20.500.12556/RUL-182245 Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits One of the premier utilities of present-day noisy quantum computers is simulation of many-body quantum systems. We study how long in time is such a discrete-time simulation representative of a continuous time Hamiltonian evolution; namely, a finite time step introduces so-called Trotterization errors. We demonstrate that the truncated operator propagator (Ruelle-Pollicott resonances) is a powerful tool to that end, as well as to study prethermalization and discrete-time crystals, including finding those phenomena at large gate duration. We show that the effective energy is more stable than suggested by Trotter errors—a manifestation of prethermalization—while all other observables are not. Even the most stable observable though deteriorates in the thermodynamic limit. Different than in classical systems with the strongest chaos, where the faithfulness time (the shadowing time) can be infinite, in quantum many-body chaotic systems it is finite. A corollary of our results is also that, opposite of previous claims, there is no Trotterization transition in nonintegrable many-body quantum systems. We demonstrate our results on a one-dimensional (1D) kicked Ising model, as well as on a 1D kicked XX model and a 2D kicked Ising model. The truncated propagator is also used to calculate the energy diffusion constant in the tilted-field Ising model with high accuracy. quantum chaos quantum circuits quantum simulation quantum transport 1-dimensional spin chains Floquet systems quantum many-body systems kvantni kaos kvantna vezja kvantne simulacije kvantni transport enodimenzionalne spinske verige Floquetovi sistemi kvantni večdelčni sistemi true false true Angleški jezik Slovenski jezik Članek v reviji 2026-05-05 09:22:50 2026-05-05 09:22:51 2026-06-02 10:13:10 0000-00-00 00:00:00 2026 0 0 Str. 021017-1-021017-23 iss. 2 Vol. 16 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 530.145 2160-3308 10.1103/69d7-83xh 276527619 https://journals.aps.org/prx/abstract/10.1103/69d7-83xh 1 f156f436-4852-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233319 69d7-83xh.pdf 69d7-83xh.pdf 1 F3DA322ADC143FA764DEC28981E74421 c08b2b1e1804a38e6e979f6e9616ad687312bee7389947d52a6d83c107475c82 2d87f7b7-4853-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233320 Fakulteta za matematiko in fiziko 0 0 0