Full Poncelet Theorem in Minkowski dS and AdS Spaces

We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in projective geometry. We then establish the full Poncelet theorem which holds in projective geometry in n-dimensional Minkowski space and in their quadratic surfaces including de Sitter and AdS spaces.     

Quantum simulation and quantum computation of noisy-intermediate scale

In the past years, great progresses have been made on quantum computation and quantum simulation. Increasing the number of qubits in the quantum processors is expected to be one of the main motivations in the next years, while noises in manipulation of quantum states may still be inevitable even the precision will improve. For research in this direction, it is necessary to review the available results about noisy multiqubit quantum computation and quantum simulation. The review focuses on multiqubit state generations, quantum computational advantage, and simulating physics of quantum many-body systems. Perspectives of near term noisy intermediate-quantum processors will be discussed.     

Zn格点模型的量子仿射变形代数

应用两种不同的星三角关系及其对应的Boltzmann面权,通过反对称聚合,构造出了在椭圆情形下的q变形仿射代数.     

量子计算与量子模拟

量子计算和量子模拟在过去的几年里发展迅速,今后涉及多量子比特的量子计算和量子模拟将是一个发展的重点.本文回顾了该领域的主要进展,包括量子多体模拟、量子计算、量子计算模拟器、量子计算云平台、量子软件等内容,其中量子多体模拟又涵盖量子多体动力学、时间晶体及多体局域化、量子统计和量子化学等的模拟.这些研究方向的回顾是基于对现阶段量子计算和量子模拟研究特点的考虑,即量子比特数处于中等规模而量子操控精度还不具有大规模逻辑门实现的能力,研究处于基础科研和实用化的过渡阶段,因此综述的内容主要还是希望管窥今后的发展.     

19顶角模型反射方程的常数解

通过直接解反射方程,给出了19顶角模型A2(2)模型反射方程的所有矩阵元非零形式以及其它几种非对角形式的常数解.     

15顶角模型反射方程的常数解

得到了15顶角模型A2(1)模型和超对称t–J模型反射方程的非对角解,结果发现,A2(1)模型具有三种形式的非对角解,超对称t–J模型具有一种形式的非对角解,每种形式的非对角解均含有两个解,每个非对角解中均含有三个任意参数.关于对角解也得到了一些新的形式的解.     

量子计算新进展:硬件、算法和软件专题编者按

1980年, 美国科学家 Paul Benioff和前苏联科学家 Yuri Manin提出了量子计算的概念, 1981年诺贝奖费曼提出了量子模拟, 1985年David Deutsch证明了量子计算概念的普适性. 至此,完成了建立量子计算概念的第一个阶段. 1986-1993年, 是量子计算机研究的自由探索阶段. 19...     

Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.     

椭圆量子群极小表示的系数代数

给出了对应于A(1)n–1面模型的玻尔兹曼权的L矩阵及FelderAn系列椭圆量子群的极小表示(所有矩阵元均为c数)的系数代数.这个代数满足杨–Baxter方程.同时,对此代数还给出了一组PBW基.     

推广t-J模型的坐标Bethe Ansatz方法

利用坐标Bethe Ansatz方法,研究了推广的t—J模型的精确解,导出了两组Bethe Ansatz方程;同时证明了在两体散射问题中的散射矩阵正是三角型的非对称六顶角R矩阵.