4 papers
Optimal Quantum Eigenvalue Transformation via Linear Combinations of Hermitian Matrices
Yanqiao Wang, Yixuan Liang, Hongjia Chen +1
We discover two complementary linear-combination-of-Hermitian-matrices (LCHM) formulations to achieve a general non-normal matrix eigenvalue transformation . Firstly, for $A=…
Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions
Yixuan Liang, Jin-Peng Liu
We give detailed analysis and circuit design of structure-preserving quantum algorithms for second-order linear evolutionary PDEs, including parabolic equations and hyperbolic equa…
Inertia of partial transpose of positive semidefinite matrices
Yixuan Liang, Jiahao Yan, Dongran Si +1
We show that the partial transpose of positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4). It solves an open problem in "LINEAR AND MULTILINEAR ALGEB…
Quantifying the entanglement of quantum states under the geometry method
Xian Shi, Lin Chen, Yixuan Liang
Quantifying entanglement is an important issue in quantum information theory. Here we consider the entanglement measures through the trace norm in terms of two methods, the modifie…