# Quantum Power Flow

arXiv: https://arxiv.org/abs/2104.04888 · HTML: https://mlsanity.com/paper/2104.04888/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2021.

## Built on by (most cited first, 4 of 4)

- [Quantum Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2311.06293/) (2023)
- [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)
- [Quantum Neural Networks for Solving Power System Transient Simulation Problem](https://mlsanity.com/paper/2405.11427/) (2024)
- [Learning AC Power Flow Solutions using a Data-Dependent Variational Quantum Circuit](https://mlsanity.com/paper/2509.03495/) (2025)

## Abstract (arXiv)

This letter is a proof of concept for quantum power flow (QPF) algorithms which underpin various unprecedentedly efficient power system analytics exploiting quantum computing. Our contributions are three-fold: 1) Establish a quantum-state-based fast decoupled model empowered by Hermitian and constant Jacobian matrices; 2) Devise an enhanced Harrow-Hassidim-Lloyd (HHL) algorithm to solve the fast decoupled QPF; 3) Further improve the HHL efficiency by parameterizing quantum phase estimation and reciprocal rotation only at the beginning stage. Promising test results validate the accuracy and efficacy of QPF and demonstrate QPF's enormous potential in the era of quantum computing.