Abstract Differential-algebraic equations (DAEs) are critical for modeling various real-world phenomena, yet their inherent complexity poses significant challenges for numerical methods. Recent advancements in quantum computing offer promising avenues for addressing these challenges. Given the constraints of quantum hardware in the noisy intermediate-scale quantum era, researchers are actively exploring the application potential of the quantum neural network (QNN). In this work, a novel QNN is introduced for solving DAEs. Our contributions encompass three main aspects: 1) The design of a differentiable quantum neural network for solving differential-algebraic equations (DQNN-DAEs); 2) The proposal of the differentiable quantum neuron to reduce the quantum measurement times required for mimicking the first-order differential terms; 3) The development of an adaptive raster interval strategy and an adaptive equation weight strategy to strengthen the performance of DQNN-DAEs. In the case study, DQNN-DAEs is integrated into the transient stability analysis of power systems. Experiments on both quantum simulators and real quantum hardware demonstrate that DQNN-DAEs can handle DAEs effectively. This framework paves the way for the application of QNN to a broad range of complex systems in engineering, physics, and beyond.
Abstract Differential-algebraic equations (DAEs) are critical for modeling various real-world phenomena, yet their inherent complexity poses significant challenges for numerical methods. Recent advancements in quantum computing offer promising avenues for addressing these challenges. Given the constraints of quantum hardware in the noisy intermediate-scale quantum era, researchers are actively exploring the application potential of the quantum neural network (QNN). In this work, a novel QNN is introduced for solving DAEs. Our contributions encompass three main aspects: 1) The design of a differentiable quantum neural network for solving differential-algebraic equations (DQNN-DAEs); 2) The proposal of the differentiable quantum neuron to reduce the quantum measurement times required for mimicking the first-order differential terms; 3) The development of an adaptive raster interval strategy and an adaptive equation weight strategy to strengthen the performance of DQNN-DAEs. In the case study, DQNN-DAEs is integrated into the transient stability analysis of power systems. Experiments on both quantum simulators and real quantum hardware demonstrate that DQNN-DAEs can handle DAEs effectively. This framework paves the way for the application of QNN to a broad range of complex systems in engineering, physics, and beyond.
Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and computationally demanding task of simulating power system transients through solving differential-algebraic equations (DAEs). We introduce two novel Quantum Neural Networks (QNNs): the Sinusoidal-Friendly QNN and the Polynomial-Friendly QNN, proposing them as effective alternatives to conventional simulation techniques. Our application of these QNNs successfully simulates two small power systems, demonstrating their potential to achieve good accuracy. We further explore various configurations, including time intervals, training points, and the selection of classical optimizers, to optimize the solving of DAEs using QNNs. This research not only marks a pioneering effort in applying quantum computing to power system simulations but also expands the potential of quantum technologies in addressing intricate engineering challenges.
Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.
We introduce a quantum algorithm for simulating the dynamics of electrical circuits consisting of resistors, inductors and capacitors (aka RLC circuits) along with power sources. Given oracle access to the connectivity of the circuit and values of the electrical elements, our algorithm prepares a quantum state that encodes voltages and current values either at a specified time or the history of their evolution over a time-interval. For an RLC circuit with N components, our algorithm runs in time polylog(N) under mild assumptions on the connectivity of the circuit and values of its components. This provides an exponential speed-up over classical algorithms that take poly(N) time in the worst-case. Our algorithm can be used to estimate energy across a set of components or dissipated power in polylog(N) time, a problem that we prove is BQP-hard and therefore unlikely to be efficiently solved by classical algorithms. The main challenge in simulating the dynamics of RLC circuits is that they are governed by differential-algebraic equations (DAEs), a coupled system of differential equations with hidden algebraic constraints. Consequentially, existing quantum algorithms for ordinary differential equations cannot be directly utilized. We therefore develop a quantum DAE solver for simulating the time-evolution of linear DAEs. For RLC circuits, we employ modified nodal analysis to create a system of DAEs compatible with our quantum algorithm. We establish BQP-hardness by demonstrating that any network of classical harmonic oscillators, for which an energy-estimation problem is known to be BQP-hard, is a special case of an LC circuit. Our work gives theoretical evidence of quantum advantage in simulating RLC circuits and we expect that our quantum DAE solver will find broader use in the simulation of dynamical systems.
The rapid advancements in quantum computing (QC) and machine learning (ML) have led to the emergence of quantum machine learning (QML), which integrates the strengths of both fields. Among QML approaches, variational quantum circuits (VQCs), also known as quantum neural networks (QNNs), have shown promise both empirically and theoretically. However, their broader adoption is hindered by reliance on quantum hardware during inference. Hardware imperfections and limited access to quantum devices pose practical challenges. To address this, the Quantum-Train (QT) framework leverages the exponential scaling of quantum amplitudes to generate classical neural network parameters, enabling inference without quantum hardware and achieving significant parameter compression. Yet, designing effective quantum circuit architectures for such quantum-enhanced neural programmers remains non-trivial and often requires expertise in quantum information science. In this paper, we propose an automated solution using differentiable optimization. Our method jointly optimizes both conventional circuit parameters and architectural parameters in an end-to-end manner via automatic differentiation. We evaluate the proposed framework on classification, time-series prediction, and reinforcement learning tasks. Simulation results show that our method matches or outperforms manually designed QNN architectures. This work offers a scalable and automated pathway for designing QNNs that can generate classical neural network parameters across diverse applications.
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics' differential-algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.
Quantum Neural Networks (QNNs) represent a promising paradigm in artificial intelligence, leveraging the unique properties of quantum mechanics to potentially surpass classical neural networks. This paper investigates a novel approach to QNNs – Adaptive Quantum Neural Network Adjustment – designed to dynamically optimize network parameters, thereby enhancing performance across a range of applications. We propose a mechanism that iteratively adjusts the network's weights based on feedback from a quantum-enhanced learning process, fostering a more robust and adaptable system. The paper details the architecture of the adaptive adjustment mechanism, explores its impact on network performance through simulations, and provides a preliminary analysis of its potential benefits. The core of the work centers around a novel quantum-inspired optimization strategy to address the limitations of traditional training methods. This research highlights the potential of incorporating adaptive adjustment into QNN architectures to achieve superior results.