New theory ranks the complexity of quantum system simulations

He-Ran Wang for Advanced Study at Tsinghua University, Ilya Vilkoviskiy and Dmitry A. Abanin of Princeton University and École Polytechnique Fédérale de Lausanne have identified three qualitatively distinct scalings of temporal entanglement entropy when analyzing quantum circuits. This work establishes a hierarchy of computational resources needed for accurate simulations of quantum many-body dynamics. The researchers’ analysis reveals that certain quantum dynamics can be efficiently computed using a Monte Carlo algorithm, indicating these systems possess characteristics that allow for this approach. Their results connect quantum many-body dynamics with group theory, offering new insight into the complexity of these systems and their physical characteristics. This hierarchy dictates the computational resources needed for accurate tensor-network representations of the influence matrix (IM), a tool used to characterize quantum many-body dynamics and its multitime correlations. Abanin focuses on a family of brickwork quantum circuits ranging from integrable to chaotic regimes. Beyond these simplified scenarios, the researchers also introduced an operational measure of quantum…