Center for Quantum Frontier of Research and Technology (Seminar)
Low Rank Approximation of Entangled Bipartite Systems
Speaker : Prof. Matthew M. Lin (Dept. of Math., NCKU)
Time :
2021 / 12 / 13
12:10
Abstract :
Gauging the distance between a mixed state and its nearest separable state is important but challenging in the quantum mechanical system. We, in this talk, propose a dynamical system approach to tackle low rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. The theory, algorithms, and some numerical experiments will be presented in this talk.
References
[1] M. T. Chu and M. M. Lin, A Complex-Valued Gradient Flow for the Entangled Bipartite Low Rank Approximation, Computer Physics Communications, accepted 2021.
Gauging the distance between a mixed state and its nearest separable state is important but challenging in the quantum mechanical system. We, in this talk, propose a dynamical system approach to tackle low rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. The theory, algorithms, and some numerical experiments will be presented in this talk.
References
[1] M. T. Chu and M. M. Lin, A Complex-Valued Gradient Flow for the Entangled Bipartite Low Rank Approximation, Computer Physics Communications, accepted 2021.
