Estimating the global Lipschitz constant of neural networks is crucial for understanding and improving their robustness and generalization capabilities. However, precise calculations are NP-hard, and current semidefinite programming (SDP) methods face challenges such as high memory usage and slow processing speeds. In this paper, we propose HiQ-Lip, a hybrid quantum-classical hierarchical method that leverages Coherent Ising Machines (CIMs) to estimate the global Lipschitz constant. We tackle the estimation by converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement a multilevel graph coarsening and refinement strategy to adapt to the constraints of contemporary quantum hardware. Our experimental evaluations on fully connected neural networks demonstrate that HiQ-Lip not only provides estimates comparable to state-of-the-art methods but also significantly accelerates the computation process. In specific tests involving two-layer neural networks with 256 hidden neurons, HiQ-Lip doubles the solving speed and offers more accurate upper bounds than the existing best method, LiPopt. These findings highlight the promising utility of small-scale quantum devices in advancing the estimation of neural network robustness.

• DRL framework for joint retrieval and relocation scheduling in multideep warehouses. • Heterogeneous graph representation captures diverse storage entity types. • Instance-Invariant Baseline Regularization enables stable policy learning. • A computationally e!cient lower bound is derived as the instanceinvariant baseline. • Trained policy achieves lower makespan across various unseen warehouse configurations. Multi-deep automated vehicle storage and retrieval systems (AVS/RS) offer high storage density, making them increasingly prevalent in modern logistics. However, their operational efficiency is often constrained by the need to relocate blocking items during retrieval. In this work, we consider a realistic scenario where only a subset of stored items is requested, and relocation naturally arises when target items are blocked by non-requested ones. We propose a deep reinforcement learning (DRL) framework for makespan minimization in multi-deep AVS/RS. The framework features a heterogeneous graph-based state representation that captures three distinct entity types (requested items, non-requested items, and empty locations) along with their structural relationships. The action space is designed to correspond to these node types, enabling the agent to handle both retrieval and relocation decisions within a unified framework. To address the high variance inherent in this problem, we propose the Instance-Invariant Baseline Regularization, which decouples the agent’s performance from the instance’s inherent complexity by deriving a computationally efficient lower bound for each state. Extensive experiments validate the effectiveness of the proposed approach. The agent trained with the proposed regularization demonstrates stable convergence and, more crucially, strong generalization across 64 unseen warehouse configurations of varying scale, consistently outperforming heuristic baselines. These results highlight the potential of DRL for intelligent decision-making in complex warehouse management problems.

Special-purpose and general-purpose quantum computers offer two distinct paths toward practical quantum computing applications. While both accelerate solutions to classical problems, little research has explored how integrating different quantum systems can enhance quantum computing. This work presents a novel approach that uses a coherent optical quantum computer to optimize qubit layout mapping for superconducting quantum processors. It formulates qubit mapping as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling efficient placement of quantum circuits onto IBM’s heavy-hex topology. Using the QBoson 550w optical Ising machine to solve and post-process this model, we tested 54 quantum circuits and achieved an 88.07% reduction in SWAP gate count. This result outperforms Qiskit’s LookaheadSwap and SabreSwap routing methods by at least 21.35% when those methods are executed without prior layout optimization. Our approach surpasses TrivialLayout, DenseLayout, and SabreLayout in Qiskit, delivering at least 7.06% better optimization. Additionally, we demonstrated that the quantum approach offers notable advantages in solution success rate and efficiency, as its solution time is below the millisecond level, and it can maintain an optimization rate comparable to that of classical quadratic solvers (e.g., Gurobi and CPLEX) for the QUBO model. To our knowledge, our work is the first deep integration of optical and superconducting quantum systems, introducing a new paradigm where quantum computing optimizes itself—unlocking new possibilities for self-improving quantum architectures.

Massive multiple-input multiple-output (MIMO) has gained widespread popularity in recent years due to its ability to increase data rates, improve signal quality, and provide better coverage in challenging environments. In this paper, we investigate the MIMO beam selection (MBS) problem, which is proven to be NP-hard and computationally intractable. To deal with this problem, quantum computing that can provide faster and more efficient solutions to large-scale combinatorial optimization is considered. MBS is formulated in a quadratic unbounded binary optimization form and solved with Coherent Ising Machine (CIM) physical machine. We compare the performance of our solution with two classic heuristics, simulated annealing and Tabu search. The results demonstrate an average performance improvement by a factor of 261.23 and 20.6, respectively, which shows that CIM-based solution performs significantly better in terms of selecting the optimal subset of beams. This work shows great promise for practical 5G operation and promotes the application of quantum computing in solving computationally hard problems in communication.

Green communication has been a hot research in wireless network in recent years. The key question is how to reduce energy consumption while maintaining the quality of service. According to the conception of trading bandwidth for energy, a resource scheduling strategy based on system load conditions for LTE downlink is proposed to reduce energy consumption by improving energy efficiency at the cost of spectral efficiency. The two proposed algorithms can greatly reduce transmit power while meeting the users' data rate are requirements, and ensure the realization of the fairness among users.