Computational methods in support of quantum dynamics simulations

Anonymous, Jia Yin, Siyuan Niu +2 more

Eugeniy Polyakov, P. N. Vorontsov‐Velyaminov, Alexander P. Lyubartsev

A method of stochastic positive P-representation for the computer simulation of thermal equilibrium and dynamical properties of many-particle quantum systems with interactions is proposed and thoroughly analyzed. The testing procedure of the method includes the evaluation of spatial correlation functions for the one-dimensional Bose-gas with delta-repulsion between particles, both in the state of thermal equilibrium and in the dynamical evolution from a given initial state. This work was supported by the Russian Foundation for Basic Research (project number 08–02–00041) and by the Royal Swedish Academy of Sciences.

Jincheng Zhang

Dynamic Topology Field Theory Quantum Optimization addresses the challenges of quantum computing optimization by introducing a novel dynamic topology field theory framework. This framework leverages quantum entanglement to simulate quantum computations, enabling real-time parameter adjustment that significantly enhances quantum computing efficiency. The core mechanism centers around utilizing quantum entanglement to dynamically model and optimize quantum parameter sets, providing a significant advancement over traditional static optimization methods. This paper explores the theoretical foundations, implementation details, and initial experimental results supporting the proposed approach.

Innocenzo Fulginiti, Alessandro Poggiali, Christian B. Mendl

Dynamic circuits, which incorporate mid-circuit measurements and classically controlled operations, extend the expressive power of quantum programs and are central to applications such as quantum error correction, state preparation, and distributed quantum algorithms. However, their classical simulation is challenging due to the exponential growth of execution branches induced by mid-circuit measurements. In this work, we develop a tensor network approach for simulating dynamic circuits by extending a DMRG-based method for quantum circuit simulation to support dynamic circuit operations. To address the exponential proliferation of execution branches, we introduce and compare two strategies: a single-path stochastic approach that samples individual measurement outcomes, and a multi-path approach that maintains an ensemble of branches. We benchmark these methods on standard dynamic circuits, including the teleportation protocol and GHZ state preparation, as well as on random dynamic circuits. Our analysis explores the trade-offs between simulation accuracy and computational efficiency. These results provide a practical and scalable framework for the classical simulation of dynamic circuits.

Yihe Xu, Chungen Liu, Haibo Ma

Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples.