Multi Dimensional Quantum Dynamics

Mauricio Domingues Coutinho-Neto, Alexandra Viel, Uwe Manthe

Guoxin Yang

On October 21, 2020, the invention “A multi-level and multi-dimensional dynamic system motion model construction and simulation method” was accepted by the State Intellectual Property Office of China. Through the construction and simulation of the motion model of a multi-level and multi-dimensional dynamic system, the motion trajectory of the motion factors in each dynamic system is nested and substituted into the next dynamic subsystem to establish the motion trajectory of the motion factors in its dynamic subsystem. Until the dynamic trajectory model of the motion factors in the minimum dynamic subsystem is obtained, the motion model of a multi-level and multi-dimensional dynamic system is constructed, which reveals the motion law that can unify the microscopic particles and all the motion factors in the macroscopic universe. Multiple dynamic systems are entangled systems. If the entanglement properties are obtained not by ``absolutely simultaneous'' measurements of the entangled particles, it just proves that there is no non-local hyper-distance action.

Jincheng Zhang

This paper introduces a novel framework for quantum computation termed Dimension Multi-Adaptive Quantum Adaptive Computation (DMAC). The core principle of DMAC leverages quantum self-adaptation to dynamically adjust the dimensionality of quantum states during computation, optimizing performance and accommodating complex models. We propose a novel quantum model architecture that iteratively refines the quantum state's dimensionality based on the input problem characteristics. This dynamic dimensionality adjustment allows for improved efficiency and accuracy compared to static dimensionality schemes. The paper details the model's design, its application to a specific problem, and its advantages in achieving optimal results. The research highlights the potential of DMAC to address challenges in quantum machine learning and computational modeling.

János A. Bergou, Mark S. Hillery, Mark E. Saffman

Lushuai Cao, Sven Krönke, Oriol Vendrell +1 more

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.