Long-range nonstabilizerness from quantum codes, orders, and correlations
演讲者
魏付川
时间
2025年06月06日 16:00 至 17:30
地点
Shuangqing-B627
线上
Zoom 230 432 7880
(BIMSA)
摘要
We investigate long-range magic (LRM), defined as nonstabilizerness that cannot be (approximately) erased by shallow local unitary circuits. In doing so, we prove a robust generalization of the Bravyi-König theorem. By establishing connections to the theory of fault-tolerant logical gates on quantum error-correcting codes, we show that certain families of topological stabilizer code states exhibit LRM. Then, we show that all ground states of topological orders that cannot be realized by topological stabilizer codes, such as Fibonacci topological order, exhibit LRM, which yields a "no lowest-energy trivial magic" result. Building on our considerations of LRM, we discuss the classicality of short-range magic from e.g. preparation and learning perspectives, and put forward a "no low-energy trivial magic" (NLTM) conjecture that has key motivation in the quantum PCP context. Our study leverages and sheds new light on the interplay between quantum resources, error correction and fault tolerance, complexity theory, and many-body physics.