Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations
Zongping Gong, Nobuyuki Yoshioka, Naoyuki Shibata, Ryusuke Hamazaki
Abstract
In the accompanying letter [Gong et al., Phys. Rev. Lett. 124, 210606 (2020)], we introduced a universal error bound for constrained unitary dynamics within a well-gapped energy band of an isolated quantum system. Here, we provide the full details on the derivation of the bound. In addition, we generalize the result to isolated quantum many-body systems by employing the local Schrieffer-Wolff transformation, obtaining an error bound that grows polynomially in time. We also generalize the result to Markovian open quantum systems and quantitatively explain the quantum Zeno effect.
Topics & Concepts
QuantumDynamics (music)Statistical physicsQuantum dynamicsComputer scienceApplied mathematicsMathematicsTheoretical computer sciencePhysicsQuantum mechanicsAcousticsQuantum many-body systemsQuantum chaos and dynamical systemsQuantum Information and Cryptography