The integration of high-penetration renewable energy introduces significant stochasticity and non-convexity into power system dispatching, challenging the computational limits of classical optimization. While Variational Quantum Algorithms (VQAs) on Noisy Intermediate-Scale Quantum (NISQ) devices offer a promising path for combinatorial acceleration, existing approaches typically treat the power grid as a "black box", suffering from poor scalability (barren plateaus) and frequent violations of physical constraints. Bridging these gaps, this paper proposes a Physics-Informed Hybrid Quantum-Classical Dispatching (PI-HQCD) framework. We construct a topology-aware Hamiltonian that explicitly embeds linearized power flow equations, storage dynamics, and multi-timescale coupling directly into the quantum substrate, significantly reducing the search space dimensionality. We further derive a noise-adaptive regularization mechanism that theoretically bounds the effective Lipschitz constant of the objective function, guaranteeing convergence stability under realistic quantum measurement noise. Numerical experiments on the IEEE 39-bus benchmark and a 118-bus regional grid demonstrate that PI-HQCD achieves superior economic efficiency and higher renewable utilization compared to stochastic dual dynamic programming (SDDP). Theoretical analysis confirms that this topology-aware design leads to an O(1/N) gradient variance scaling, effectively mitigating barren plateaus and ensuring scalability for larger networks. This work establishes a rigorous paradigm for embedding engineering physics into quantum computing, paving the way for practical quantum advantage in next-generation grid operations.
The integration of high-penetration renewable energy introduces significant stochasticity and non-convexity into power system dispatching, challenging the computational limits of classical optimization. While Variational Quantum Algorithms (VQAs) on Noisy Intermediate-Scale Quantum (NISQ) devices offer a promising path for combinatorial acceleration, existing approaches typically treat the power grid as a "black box", suffering from poor scalability (barren plateaus) and frequent violations of physical constraints. Bridging these gaps, this paper proposes a Physics-Informed Hybrid Quantum-Classical Dispatching (PI-HQCD) framework. We construct a topology-aware Hamiltonian that explicitly embeds linearized power flow equations, storage dynamics, and multi-timescale coupling directly into the quantum substrate, significantly reducing the search space dimensionality. We further derive a noise-adaptive regularization mechanism that theoretically bounds the effective Lipschitz constant of the objective function, guaranteeing convergence stability under realistic quantum measurement noise. Numerical experiments on the IEEE 39-bus benchmark and a 118-bus regional grid demonstrate that PI-HQCD achieves superior economic efficiency and higher renewable utilization compared to stochastic dual dynamic programming (SDDP). Theoretical analysis confirms that this topology-aware design leads to an O(1/N) gradient variance scaling, effectively mitigating barren plateaus and ensuring scalability for larger networks. This work establishes a rigorous paradigm for embedding engineering physics into quantum computing, paving the way for practical quantum advantage in next-generation grid operations.
This study introduces a hybrid quantum-classical dispatching framework designed for power systems with high renewable penetration. The proposed method integrates a variational quantum algorithm with classical optimization to provide noise-resilient performance under realistic hardware constraints. Extensive numerical tests and a real-world case study demonstrate significant improvements in cost reduction, dispatch reliability, and robustness to device noise. The approach highlights the potential of near-term quantum computing to address critical challenges in renewable energy integration. The results bridge the gap between quantum algorithms and practical energy system operations, offering a pathway for sustainable and efficient power system management.
The increasing complexity of modern energy systems—driven by distributed renewable generation, dynamic grid behavior, and multi-scale interactions—necessitates computational models capable of capturing nonlinearities, stochastic variability, and high-dimensional optimization landscapes. Embedding-based quantum simulations offer a promising path forward by integrating quantum solvers into classical energy modeling frameworks, enabling more accurate analysis of localized subsystems while maintaining tractable large-scale system evaluations. This study investigates quantum embedding techniques applied to power flow analysis, renewable integration, grid stability assessment, and energy storage optimization. By partitioning complex energy networks into quantum-treated active regions embedded within classical architectures, the approach enhances the fidelity of system-level simulations while reducing computational overhead. The research highlights the potential of hybrid quantum–classical workflows to accelerate decision-making in smart grid design, improve forecasting under uncertainty, and support the development of sustainable engineering solutions. The results outline a roadmap for deploying quantum-embedded simulations in future energy infrastructures.
Scenario-based stochastic optimization is a prevalent method for the economic dispatch of renewables-rich power systems. To reduce the time and space complexities for generating massive scenarios and solving pertinent mixed-integer stochastic optimization efficiently, quantum computing can provide critical assistance. To this end, we first propose the unified quantum amplitude estimation (UQAE) to generate massive scenarios with quadratic acceleration by a few qubits, after which the dimension of state variables embedded in the two-stage stochastic optimization also decreases exponentially. Then, by utilizing quantum-classical Benders decomposition, we accelerate the mixed integer master problem in the first stage on quantum processing units, while convex subproblems are solved on central processing units. Especially considering limited qubits in the noisy intermediate-scale quantum era, we propose to reduce the scale of master problem by scenario clustering and cut selection using the customized quantum approximation optimization algorithm (QAOA). Mathematically, we not only prove the decreases of complexities by UQAE-QAOA but also give the feasible ranges of penalty factors for transforming constrained problems into Ising models. Finally, we perform numerical experiments on modified IEEE systems to test the efficiency and accuracy of UQAE-QAOA, as well as the scalability of the designed quantum scheme.
Scalable combinatorial optimization under resource-constrained quantum hardware remains a fundamental challenge in the Noisy Intermediate-Scale Quantum (NISQ) era, due to the mismatch between exponentially growing solution spaces and limited quantum computational capacity. In this work, we propose a NISQ-aware hybrid quantum-classical optimization framework that reformulates large-scale combinatorial optimization as a resource-bounded distribution evolution process. Instead of directly optimizing individual solutions, the proposed framework operates on a probabilistic representation of the solution space, enabling efficient exploration under hardware constraints. Specifically, large problem instances are decomposed into qubit-compatible subproblems via clustering-based decomposition, ensuring resource-bounded optimization. Within each subproblem, a quantum genetic algorithm evolves the solution distribution, while periodically embedded amplitude amplification acts as a controlled quantum enhancement mechanism that accelerates convergence without increasing circuit depth. A classical refinement stage ensures global solution consistency. Extensive experiments on benchmark and synthetic datasets demonstrate that the proposed framework consistently outperforms classical and quantum-inspired baselines, with performance gains that become more pronounced as problem scale increases. This scale-dependent behavior indicates that scalability is achieved through structured decomposition rather than increased quantum complexity. Noise simulations further confirm robustness under realistic NISQ conditions, and ablation studies validate that both quantum evolutionary search and amplitude amplification contribute significantly to performance improvements.
Abstract The arrival of noisy intermediate-scale quantum (NISQ) devices defines an era in which quantum utility is fundamentally constrained by finite coherence times, limited qubit counts, gate infidelities, restricted connectivity, and measurement noise. Within this regime, hybrid quantum-classical frameworks have emerged as the dominant operational paradigm, particularly for quantum machine learning (QML). This review identifies a fundamental trade-off between expressivity, trainability, and noise resilience that governs the performance and scalability of NISQ-era QML systems. To contextualize these challenges, we introduce the resource-constrained iterative routing framework, a hardware-aware conceptual architecture that integrates topology-aware classical compression and distributed quantum orchestration to maintain circuit depths within device-dependent limits while routing representations toward symmetry-constrained Hilbert subspaces to mitigate noise-induced barren plateaus. Furthermore, we shift the discussion of quantum advantage away from asymptotic fault-tolerant complexity toward the notion of operational NISQ advantage based on finite-resource scaling, trainability preservation, and sampling complexity. We evaluate the practical resource efficiency of variational quantum algorithms, quantum kernel methods, and quantum neural networks across superconducting, trapped-ion, neutral-atom, and photonic platforms. The review also examines reproducibility challenges, emphasizing benchmarking against optimized classical baselines, and discusses strategies for managing the sampling overhead of error mitigation alongside distributed execution and quantum circuit compilation. Ultimately, NISQ in Practice positions hybrid QML as a physically constrained computational paradigm while outlining a pathway from contemporary noisy workflows toward early fault-tolerant quantum architectures.
Scenario-based stochastic optimization is commonly deemed as an effective method for the economic dispatch of a renewables-rich power system which features a massive number of widely dispersed renewable energy sources (RESs). However, it is rather computationally challenging to simulate RES uncertainties with high accuracy on classic computers, due primarily to the generation of massive RESs scenarios and the solution of pertinent optimization problems that are by nature NP-hard mixed-integer programs. To this end, we design a quantum-assisted scheme to accelerate the stochastic optimization for power system economic dispatch without losing accuracy. We first propose the unified quantum amplitude estimation to characterize RES uncertainties, thereby generating massive scenarios by a few qubits to reduce state variables. Then, strong Benders cuts are selected and formed under some specific scenarios so as to tune the solution scale of Benders master problem in the iterative process, all of which are implemented by customized quantum approximation optimization algorithms. Finally, numerical experiments are conducted on the modified IEEE 6-bus system to test the efficacy of the proposed quantum-assisted scheme.