量子拓樸快遞方法 Quantum Topology Express Method

We proposed a formula for the ${\mathbb{Z}}_{2}$ invariant for topological insulators, which remains valid without translational invariance. Our formula is a local expression, in the sense that the contributions mainly come from quantities near a point. Using almost commute matrices, we proposed a method to approximate this invariant with local information. The validity of the formula and the approximation method is proved.We proposed a formula for the ${\mathbb{Z}}_{2}$ invariant for topological insulators, which remains valid without translational invariance. Our formula is a local expression, in the sense that the contributions mainly come from quantities near a point. Using almost commute matrices, we proposed a method to approximate this invariant with local information. The validity of the formula and the approximation method is proved.

arXiv:1905.12649Physical review. B./Physical review. BNov 4, 201914 citations

Quantum Computing and Quantum Topology

Louis Hirsch Kauffman, Samuel J. Lomonaco

Chapman & Hall/CRC applied mathematics and nonlinear science seriesSep 19, 20070 citations

REDUCED QUANTUM TOPOLOGICAL TRAJECTORY IN COHERENCE AND DECOHERENCE

Xuguang Shi, Yi-Shi Duan

We have studied the topological expression of the reduced quantum trajectory using ϕ-mapping topological current theory and reduced density matrix theory. Moreover, we have proposed a new topological expression called the reduced quantum topological trajectory. Ignoring the coefficients of the winding number, we have found that the expression for the reduced quantum topological trajectory is the same for coherence as it is for decoherence. Under certain conditions, the vorticity of the reduced quantum topological trajectory is a topological invariant.We have studied the topological expression of the reduced quantum trajectory using ϕ-mapping topological current theory and reduced density matrix theory. Moreover, we have proposed a new topological expression called the reduced quantum topological trajectory. Ignoring the coefficients of the winding number, we have found that the expression for the reduced quantum topological trajectory is the same for coherence as it is for decoherence. Under certain conditions, the vorticity of the reduced quantum topological trajectory is a topological invariant.

Modern Physics Letters AMay 30, 20113 citations

Combinatorial quantum method in 3-dimensional topology

知忠大槻

Mathematical Society of Japan eBooksJan 1, 19990 citations

We proposed a formula for the

{\mathbb{Z}}_{2}

invariant for topological insulators, which remains valid without translational invariance. Our formula is a local expression, in the sense that the contributions mainly come from quantities near a point. Using almost commute matrices, we proposed a method to approximate this invariant with local information. The validity of the formula and the approximation method is proved.