In this paper, we generalize the construction of the inverse transgression map done by Adem, A., Ruan, Y. and Zhang, B. in [A stringy product on twisted orbifold K-theory. Morfismos, 11, 33 64 （2007）] and give a dif...In this paper, we generalize the construction of the inverse transgression map done by Adem, A., Ruan, Y. and Zhang, B. in [A stringy product on twisted orbifold K-theory. Morfismos, 11, 33 64 （2007）] and give a different proof to the statement that the image of the inverse transgression map for a gerbe with connection over an orbifold is an inner local system on its inertia orbifold.展开更多
Photons exhibit advantages including high speed,low power consumption,and resistance to electromagnetic interference.Integrated optics,which utilizes photons as information carriers,has shown superior performance for ...Photons exhibit advantages including high speed,low power consumption,and resistance to electromagnetic interference.Integrated optics,which utilizes photons as information carriers,has shown superior performance for information transmission and processing,making it a promising candidate for advanced integrated chips.Unlike microelectronic chips,which primarily rely on silicon,integrated photonics has been successfully developed across a diverse range of material platforms,including silicon.展开更多
Nonadiabatic holonomic quantum computers serve as the physical platform for nonadiabatic holonomic quantum computation.As quantum computation has entered the noisy intermediate-scale era,building accurate intermediate...Nonadiabatic holonomic quantum computers serve as the physical platform for nonadiabatic holonomic quantum computation.As quantum computation has entered the noisy intermediate-scale era,building accurate intermediate-scale nonadiabatic holo-nomic quantum computers is clearly necessary.Given that measurements are the sole means of extracting information,they play an indispensable role in nonadiabatic holonomic quantum computers.Accordingly,developing methods to reduce measurement errors in nonadiabatic holonomic quantum computers is of great importance.However,while much attention has been given to the research on nonadiabatic holonomic gates,the research on reducing measurement errors in nonadiabatic holonomic quantum computers is severely lacking.In this study,we propose a measurement error reduction method tailored for intermediate-scale nonadiabatic holonomic quantum computers.The reason we say this is because our method can not only reduce the measurement errors in the computer but also be useful in mitigating errors originating from nonadiabatic holonomic gates.Given these features,our method significantly advances the construction of accurate intermediate-scale nonadiabatic holonomic quantum computers.展开更多
A stochastic holonomy along a loop obtained from the OU process on the path space over acompact Riemannian manifold is computed. The result shows that the stochastic holonomy just gives theparallel transport with resp...A stochastic holonomy along a loop obtained from the OU process on the path space over acompact Riemannian manifold is computed. The result shows that the stochastic holonomy just gives theparallel transport with respect to the Markov connection along the OU process on the path space.展开更多
The author surveys Connes' results on the longitudinal Laplace operator along a(regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it i...The author surveys Connes' results on the longitudinal Laplace operator along a(regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator(unbounded) and has the same spectrum in every(faithful) representation, in particular, in L2 of the manifold and L2 of a leaf.The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11071176)
文摘In this paper, we generalize the construction of the inverse transgression map done by Adem, A., Ruan, Y. and Zhang, B. in [A stringy product on twisted orbifold K-theory. Morfismos, 11, 33 64 （2007）] and give a different proof to the statement that the image of the inverse transgression map for a gerbe with connection over an orbifold is an inner local system on its inertia orbifold.
基金supported by the National Key Research and Development Program of China(2024YFB4608100)the Young Top-Notch Talent for Ten Thousand Talent Program,and the National Natural Science Foundation of China(12374350).
文摘Photons exhibit advantages including high speed,low power consumption,and resistance to electromagnetic interference.Integrated optics,which utilizes photons as information carriers,has shown superior performance for information transmission and processing,making it a promising candidate for advanced integrated chips.Unlike microelectronic chips,which primarily rely on silicon,integrated photonics has been successfully developed across a diverse range of material platforms,including silicon.
基金supported by the National Natural Science Foundation of China(Grant No.12174224)。
文摘Nonadiabatic holonomic quantum computers serve as the physical platform for nonadiabatic holonomic quantum computation.As quantum computation has entered the noisy intermediate-scale era,building accurate intermediate-scale nonadiabatic holo-nomic quantum computers is clearly necessary.Given that measurements are the sole means of extracting information,they play an indispensable role in nonadiabatic holonomic quantum computers.Accordingly,developing methods to reduce measurement errors in nonadiabatic holonomic quantum computers is of great importance.However,while much attention has been given to the research on nonadiabatic holonomic gates,the research on reducing measurement errors in nonadiabatic holonomic quantum computers is severely lacking.In this study,we propose a measurement error reduction method tailored for intermediate-scale nonadiabatic holonomic quantum computers.The reason we say this is because our method can not only reduce the measurement errors in the computer but also be useful in mitigating errors originating from nonadiabatic holonomic gates.Given these features,our method significantly advances the construction of accurate intermediate-scale nonadiabatic holonomic quantum computers.
基金This work was supported partly by the National Natural Science Foundation of China (Grant No. 10101002).
文摘A stochastic holonomy along a loop obtained from the OU process on the path space over acompact Riemannian manifold is computed. The result shows that the stochastic holonomy just gives theparallel transport with respect to the Markov connection along the OU process on the path space.
基金supported by a Marie Curie Career Integration Grant(No.FP7-PEOPLE-2011-CIG,No.PCI09-GA-2011-290823)the FCT(Portugal)with European Regional Development Fund(COMPETE)national funds through the project PTDC/MAT/098770/2008
文摘The author surveys Connes' results on the longitudinal Laplace operator along a(regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator(unbounded) and has the same spectrum in every(faithful) representation, in particular, in L2 of the manifold and L2 of a leaf.The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum.
