Speaker
Description
Magic state resources, also known as the non-stabilizerness, quantify the beyond-Clifford operations necessary for universal quantum computing and are related to complexity of representing states of quantum many-body systems on classical computers. How rapidly are magic resources generated by generic many-body dynamics under constraints of locality? What can we say about non-stabilizerness of time-evolved state in the limit of long-time evolution under many-body Hamiltonians? In this talk, I will address these questions by discussing non-stabilizerness of Haar-random states, and its relation with non-stabilizerness of eigenstates of ergodic many-body systems [1]. Subsequently, I will discuss the problem of magic spreading in brick-wall random unitary circuits [2], which combine principles of locality and unitarity, serving as a minimal model of ergodic many-body dynamics. This model shows that magic resources equilibrate on timescales logarithmic in system size N, akin to Hilbert space delocalization measures, but differently from entanglement entropy. I will discuss how this results extend to ergodic [3] and many-body localized [4] systems.
[1] X. Turkeshi, A. Dymarsky, P. Sierant, Phys. Rev. B 111, 054301 (2025)
[2] X. Turkeshi, E. Tirrito, P. Sierant, Nat Commun 16, 2575 (2025)
[3] E. Tirrito, X. Turkeshi, P. Sierant, Phys. Rev. Lett. 135, 220401 (2025)
[4] P. R. Nicácio Falcão, P. Sierant, J. Zakrzewski, E. Tirrito