Let K/Q be any abelian extension where Q is the field of rational numbers. By Galois theory and the Frobenius formula for induced characters, we prove that there exists a metabelian group G and an irreducible characte...Let K/Q be any abelian extension where Q is the field of rational numbers. By Galois theory and the Frobenius formula for induced characters, we prove that there exists a metabelian group G and an irreducible character X of G such that K=Q（X）.展开更多
Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiab...Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics.It is shown that a non-Abelian gauge potential is achieved only for a single atom,whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble.More importantly,two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted.The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes,which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.展开更多
we have discussed structures of Abelian group G by order |A(G) |of automoorphism group and have obtained all types of finite Abelian grooup G when the order of A(G) equals 27pq(p,q are odd primmes).
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 o...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.展开更多
In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain...In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.展开更多
基金Supported by the National Program for the Basic Science Researches of China(G19990751)
文摘Let K/Q be any abelian extension where Q is the field of rational numbers. By Galois theory and the Frobenius formula for induced characters, we prove that there exists a metabelian group G and an irreducible character X of G such that K=Q（X）.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10904092,10934004,60978018,11074184,and 11074154the Zhejiang Provincial Natural Science Foundation under Grant No.Y6090001
文摘Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics.It is shown that a non-Abelian gauge potential is achieved only for a single atom,whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble.More importantly,two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted.The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes,which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.
文摘we have discussed structures of Abelian group G by order |A(G) |of automoorphism group and have obtained all types of finite Abelian grooup G when the order of A(G) equals 27pq(p,q are odd primmes).
基金the National Natural Science Foundation of China(Grants Nos.92065204,12075128,T2225008,12174342,12274368,12274367,U20A2076,and 11725419)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0300200)+2 种基金the Zhejiang Province Key Research and Development Program(Grant No.2020C01019)supported by Tsinghua Universitythe Shanghai Qi Zhi Institute。
文摘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.
基金supported by NSF of China(11671057)NSF of Chongqing(cstc2020jcyj-msxmX0694)the Fundamental Research Funds for the Central Universities(2018CDQYST0023).
文摘In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.
