Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits

Žnidarič, Marko (author)

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.

• Language: English
• Keywords: quantum chaos, quantum circuits, quantum simulation, quantum transport, 1-dimensional spin chains, Floquet systems, quantum many-body systems
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 021017-1-021017-23
• Numbering: Vol. 16, iss. 2
• PID: 20.500.12556/RUL-182245
• UDC: 530.145
• ISSN on article: 2160-3308
• DOI: 10.1103/69d7-83xh
• COBISS.SI-ID: 276527619
• Publication date in RUL: 05.05.2026

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., X
• Publisher: American Physical Society
• ISSN: 2160-3308
• COBISS.SI-ID: 19686152

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kvantni kaos, kvantna vezja, kvantne simulacije, kvantni transport, enodimenzionalne spinske verige, Floquetovi sistemi, kvantni večdelčni sistemi