6 papers
Triangular Prism Equations and Categorification
Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren +1
We introduce the triangular prism equations (TPE) for fusion categories, obtained by evaluating triangular prisms in terms of tetrahedra. Using an oriented graphical calculus, we s…
Topological Orders from Reflection Positive Frustration-free Hamiltonians
Zhengwei Liu, Zishuo Zhao
We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection po…
Test Schwartz functions at for theta lifts of Hida families
Zheng Liu
We construct Hida families of theta lifts from definite orthogonal and unitary groups. A major ingredient of the construction is the choice of test Schwartz functions at places div…
Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement
Zixuan Feng, Zhengwei Liu, Fan Lu +1
We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Cla…
2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond
Byungmin Kang, Chen Zhao, Zhengwei Liu +2
Simulating generic quantum states and dynamics is practically intractable using classical computers. However, certain special classes -- namely Clifford and matchgate circuits -- p…
Classification of exchange relation planar algebras through sieving forest fusion graphs
Fan Lu, Zhengwei Liu
We suggest a classification scheme for subfactorizable fusion bialgebras, particularly for exchange relation planar algebras. This scheme begins by transforming infinite diagrammat…