Quantum Neural Networks for Power Flow Analysis

TL;DR

This work investigates quantum neural networks (QNNs) for power flow (PF) analysis, proposing both a pure QNN and a hybrid quantum-classical neural network (QCNN) to serve as data-driven surrogates for PF. Using 4-bus and supplementary 33-bus test systems, the authors encode inputs with a feature map, process them via parameterized quantum circuits, and train with gradient-based optimization, comparing against a classical feed-forward NN. The results show that QCNNs provide superior generalization, robustness to noisy training data, and data efficiency (approximately fourfold less data needed to match QCNN performance) while achieving competitive accuracy to iterative NR solvers; QNNs also outperform classical NNs in several metrics. The study demonstrates the potential of QCNNs to operate in the NISQ/FTQ era, serving as fast surrogate PF estimators and potentially seeding NR iterations, with practical validation through 4-bus and 33-bus simulations and explicit analysis of shot convergence and hardware-noise effects.

Abstract

This paper explores the potential application of quantum and hybrid quantum-classical neural networks in power flow analysis. Experiments are conducted using two datasets based on 4-bus and 33-bus test systems. A systematic performance comparison is also conducted among quantum, hybrid quantum-classical, and classical neural networks. The comparison is based on (i) generalization ability, (ii) robustness, (iii) training dataset size needed, (iv) training error, and (v) training process stability. The results show that the developed hybrid quantum-classical neural network outperforms both quantum and classical neural networks, and hence can improve deep learning-based power flow analysis in the noisy-intermediate-scale quantum (NISQ) and fault-tolerant quantum (FTQ) era.

Figures (13)

• Figure 1: Schematic depiction of the NN designed for PF analysis. $\vec{x} \in \{(\vec{p}_i,\vec{q}_i): i=1,2,\dots,n\}$ and $\vec{y} \in \{(\vec{v}_i,\vec{\delta}_i): i=1,2,\dots,n\}$ respectively represent the input features and output labels, where $n$ is the number of buses.
• Figure 2: Schematic representation of the quantum state, which can be in a superposition of states $|0\rangle$ and $|1\rangle$. $\phi$ and $\varphi$ determine the probability amplitude of the state being $|0\rangle$ and $|1\rangle$, respectively. The qubit can be manipulated by applying quantum gates to change $\phi$ and $\varphi$.
• Figure 3: Schematic representation of a PQC involving a pair of qubits. It includes both parameterized gate $R_{y}(w^{r})$ with adjustable parameter $w^{r}$, and non-parameterized gate $H$. $CNOT$ gate entangles the second qubit to the first, executing a two-qubit operation. Finally, the measurement is performed to determine the expectation values of the involved qubits.
• Figure 4: Schematic depiction of the QNN designed for PF analysis, including a feature map, an ansatz, and the measurement. $\vec{x} \in \{(\vec{p}_i,\vec{q}_i): i=1,2,\dots,n\}$ and $\vec{y} \in \{(\vec{v}_i,\vec{\delta}_i): i=1,2,\dots,n\}$ respectively represent the input features and output labels, where $n$ is the number of buses.
• Figure 5: Schematic depiction of the QCNN designed for PF analysis with a PQC replacing one hidden layer. $\vec{x} \in \{(\vec{p}_i,\vec{q}_i): i=1,2,\dots,n\}$ and $\vec{y} \in \{(\vec{v}_i,\vec{\delta}_i): i=1,2,\dots,n\}$ respectively represent the input features and output labels, where $n$ is the number of buses. The data flow starts from a hidden layer, passes through the PQC, and continues to the subsequent hidden layer after the measurement.