Structure and quantum-dynamics relationship in spin networks

Joachim Stolze, Taras Verkholyak, Oleg Derzhko +1 more

Yuuki Nakamiya, Mitsunaga Kinjo, Osamu Takahashi +2 more

It has been known that a variety of optimization problems can be solved with a neural network, and that a quantum computer executes real parallel computation. A quantum neural network has been proposed to incorporate quantum dynamics into a neural network. In this study, we test the possibility of actual implementation of a quantum neural network with a nuclear spin as a qubit. First, we introduce the relationship between a spin and a neuron, then describe the adiabatic Hamiltonian evolution applied for the state change. Next, we describe a real spin quantum system and show the simulation results. A proposed nuclear spin system behaves as a neuron with inhibitory interactions, as expected in analogy to a Hopfield network.

Jincheng Zhang

This paper investigates the potential of quantum-inspired neural networks (QINNs) leveraging the principles of quantum entanglement to enhance feature interactions within artificial neural networks. Traditional neural networks often struggle with complex, non-linear relationships between features, leading to suboptimal performance. We propose a novel architecture where nodes are initially randomly entangled, and training dynamically adjusts the entanglement structure based on the input data. This approach mimics the correlated behavior observed in quantum systems, allowing for more efficient and nuanced feature representation. The core idea is to replace the static connections of conventional neural networks with dynamically evolving entanglement relationships. We explore the mathematical framework underlying this approach, focusing on the probabilistic nature of entanglement and its impact on information flow. The model is designed to learn complex patterns by exploiting the inherent correlations introduced by entanglement. Experimental results (simulated) demonstrate the potential of QINNs to outperform conventional neural networks in tasks requiring intricate feature interactions, suggesting a promising direction for future neural network design.

Jürg Martin Fröhlich, Antti Knowles, Enno Lenzmann

Wei-Yang Liu, Hsuan-Wei Lee

We investigate the dissipative dynamics of quantum population and coherence among different network topologies of a quantum network using a quantum spin model coupled to a thermal bosonic reservoir. Our study proceeds in two parts. First, we analyze a small network of Ising spins embedded in a large dissipative bath, modeled via the Lindblad master equation, where temperature arises naturally from system-bath coupling. This approach reveals how network topology shapes quantum dissipative dynamics, providing a basis for controlling quantum coherence through tailored network structures. Second, we propose a mean-field approach that extends the network to larger scales and captures dissipative dynamics in large-scale networks, connecting network topology to quantum coherence in complex systems and revealing the sensitivity of quantum coherence to network structure. Our results highlight how dissipative quantum dynamics depend on network topology, providing insight into the coherent dynamics of entangled states in networks. These results may be extended to dynamics in complex systems such as opinion propagation in social models, epidemiology, and various condensed-phase and biological systems.

P. Bruno