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Main Author: Znidaric, Marko
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2505.15521
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author Znidaric, Marko
author_facet Znidaric, Marko
contents 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 to previous claims, there is no Trotterization transition in non-integrable many-body quantum systems. We demonstrate our results on a one-dimensional (1d) kicked Ising model, as well as on 1d kicked XX model and 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_15521
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
Znidaric, Marko
Quantum Physics
Strongly Correlated Electrons
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 to previous claims, there is no Trotterization transition in non-integrable many-body quantum systems. We demonstrate our results on a one-dimensional (1d) kicked Ising model, as well as on 1d kicked XX model and 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.
title Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
topic Quantum Physics
Strongly Correlated Electrons
url https://arxiv.org/abs/2505.15521