Dynamics in the Decompositions Approach to Quantum Mechanics

John Harding

Yuzuru Kato, Hiroya Nakao

Dynamic mode decomposition (DMD) is a data-driven method for the estimation, prediction, and control of complex dynamical systems, which has gained much attention in the fields of nonlinear dynamics and fluid mechanics. A DMD method for quantum spin systems, described by a linear dynamical system of a finite-dimensional set of observables, has been proposed recently. In this study, we propose two DMD methods applicable to infinite-dimensional open quantum systems, which use time-series data obtained by quantum state tomography. First, we propose a kernel DMD method for a data-driven spectral analysis of the Liouville superoperator. Second, we propose a method for the parameter estimation of the Liouville superoperator, which incorporates prior knowledge of the model structure into DMD. The proposed methods can accurately reconstruct the system dynamics and show that DMD frameworks can be applicable to infinite-dimensional open quantum systems.

L. Lanz, Luigi A. Lugiato, G. Ramella

Jincheng Zhang

Quantum state decomposition is a crucial challenge in quantum computing, enabling efficient manipulation and computation of quantum states. This paper introduces a novel dynamic topology-based quantum state decomposition method that leverages the inherent structure of quantum systems to achieve high accuracy and computational efficiency. We propose a novel algorithm that dynamically adjusts the quantum state based on topological principles, allowing for precise state manipulation and improved quantum processing. The core mechanism involves constructing a dynamically evolving decomposition topology, which significantly enhances the fidelity of state operations. This approach offers a significant advancement over traditional methods and addresses key limitations in quantum state manipulation.

Holger Friedrich Hofmann

Jincheng Zhang

Abstract: This paper introduces an adaptive matrix decomposition algorithm based on quantum error correction that dynamically adjusts the decomposition strategy based on the computation target and environmental noise. The core mechanism leverages quantum state interactions to optimize the decomposition process, offering a more flexible and robust approach compared to traditional methods. The algorithm's effectiveness stems from its ability to adapt to complex, dynamic environments, leading to improved accuracy and resilience.