The Quantum Approximate Optimization Algorithm (QAOA) is applied to Networked Microgrids (NMs) in this paper to search for the maximum power exchange section, which is playing an essential role in operating NMs. Mathematically, obtaining the maximum power section is to solve a Max-Cut problem over the modeling graph of NMs. Considering the integration and fluctuations of Distributed Energy Resources (DERs), the maximum power section will change frequently. To efficiently get the section, QAOA provides a powerful solution by leveraging quantum resources. The performance of QAOA highly depends on the critical parameters of quantum circuits. We find the designed parameters for QAOA are still effective under wide range change of output power of energy resources. Tests on a typical NMs system verify the effectiveness of the QAOA method in efficiently searching for the maximum power sections of NMs.
The Quantum Approximate Optimization Algorithm (QAOA) is applied to Networked Microgrids (NMs) in this paper to search for the maximum power exchange section, which is playing an essential role in operating NMs. Mathematically, obtaining the maximum power section is to solve a Max-Cut problem over the modeling graph of NMs. Considering the integration and fluctuations of Distributed Energy Resources (DERs), the maximum power section will change frequently. To efficiently get the section, QAOA provides a powerful solution by leveraging quantum resources. The performance of QAOA highly depends on the critical parameters of quantum circuits. We find the designed parameters for QAOA are still effective under wide range change of output power of energy resources. Tests on a typical NMs system verify the effectiveness of the QAOA method in efficiently searching for the maximum power sections of NMs.
The maximum power exchange section is playing an important role in analyzing the interoperation of network microgrids. Mathematically, the problem is formulated into a weighted Max-Cut problem, which is non-deterministic polynomial-time hard (NP-hard). A Quantum Approximate Optimization Algorithm (QAOA) is introduced in this paper to search the approximate maximum power exchange sections in networked microgrids. QAOA is a hybrid quantum-classical algorithm, which uses a classical optimizer to train a parametrized quantum circuit. Layer number and angle parameters of the quantum circuit are discussed, which highly impact the performance of QAOA. Numerical examples on a typical reconfigurable networked microgrid system test and verify the effectiveness of QAOA in getting the maximum power exchange sections. This quantum computing implementation sheds light on the development of quantum algorithms to resolve the challenges in power systems that are hard to solve by classical computers.
Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems. It is especially promising for Distributed Energy Resources (DERs) dominant systems that have been widely developed to promote energy sustainability. In those systems, knowing the maximum sections of power and data delivery is essential for monitoring, operation, and control. However, high computational effort is required. By leveraging quantum resources, Quantum Approximate Optimization Algorithm (QAOA) provides a means to search for these sections efficiently. However, QAOA performance relies heavily on critical parameters, especially for weighted graphs. Here we present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density. We verify the strategy with 39,774 expectation value calculations. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots its practical application to power systems in noisy intermediate-scale quantum devices.
Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems, especially for Distributed Energy Resources (DERs) dominant cyber-physical systems that have been widely developed to promote energy sustainability. The systems’ maximum power or data sections are essential for monitoring, operation, and control, while high computational effort is required. Quantum Approximate Optimization Algorithm (QAOA) provides a promising means to search for these sections by leveraging quantum resources. However, its performance highly relies on the critical parameters, especially for weighted graphs. We present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density, and verify the strategy with 39, 774 instances. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots the practical application of quantum technique to power systems in noisy intermediate-scale quantum devices, heralding its next-generation computation in the quantum era.
The quantum approximate optimization algorithm (QAOA) is an efficient method for solving combinatorial optimization problems in quantum computing. These problems involve finding the best solution from a finite set of possibilities. At its core, the QAOA uses an Ansatz circuit composed of alternating unitary operators, the mixing and problem Hamiltonians, that are controlled by a set of parameters. Its goal is to find the optimal parameters so that the final quantum state of the circuit encodes the problem’s solution. While this parameter optimization is often handled by classical optimizers, including constrained optimization by linear approximations (COBYLA) and Nelder–Mead, these methods frequently present local extrema. Therefore, we developed a layerwise grid search (LGS) method as an alternative. Since a full grid search is too time-consuming, the LGS method significantly reduces the search time while still finding a good solution. To demonstrate its effectiveness, we present experimental results for the max-cut problem, comparing the performance of our LGS method against conventional classical optimizers.
The exponential growth of urban populations has necessitated the development of advanced energy models to manage resources efficiently and mitigate carbon emissions. Traditional approaches to urban energy modeling are hampered by computing limitations, primarily due to the computational power required and the inefficiencies of classical algorithms when handling high-dimensional search spaces.This paper explores the application of Quantum Approximate Optimization Algorithm (QAOA) to solve large-scale urban energy models, presenting a novel approach that leverages the computational advantages of quantum computing. QAOA offers several key benefits in this context, including enhanced capability to navigate and optimize within complex, high-dimensional search spaces. Its hybrid quantum-classical nature allows for significant improvements in computational efficiency and solution accuracy. Additionally, QAOA provides robustness against local minima, a common challenge in classical optimization techniques, thereby yielding more optimal solutions for energy distribution and management.By addressing the current constraints faced by classical computers, such as their inability to efficiently process the vast and complex data inherent in urban energy systems, this study demonstrates the potential for quantum algorithms to revolutionize urban planning and smart city development. The research highlights key areas where QAOA can outperform classical methods, offering enhanced accuracy and speed in optimizing energy distribution, reducing overall carbon emissions, and contributing to more sustainable urban environments. Our findings indicate that quantum computing holds significant promise in overcoming the existing barriers, providing a robust framework for the future of urban energy management.
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently know about the capabilities of QAOA, or of the difficulty of the requisite parameters optimization. Here, we study the performance of QAOA on the MaxCut combinatorial optimization problem, optimizing the quantum circuits on a classical computer using automatic differentiation and stochastic gradient descent, using QuantumFlow, a quantum circuit simulator implemented with TensorFlow. We find that we can amortize the training cost by optimizing on batches of problems instances; that QAOA can exceed the performance of the classical polynomial time Goemans-Williamson algorithm with modest circuit depth, and that performance with fixed circuit depth is insensitive to problem size. Moreover, MaxCut QAOA can be efficiently implemented on a gate-based quantum computer with limited qubit connectivity, using a qubit swap network. These observations support the prospects that QAOA will be an effective method for solving interesting problems on near-term quantum computers.