This paper investigates the use of Quantum Annealing (QA) devices for optimizing unit scheduling in renewable energy systems, addressing the challenge of energy balancing with intermittent generation. We compare two approaches for encoding inequality constraints in Quadratic Unconstrained Binary Optimization (QUBO) formulations: (a) the conventional slack-variable-based method and (b) a novel soft-encoding technique called unbalanced penalization. This first application of unbalanced penalization in the energy and power systems domain, aims to disseminate knowledge about near-term applications of quantum-computing and how to make best use of it within the community. Through computational experiments, we find thatUnbalanced Penalizationconsistently outperforms the conventional method of using slack variables by reducing the number of variables in the QUBO formulation. Despite this, its inherent nature penalizes feasible solutions unevenly, preventing the ability to handle much larger problem sizes. More broadly, we observe that both methods-like most pure quantum approaches-struggle with scalability on current QA hardware, as solution quality declines with increasing problem size. In light of these limitations, we assess the feasibility of purely quantum solutions and argue that hybrid approaches remain the most practical path forward.
This paper investigates the use of Quantum Annealing (QA) devices for optimizing unit scheduling in renewable energy systems, addressing the challenge of energy balancing with intermittent generation. We compare two approaches for encoding inequality constraints in Quadratic Unconstrained Binary Optimization (QUBO) formulations: (a) the conventional slack-variable-based method and (b) a novel soft-encoding technique called unbalanced penalization. This first application of unbalanced penalization in the energy and power systems domain, aims to disseminate knowledge about near-term applications of quantum-computing and how to make best use of it within the community. Through computational experiments, we find thatUnbalanced Penalizationconsistently outperforms the conventional method of using slack variables by reducing the number of variables in the QUBO formulation. Despite this, its inherent nature penalizes feasible solutions unevenly, preventing the ability to handle much larger problem sizes. More broadly, we observe that both methods-like most pure quantum approaches-struggle with scalability on current QA hardware, as solution quality declines with increasing problem size. In light of these limitations, we assess the feasibility of purely quantum solutions and argue that hybrid approaches remain the most practical path forward.
Quantum annealing (QA) offers a physics-inspired approach for such subproblems by mapping them onto an Ising Hamiltonian, which is algebraically equivalent to a Quadratic Unconstrained Binary Optimization (QUBO) model executable on quantum annealers or hybrid solvers. However, their practical employment in wireless systems critically depends on the specific problem formulation, on the particular variable encoding, constraint handling, solver selection, hardware embedding, and fair benchmarking. This paper develops wireless-oriented QUBO modeling guidelines for QA-assisted resource allocation. We first present a beginner-friendly toy example in which a terrestrial-aerial resource-allocation problem with a fractional signal-to-interference-plus-noise ratio (SINR) maximization objective is reformulated into a two-bit QUBO via Boolean interpolation, converted into an Ising representation, and decoded back into a wireless scheduling decision. The same scheduling is applicable to UAV, aircraft, satellite, and terrestrial links in SAGIN systems. We then review the QA foundations and solver ecosystems, including binary quadratic, discrete quadratic, constrained quadratic, and hybrid models from the perspective of NG wireless optimization. Furthermore, we discuss both binary and discrete encoding, penalty-based constraint conversion, embedding overhead, solution decoding, and feasibility verification. A QUBO Compatibility Index is introduced as a lightweight diagnostic metric for assessing the associated QUBO formulation readiness, rather than a predictor of runtime or solution quality. Finally, a case study on max-min uplink power control in cell-free massive MIMO illustrates how a fairness-oriented wireless problem can be discretized, constrained, converted into the concept of a QUBO, and evaluated against classical baselines. A host of key challenges and future directions are also discussed.
Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes binary integer programming, which is still NP-hard and computationally demanding for classical methods. Quantum Annealing (QA), known for efficiently solving Quadratic Unconstrained Binary Optimization (QUBO) problems, presents a potential solution. However, existing quantum algorithms rely on slack variables to handle linear binary inequality constraints, leading to increased qubit consumption and reduced computational efficiency. To solve the problem, this paper introduces the Powell-Hestenes-Rockafellar Augmented Lagrangian Multiplier (PHR-ALM) method to eliminate the need for slack variables, making qubit consumption independent of the increasing number of Benders cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks for sequential solutions, which does not scale with the number of generators. Finally, the simulation results on both 4-generator and the IEEE bus-118 systems demonstrate the feasibility and scalability of the proposed algorithm, indicating its superior qubit and runtime efficiency over classical and baseline quantum approaches on the D-Wave QPU platform.
This paper investigates several Quadratic Unconstrained Binary optimisation (QUBO) formulations for the parallel machine scheduling problem P m | | C max with the goal of assessing their suitability for quantum annealing and related heuristic optimisation methods. Three QUBO models are constructed, ranging from formulations derived from classical integer and one-hot encodings to a more compact load-balancing based representation. Extensive computational experiments using Simulated Annealing (SA) and Quantum Annealing (QA) reveal substantial differences in scalability and solution quality among the formulations. The alternative load-balanced model consistently yields near-optimal makespans, typically within 1%–3% of the theoretical lower bound, highlighting its stability and effectiveness compared to the more penalty sensitive formulations, whose performance deteriorates for larger instances. Sensitivity analyses further reveal that the appropriate selection of penalty weights and problem-specific parameter tuning significantly influences both solution accuracy and computational effort in QUBO formulations. While current quantum hardware limitations restrict experimentation to small problem sizes, the findings illustrate how compact QUBO designs can better exploit quantum optimisation frameworks. The insights gained in this study provide practical modelling guidelines for future quantum scheduling research and lay the groundwork for extending QUBO-based approaches to more complex scheduling environments. • Three QUBO formulations are compared for identical parallel machine scheduling. • A compact load-balancing QUBO avoids auxiliary variables. • Load balancing yields makespans on average within 1–3%. • Both simulated and quantum annealing produce near-optimal schedules. • Penalty selection and encoding strongly affect scalability and solution quality.
Abstract Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D -Wave Advantage and D -Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.
As global energy demand continues to rise, efficient energy management is essential to support the growing integration of renewable energy in the energy mix while controlling operational costs. This paper introduces a method that leverages non-exact Quadratic Unconstrained Binary Optimization (QUBO) formulation combined with tailored post-processing to boost the optimization of the energy management problem of 5G base stations. Unlike traditional rule-based approaches, which rely heavily on domain expertise and manual design, we propose a systematic QUBO-based framework suitable for Quantum Annealing (QA). The proposed formulation significantly reduces the number of decision variables (from 1995 in an exact QUBO to approximately 144) making it compatible with current QA hardware while producing high-quality solutions. Furthermore, the post-processing steps further improve solution quality, increasing the global optimal solution achievement rate by 10–15% depending on the solver. Experimental results demonstrate that the proposed method is deployable on current hardware and achieves performance comparable to conventional rule-based systems. Such observations highlight the potential of such designs in solving real-world optimization challenges.
Power grid modernization is essential for ensuring the reliability, efficiency, and sustainability of power systems in response to increasing demand, supply uncertainty, and decentralization of resources. This dissertation investigates the application of quantum computing (QC) in solving two challenging power grid problems, including Unit Commitment (UC) and Vehicle-to-Grid (V2G) optimization. Through novel approaches in quantum modeling, this work seeks to advance computational strategies that could support grid modernization efforts as grid complexity grows beyond the capabilities of classical optimization methods. The first part of this research introduces QC and the core mechanics of quantum physics that are vital to understanding quantum computations. Different methods of QC and their histories are discussed, including gate-based models and quantum annealing. Quantum annealing (QA) is the focus of the rest of the chapter, discussing the QA process, the mathematics behind it, and the reformulations required to make an optimization problem quantum-compatible. In the second part, a hybrid quantum-classical model is developed to solve the UC problem, combining QA with classical solvers to balance computational efficiency and solution accuracy. The results are compared to a classical deterministic and metaheuristic solutions, which reveals that while classical models outperform quantum solutions at smaller scales, the hybrid approach offers promising advantages in handling more complex grid configurations. This hybrid model provides a pathway for QC to enhance classical optimization techniques, especially as hardware and embedding algorithms continue to evolve. A novel discretization strategy is introduced that is designed to solve the UC problem more efficiently compatible with quantum annealing (QA) hardware. By representing continuous variables as binary variables using a logarithmic binning technique, this approach aims to reduce the number of binary variables needed for problem reformulation. Results show that this novel discretization significantly decreased computational time and yielded fewer binary variables, although further adjustments are needed to improve solution accuracy and optimality. The final part examines the feasibility of using a quantum model to optimize V2G scheduling. This quantum model, aimed at minimizing EV charging costs over a 24-hour period, achieves a reasonable optimality rate relative to a classical deterministic solution for a studied test system. The study demonstrates QC’s potential for real-world applications, albeit on a limited scale, and highlights the scalability possibilities for broader V2G network management as quantum technology matures. This is followed by a review of existing methods for V2G and mobile energy storage system optimization, with a focus on enhancing grid resilience and a discussion around potential quantum advantages and pathways for future utilization. Collectively, these findings demonstrate that while QC in grid optimization is still in its nascent stages, it holds substantial promise for meeting the computational demands of the future power grid. This research paves the way for continued exploration of quantum-enhanced solutions to support grid modernization in the era of renewable energy integration, electrification, and continually increasing complexity.