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Digital Simulation of Projective Non-abelian Anyons with 68 Superconducting Qubits

Chinese Physics Letters 2023年第6期40卷 1-7页

作者： Shibo Xu Zheng-Zhi Sun Ke Wang Liang Xiang Zehang Bao Zitian Zhu Fanhao Shen Zixuan Song Pengfei Zhang Wenhui Ren Xu Zhang Hang Dong Jinfeng Deng Jiachen Chen Yaozu Wu Ziqi Tan Yu Gao Feitong Jin Xuhao Zhu Chuanyu Zhang Ning Wang Yiren Zou Jiarun Zhong Aosai Zhang Weikang Li Wenjie Jiang Li-Wei Yu Yunyan Yao Zhen Wang Hekang Li Qiujiang Guo Chao Song H.Wang Dong-Ling Deng School of Physics ZJU-Hangzhou Global Scientific and Technological Innovation CenterInterdisciplinary Center for Quantum Informationand Zhejiang Province Key Laboratory of Quantum Technology and DeviceZhejiang UniversityHangzhou 310027China Center for Quantum Information IIISTsinghua UniversityBeijing 100084China Theoretical Physics Division Chern Institute of Mathematics and LPMCNankai UniversityTianjin 300071China Hefei National Laboratory Hefei 230088China Shanghai Qi Zhi Institute Shanghai 200232China

Non-abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of *** 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 *** are the building blocks of topological quantum ***,experimental observation of non-abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto,in spite of various theoretical ***,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 *** 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 *** 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 ***,we demonstrate how to implement both single-and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical *** results demonstrate a versatile quantum digital approach for simulating non-abelian anyons,offering a new lens into the study of such peculiar quasiparticles.

关键词： topological abelian quantum

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Non-abelian generalizations of the Hofstadter model:spin-orbit-coupled butterfly pairs

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Light(Science & Applications) 2020年第1期9卷 302-314页

作者： Yi Yang Bo Zhen John D.Joannopoulos Marin Soljacic Department of Physics and Research Laboratory of Electronics Massachusetts Institute of TechnologyCambridgeMA 02139USA Department of Physics and Astronomy University of PennsylvaniaPhiladelphiaPA 19104USA

The Hofstadter model,well known for its fractal butterfly spectrum,describes two-dimensional electrons under a perpendicular magnetic field,which gives rise to the integer quantum Hall *** by the real-space building blocks of non-abelian gauge fields from a recent experiment,we introduce and theoretically study two non-abelian generalizations of the Hofstadter *** model describes two pairs of Hofstadter butterflies that are spin–orbit *** contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges,the corresponding non-abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge *** derive the genuine(necessary and sufficient)non-abelian condition for the two models from the commutativity of their arbitrary loop *** zero energy,the models are gapless and host Weyl and Dirac points protected by internal and crystalline ***(8-fold),triple(12-fold),and quadrupole(16-fold)Dirac points also emerge,especially under equal hopping phases of the non-abelian *** other fillings,the gapped phases of the models give rise to topological *** conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

关键词： generalization gauge abelian

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Linear estimate of the number of zeros of abelian integrals for quadratic centers having almost all their orbits formed by cubics

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Science China Mathematics 2002年第8期45卷 964-974页

作者：赵育林张芷芬李伟固李承治 Department of Mathematics Zhongshan University Guangzhou China School of Mathematical Sciences Peking University Beijing China

We study the number of zeros of abelian integrals for the quadratic centers having almost all their orbits formed by cubics, when we perturb such systems inside the class of all polynomial systems of degree n.

关键词： abelian integrals, quadratic integrable system.

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Finite abelian Groups with the Strong Endomorphism Kernel Property

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Acta Mathematica Sinica,English Series 2020年第9期36卷 1076-1082页

作者： Jie FANG Zhong Ju SUN School of Mathematics and Systems Science Guangdong Polytechnic Normal UniversityGuangzhou 510665P.R.China

An endomorphism h of a group G is said to be strong whenever for every congruenceθon G,(x,y)∈θimplies(h(x),h(y))∈θfor every x,y∈G.A group G is said to have the strong endomorphism kernel property if every congruence on G is the kernel of a strong *** this note,we study the strong endomorphism kernel property in the class of abelian *** particular,we show that a finite abelian group has the strong endomorphism kernel property if and only if it is cyclic.

关键词： Strong endomorphism kernel property congruence abelian group cyclic group

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A result about abelian automorphism groups

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Science China Mathematics 1997年第5期40卷 494-500页

作者：班桂宁俞曙霞 Department of Mathematics Guangxi University Nanning 530004 China

Some new techniques are given to prove that two sorts of abelian groups cannot function as the full automorphism groups of the finite groups. With generality these techniques made a breakthrough in MacHale’s problem.

关键词： finite group p-group automorphism abelian group defining relation.

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Structure and prime decomposition law and relative extensions of abelian fields with prime power degree

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Science China Mathematics 1999年第8期42卷 816-824页

作者：张贤科 Department of Mathematics Tsinghua University Beijing China

Let L be an abelian extension of the rationals Q whose Galois group Gal(L) is an abelian (q-group q is any prime number). The explicit law of prime decomposition in L for any prime number p, the inertia group, residue class degree, and discriminant of L are given here; such fields L are classified into 4 or 8 classes according as q is odd or even with clear description of their structures. Then relative extension L/K is studied. L/K is proved to have a relative integral basis under certain simple conditions; relative discriminant D(L/K) is given explicitly; and necessary and sufficient conditions are obtained for D(L/K) to be generated by a rational square (and by a rational). In particular, it is proved that L/K has a relative integral basis and that D(L/K) is generated by a rational square if [L: K]≥x~* or x~*+1 (according as q is odd or even), where x~* is the exponent of Gal(L). These results contain many related results on similar fields in literature.

关键词： algebraic number field abelian field prime decomposition relative extension inertia group.

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A Hierarchy in Majorana Non-abelian Tests and Hidden Variable Models

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Chinese Physics Letters 2023年第10期40卷 13-18页

作者：钱鹏刘东 Beijing Academy of Quantum Information Sciences Beijing 100193China State Key Laboratory of Low Dimensional Quantum Physics Department of PhysicsTsinghua UniversityBeijing 100084China Frontier Science Center for Quantum Information Beijing 100184China Hefei National Laboratory Hefei 230088China

The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically protected quantum information ***,a deficient design in those tests could be very dangerous and reach false-positive conclusions.A careful theoretical analysis is necessary so as to develop loophole-free *** introduce a series of classical hidden variable models to capture certain key properties of Majorana system:non-locality,topologically non-triviality,and quantum *** models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana nonabelian tests:fusion tests,braiding tests and test set with joint *** find a hierarchy among those Majorana tests with increasing experimental complexity.

关键词： abelian topological quantum

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Relative integral bases of abelian q-fields

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Chinese Science Bulletin 1996年第13期41卷 1065-1068页

作者：张贤科 Department of Mathematics Tsinghua University Beijing 100084 China

Let O_L and O_K denote the rings of integers in the algebraic number fields L and K, respectively, where K is a subfield of L. If O_L is a free O_K-module, then L/K is said to have a relative integral basis. Artin and Frhlich raised and studied the problem of existence of a relative integral basis for a number field L. The nroblem was treated

关键词： number field abelian field relative integral basis character group.

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AN　HARMONIC　ANALYSIS　FOR　OPERATORS　IN　THE　CASE　OF　A　LOCALLY　COMPACT　abelian　GROUP：***　***　THEOREMS

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Acta Mathematica Scientia 1994年第2期14卷 130-138页

作者：于树模 Dept. of Math. Fudan Univ. Shanghai 200433 China

Let G be a locally compact abelian group, B a homogeneous Banach algebra without the order on G. at denotes the set of all integrable operators with respect to right translation on B(see [2]). Under some convenient conditions we obtain the following results:both the first F. and M. Riesz Theorem for operators in and the second F. and M. Riesz Theorem for operators in hold.

关键词： CASE ANALYSIS THEOREMS abelian COMPACT FOR GROUP HARMONIC IN LOCALLY

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Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1 and CHEN Xiaoman 2 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China 2. Laboratory of Mathematics for Nonlinear Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, China Department of Mathematics Shanghai Normal University Shanghai China Laboratory of Mathematics for Nonlinear Sciences and Institute of Mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.

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