BIMSA > YMSC-BIMSA Quantum Information Seminar Long-range nonstabilizerness from quantum codes, orders, and correlations
Long-range nonstabilizerness from quantum codes, orders, and correlations
Organizers
Song Cheng , Da Wei Ding , Jin Peng Liu , Zheng Wei Liu , Ziwen Liu
Speaker
Fuchuan Wei
Time
Friday, June 6, 2025 4:00 PM - 5:30 PM
Venue
Shuangqing-B627
Online
Zoom 230 432 7880 (BIMSA)
Abstract
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.