# Quantum Power Flows: From Theory to Practice

arXiv: https://arxiv.org/abs/2211.05728 · HTML: https://mlsanity.com/paper/2211.05728/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 10 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Quantum Interior Point Methods for Semidefinite Optimization](https://mlsanity.com/paper/2112.06025/) (2021)
- [Quantum Computing for Power Flow Algorithms: Testing on real Quantum Computers](https://mlsanity.com/paper/2204.14028/) (2022)
- [A Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions](https://mlsanity.com/paper/1905.01602/) (2019)
- [Experimental Quantum Computing to Solve Network DC Power Flow Problem](https://mlsanity.com/paper/2106.12032/) (2021)

## Built on by (most cited first, 2 of 2)

- [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)
- [Learning AC Power Flow Solutions using a Data-Dependent Variational Quantum Circuit](https://mlsanity.com/paper/2509.03495/) (2025)

## Abstract (arXiv)

Climate change is becoming one of the greatest challenges to the sustainable development of modern society. Renewable energies with low density greatly complicate the online optimization and control processes, where modern advanced computational technologies, specifically quantum computing, have significant potential to help. In this paper, we discuss applications of quantum computing algorithms toward state-of-the-art smart grid problems. We suggest potential, exponential quantum speedup by the use of the Harrow-Hassidim-Lloyd (HHL) algorithms for sparse matrix inversions in power-flow problems. However, practical implementations of the algorithm are limited by the noise of quantum circuits, the hardness of realizations of quantum random access memories (QRAM), and the depth of the required quantum circuits. We benchmark the hardware and software requirements from the state-of-the-art power-flow algorithms, including QRAM requirements from hybrid phonon-transmon systems, and explicit gate counting used in HHL for explicit realizations. We also develop near-term algorithms of power flow by variational quantum circuits and implement real experiments for 6 qubits with a truncated version of power flows.