探索量子通道識別、動態流與迭代數值方法
11:20–12:20
本次演講將提供學生便當， 歡迎有意參加的同學填寫報名表單。
表單截止： 115年11月5日（四）中午12:00
若報名人數達46人，將提前關閉表單， 敬請留意。
Identifying a quantum channel shows how quantum states evolve and how information propagates through a physical system. Because exact reconstruction is NP-hard, we focus on efficient numerical approximations. We exploit the unitary structure underlying channel dynamics and formulate the problem on the Stiefel manifold, the natural geometric setting for matrices with orthonormal columns, including real orthogonal and complex unitary matrices. This formulation leads to practical reconstruction algorithms.
When a single unitary operator generates the channel, we combine the polar decomposition with the geometry of the manifold. This gives exact recovery and identifies the minimal data required.
For channels that are convex combinations of several unitaries, we develop a gradient-flow scheme on the Stiefel manifold. We prove that it converges and show that the method is accurate and flexible.
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