading codes can be designed by means of a pair of mirror multi-rate filter banks based on some optimizing criterion. This paper indicates that there exists a theoretical...It is well-known that the multi-valued CDMA spreading codes can be designed by means of a pair of mirror multi-rate filter banks based on some optimizing criterion. This paper indicates that there exists a theoretical bound in the performance of its circulating correlation property, which is given by an explicit expression. Based on this analysis, a criterion of maximizing entropy is proposed to design such codes. Computer simulation result suggests that the resulted codes outperform the conventional binary balanced Gold codes for an asynchronous CDMA system.展开更多
Hermitian systems possess unitary scattering.However,the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary.Here we prove that the ...Hermitian systems possess unitary scattering.However,the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary.Here we prove that the unitary scattering is protected by certain type of pseudo-Hermiticity and unaffected by the degree of non-Hermiticity.The energy conservation is violated in the scattering process and recovers after scattering.The subsystem of the pseudo-Hermitian scattering center including only the connection sites is Hermitian.These findings provide fundamental insights on the unitary scattering,pseudo-Hermiticity,and energy conservation,and are promising for light propagation,mesoscopic electron transport,and quantum interference in non-Hermitian systems.展开更多
For the generalized Jaynes-Cummings model Hamiltonian which can describe two collectively radiation atoms,we find its supersymmetric structure.Based on supersymmetric quantum mechanics theory,we introduce a supersymme...For the generalized Jaynes-Cummings model Hamiltonian which can describe two collectively radiation atoms,we find its supersymmetric structure.Based on supersymmetric quantum mechanics theory,we introduce a supersymmetric unitary transformation,in which the supersymmetric unitary transformation operator can be constructed by supersymmetric generators of the super-Lie algebra,to diagonalize the Hamiltonian.On doing so,its eigenvalue and eigenstates are obtained.展开更多
In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offere...In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.展开更多
An explanation of optical unitary transformation is presented for general nonoverlapping-image multimode interference(MMI)couplers with any number of input and output ports.The light transformation in the MMI coupler ...An explanation of optical unitary transformation is presented for general nonoverlapping-image multimode interference(MMI)couplers with any number of input and output ports.The light transformation in the MMI coupler can be considered as an optical field matrix acting on an input light column vector.We investigate the general phase principle of output light image.The complete proof of nonoverlapping-image MMI coupler’s optical unitarity along with the phase analysis of matrix element is provided.Based on a two-dimensional finite-difference time-domain(2 D-FDTD)simulation,the unitary transformation is obtained for a 4×4 nonoverlapping-image MMI coupler within a deviation of 4×10-2 for orthogonal invariance and 8×10-2 for transvection invariance in the C-band spectral range.A compact 1×4 splitter based on cascaded MMI coupler is proposed,showing a phase deviation less than 5.4°while maintaining a low-loss performance in C-band spectra.展开更多
Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermi...Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermite matrix are studied further,and thismust be useful for matrix theory and applications（like optimization theory,symplecticgeometry and physics etc）.In the paper,C<sup>m×n</sup>shows m×n compound matrix set,C<sub>n</sub><sup>m×n</sup>shows n step compound invertible matrix set,A<sup>*</sup> shows conjugate transpose matrix of A,展开更多
文摘Complex networks have been a prominent topic of research for several years,spanning a wide range of fields from mathematics to computer science and also to social and biological sciences.The eigenvalues of the Seidel matrix,Seidel Signless Laplacian matrix,Seidel energy,Seidel Signless Laplacian energy,Maximum and Minimum energy,Degree Sum energy and Distance Degree energy of the Unitary Cayley graphs[UCG]have been calculated.Low-power devices must be able to transfer data across long distances with low delay and reliability.To overcome this drawback a small-world network depending on the unitary Cayley graph is proposed to decrease the delay and increase the reliability and is also used to create and analyze network communication.Small-world networks based on the Cayley graph have a basic construction and are highly adaptable.The simulation result shows that the small-world network based on unitary Cayley graphs has a shorter delay and is more reliable.Furthermore,the maximum delay is lowered by 40%.
文摘In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.
基金supported by the research projects MSM0021622419 and 201/0710603
文摘Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems.Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems.We speak of pseudo-telepathy when it is able to completely eliminate the need for communication.Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game,quantum players are almost certain to make errors even though they use a winning strategy.After introducing a model for pseudotelepathy games,we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game.The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.
基金supported in part by the China Scholarship Councilthe U.S.Department of Energy,Office of Science,under Award Number DE-SC0013702+7 种基金the CUSTIPEN(China-U.S.Theory Institute for Physics with Exotic Nuclei) under the US Department of Energy Grant No.DE-SC0009971the National Natural Science Foundation of China under Grant No.11320101004the Texas Advanced Computing Centersupported in part by the Major State Basic Research Development Program(973Program) of China under Contract Nos.2015CB856904 and 2014CB845401the National Natural Science Foundation of China under Grant Nos.11475243 and 11421505the ‘‘100-talent plan’’ of Shanghai Institute of Applied Physics under Grant Nos.Y290061011and Y526011011 from the Chinese Academy of Sciencesthe Shanghai Key Laboratory of Particle Physics and Cosmology under Grant No.15DZ2272100the Shanghai Pujiang Program under Grant No.13PJ1410600
文摘We examine critically how tightly the density dependence of nuclear symmetry energy E_(sym)(q) is constrained by the universal equation of state of the unitary Fermi gas EUG(q) considering currently known uncertainties of higher order parameters describing the density dependence of the equation of state of isospin asymmetric nuclear matter. We found that E_(UG)(q) does provide a useful lower boundary for the E_(sym)(q). However, it doesnot tightly constrain the correlation between the magnitude E_(sym)(q_0) and slope L unless the curvature K_(sym)of the symmetry energy at saturation density q_0 is more precisely known. The large uncertainty in the skewness parameters affects the E_(sym)(q_0) versus L correlation by the same almost as significantly as the uncertainty in K_(sym).
基金Supported by the National Natural Science Foundation of China,。
文摘The supersymmetric partner system of Hulthen system in the s state is obtained by using a semi-unitary transformation.The physical foundation of applications of semi-unitary transformation to supersymmetric quantum mechanics is explored.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61372076 and 61701375)the 111 Project,China(Grant No.B08038)+1 种基金the Key Research and Development Plan of Shannxi Province,China(Grant No.BBD24017290001)the Foundation of Science and Technology on Communication Networks Laboratory,China(Grant No.KX172600031)
文摘We propose a method to estimate the average fidelity using the unitary 2t-design of a twirled noisy channel, which is suitable for large-scale quantum circuits. Compared with the unitary 2-design in randomized benchmarking, the unitary2t-design for the twirling of noisy channels is more flexible in construction and can provide more information. In addition,we prove that the proposed method provides an efficient and reliable estimation of the average fidelity in benchmarking multistage quantum gates and estimating the weakly gate-and time-dependent noise. For time-dependent noise, we provide a scheme of moment superoperator to analyze the noise in different experiments. In particular, we give a lower bound on the average fidelity of a channel with imperfect implementation of benchmarking and state preparation and measurement errors(SPAM).
文摘Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates,and time evolution of state vector are obtained.
文摘We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.
基金Supported by the National Natural Science Foundation of China(No.69872027)
文摘It is well-known that the multi-valued CDMA spreading codes can be designed by means of a pair of mirror multi-rate filter banks based on some optimizing criterion. This paper indicates that there exists a theoretical bound in the performance of its circulating correlation property, which is given by an explicit expression. Based on this analysis, a criterion of maximizing entropy is proposed to design such codes. Computer simulation result suggests that the resulted codes outperform the conventional binary balanced Gold codes for an asynchronous CDMA system.
基金supported by the National Natural Science Foundation of China(Grant No.11975128)。
文摘Hermitian systems possess unitary scattering.However,the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary.Here we prove that the unitary scattering is protected by certain type of pseudo-Hermiticity and unaffected by the degree of non-Hermiticity.The energy conservation is violated in the scattering process and recovers after scattering.The subsystem of the pseudo-Hermitian scattering center including only the connection sites is Hermitian.These findings provide fundamental insights on the unitary scattering,pseudo-Hermiticity,and energy conservation,and are promising for light propagation,mesoscopic electron transport,and quantum interference in non-Hermitian systems.
文摘For the generalized Jaynes-Cummings model Hamiltonian which can describe two collectively radiation atoms,we find its supersymmetric structure.Based on supersymmetric quantum mechanics theory,we introduce a supersymmetric unitary transformation,in which the supersymmetric unitary transformation operator can be constructed by supersymmetric generators of the super-Lie algebra,to diagonalize the Hamiltonian.On doing so,its eigenvalue and eigenstates are obtained.
基金This work was funded by the Natural Science Foundation of Jiangsu Province(Grant No:BK20171458)the Yangzhou University International Academic Exchange Fund.
文摘In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.
基金Project supported by the National Key Research and Development Program of China(Grant No.2018YFB2200202)the National Natural Science Foundation of China(Grant No.61804148)
文摘An explanation of optical unitary transformation is presented for general nonoverlapping-image multimode interference(MMI)couplers with any number of input and output ports.The light transformation in the MMI coupler can be considered as an optical field matrix acting on an input light column vector.We investigate the general phase principle of output light image.The complete proof of nonoverlapping-image MMI coupler’s optical unitarity along with the phase analysis of matrix element is provided.Based on a two-dimensional finite-difference time-domain(2 D-FDTD)simulation,the unitary transformation is obtained for a 4×4 nonoverlapping-image MMI coupler within a deviation of 4×10-2 for orthogonal invariance and 8×10-2 for transvection invariance in the C-band spectral range.A compact 1×4 splitter based on cascaded MMI coupler is proposed,showing a phase deviation less than 5.4°while maintaining a low-loss performance in C-band spectra.
基金Supported by the Natural Science Foundation of Chongqing
文摘Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermite matrix are studied further,and thismust be useful for matrix theory and applications（like optimization theory,symplecticgeometry and physics etc）.In the paper,C<sup>m×n</sup>shows m×n compound matrix set,C<sub>n</sub><sup>m×n</sup>shows n step compound invertible matrix set,A<sup>*</sup> shows conjugate transpose matrix of A,
