# Learning AC Power Flow Solutions using a Data-Dependent Variational Quantum Circuit

arXiv: https://arxiv.org/abs/2509.03495 · HTML: https://mlsanity.com/paper/2509.03495/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 3 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits](https://mlsanity.com/paper/2310.07528/) (2023)
- [PSSE Redux: Convex Relaxation, Decentralized, Robust, and Dynamic Approaches](https://mlsanity.com/paper/1708.03981/) (2017)
- [Quantum Computing for Power Flow Algorithms: Testing on real Quantum Computers](https://mlsanity.com/paper/2204.14028/) (2022)
- [Quantum Power Flow](https://mlsanity.com/paper/2104.04888/) (2021)
- [Convergence of the Z-Bus Method for Three-Phase Distribution Load-Flow with ZIP Loads](https://mlsanity.com/paper/1605.08511/) (2016)
- [Quantum Power Flows: From Theory to Practice](https://mlsanity.com/paper/2211.05728/) (2022)
- [Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow](https://mlsanity.com/paper/2509.00341/) (2025)

## Abstract (arXiv)

Interconnection studies require solving numerous instances of the AC load or power flow (AC PF) problem to simulate diverse scenarios as power systems navigate the ongoing energy transition. To expedite such studies, this work leverages recent advances in quantum computing to find or predict AC PF solutions using a variational quantum circuit (VQC). VQCs are trainable models that run on modern-day noisy intermediate-scale quantum (NISQ) hardware to accomplish elaborate optimization and machine learning (ML) tasks. Our first contribution is to pose a single instance of the AC PF as a nonlinear least-squares fit over the VQC trainable parameters (weights) and solve it using a hybrid classical/quantum computing approach. The second contribution is to feed PF specifications as features into a data-embedded VQC and train the resultant quantum ML (QML) model to predict general PF solutions. The third contribution is to develop a novel protocol to efficiently measure AC-PF quantum observables by exploiting the graph structure of a power network. Preliminary numerical tests indicate that the proposed VQC models attain enhanced prediction performance over a deep neural network despite using much fewer weights. The proposed quantum AC-PF framework sets the foundations for addressing more elaborate grid tasks via quantum computing.