This study introduces a cross-variable quantum-inspired transmission model on discrete networks, integrating classical local couplings with non-local associative terms to explore quantum information propagation. Using first- and second-order dynamic weights, we formulate systems of equations optimized via Monte Carlo simulations, adjusting angular, phase, and spin variables to minimize energy states. Results reveal that cross-variable couplings amplify volatility and instability, particularly in multi-particle settings, as evidenced by broader frequency spectra in wave-packet simulations. To mitigate this, a QEC-inspired regularization penalty enforces local consistency, boosting success rates from ~40-50% to 55-70% in high-noise regimes. This framework unifies micro-scale particle-wave dynamics with macro-grid flows, offering insights for robust AI architectures bridging brain-inspired hierarchies and quantum systems.
This study introduces a cross-variable quantum-inspired transmission model on discrete networks, integrating classical local couplings with non-local associative terms to explore quantum information propagation. Using first- and second-order dynamic weights, we formulate systems of equations optimized via Monte Carlo simulations, adjusting angular, phase, and spin variables to minimize energy states. Results reveal that cross-variable couplings amplify volatility and instability, particularly in multi-particle settings, as evidenced by broader frequency spectra in wave-packet simulations. To mitigate this, a QEC-inspired regularization penalty enforces local consistency, boosting success rates from ~40-50% to 55-70% in high-noise regimes. This framework unifies micro-scale particle-wave dynamics with macro-grid flows, offering insights for robust AI architectures bridging brain-inspired hierarchies and quantum systems.
This study explores quantum-inspired optimization algorithms (QIOAs) as practical tools for solving constrained combinatorial problems on classical machines. We analyze tasks that can be formulated in Ising or QUBO forms and benchmark three representative approaches: Simulated Bifurcation (SB), Quantum-Inspired Particle Swarm Optimization (QPSO), and a tensor-network (TN) method. A unified evaluation protocol is introduced that captures solution quality, feasibility, runtime, energy consumption, parameter sensitivity, and scalability. To ensure reliable performance, we develop automated penalty-adjustment and schedule-calibration strategies. Experimental results across diverse benchmarks show that SB and TN together yield the best trade-offs between accuracy and runtime: SB is efficient on dense instances with moderate penalties and low energy use, while TN is advantageous for sparse or modular networks, especially on GPUs. QPSO is competitive in smoother landscapes but more sensitive to hyperparameters. By linking performance to structural properties such as spectral gaps and constraint activity, we provide guidance for selecting suitable algorithms. Overall, QIOAs emerge as effective intermediaries between existing classical heuristics and emerging quantum devices, supported by a reproducible, energy-aware evaluation framework.
Quantum-Inspired Stochastic Differential Equation (Q-SDE) Optimization addresses the challenges of optimizing complex, stochastic systems by integrating quantum-inspired stochastic differential equation modeling. This research presents a novel optimization algorithm, the Q-SDE-based method, designed to effectively handle highly non-linear, stochastic optimization problems characterized by significant noise. We develop a framework that utilizes the inherent stochasticity of Q-SDEs, coupled with differential equation principles, to provide a robust and adaptive approach to finding optimal solutions. The core mechanism involves a dynamic adjustment of the Q-SDE's parameters to minimize the error function across a wider range of solutions, mitigating the impact of noise and enhancing the algorithm's performance in challenging scenarios. This work demonstrates the effectiveness of this approach through extensive numerical simulations and comparisons with established optimization techniques, highlighting its potential for significant improvements in the optimization of stochastic systems.
Training deep neural networks remains a computationally intensive and often challenging process. Traditional optimization methods, such as stochastic gradient descent (SGD) and its variants, frequently struggle to escape local minima and converge to optimal solutions, leading to suboptimal network performance. This paper proposes a novel approach to neural network training that leverages principles inspired by quantum mechanics. Specifically, we investigate the application of quantum-inspired optimization techniques, including simulated annealing and quantum walks, to dynamically adjust the training process. The core idea is to mimic the probabilistic exploration inherent in quantum systems to effectively navigate the complex loss landscape of neural networks. We formulate the training process as a quantum-inspired optimization problem, where the network's weights are treated as quantum bits (Qubits) and the optimization algorithm seeks to find the lowest energy state, analogous to finding the minimum loss. The proposed method demonstrates the potential for accelerating convergence and improving the overall accuracy of neural networks compared to conventional optimization strategies. Our analysis focuses on the key aspects of the approach, including the mathematical formulation of the quantum-inspired optimization problem and the selection of appropriate parameters to govern the exploration and exploitation phases. We present a theoretical framework for understanding the dynamics of this approach and discuss potential avenues for further research, including hybrid quantum-classical algorithms and the integration of quantum computing hardware.
Quantum-inspired optimization aims to leverage quantum mechanics principles to accelerate and improve optimization algorithms. This paper introduces a novel approach utilizing adaptive regularization, inspired by quantum state evolution. We develop a dynamic regularization strength adjustment mechanism, enabling the algorithm to continuously refine its search strategy. The core mechanism involves incorporating a quantum-inspired penalty term that adapts to the solution space, promoting efficient exploration and potentially leading to faster and more robust solutions compared to traditional optimization methods. This work presents a framework for dynamically adjusting regularization during the optimization process, offering a promising path toward enhanced performance in complex optimization problems.
Biological neuronal networks represent a fundamental component of complex systems, including the brain. Simulating these networks accurately and efficiently is a significant challenge, largely due to the intricate, non-linear interactions between neurons. Traditional simulation methods, often relying on numerical integration techniques like the Hodgkin-Huxley model, are computationally intensive, particularly when scaling to large networks. This paper proposes a novel approach to neuronal network simulation inspired by quantum mechanics, specifically leveraging concepts of superposition and entanglement. We introduce a framework that utilizes quantum-inspired algorithms to represent and evolve neuronal states, aiming to dramatically reduce computational overhead. The core idea involves mapping neuronal dynamics onto a quantum system, where neurons are represented by qubits, and synaptic connections are modeled as quantum gates. The simulation process then utilizes quantum algorithms to evolve the system, effectively capturing the parallel and interconnected nature of neuronal networks. We present a mathematical formulation of the simulation process, focusing on the evolution equation for neuronal states. We explore key concepts like wave function collapse and measurement in the context of neuronal network simulation, offering a potential pathway for more realistic and efficient modeling of biological neural systems. The ultimate goal is to provide a computationally tractable method for simulating large-scale neuronal networks, leading to improved understanding of brain function and potentially facilitating the development of advanced neurotechnologies. The presented framework offers a distinct alternative to conventional methods, promising significant advantages in terms of speed and scalability.
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature (London) 619, 282 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the scaling of the total evolution time with the size of the system. We also explore extensions of the circuit, including the use of time-dependent Hamiltonians and reverse digitized annealing. Additionally, we propose that classical, approximate quantum simulators can be used for the proposal step instead of the original real-hardware implementation. We observe that tensor-network simulators, even with unconverged settings, can maintain a scaling advantage over standard classical samplers. This may extend the utility of quantum-enhanced Monte Carlo as a quantum-inspired algorithm, even before the deployment of large-scale quantum hardware.