# Scalable Community Detection Using Quantum Hamiltonian Descent and QUBO Formulation

arXiv: https://arxiv.org/abs/2411.14696 · HTML: https://mlsanity.com/paper/2411.14696/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 44 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Builds on (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Clustering and Community Detection in Directed Networks: A Survey](https://mlsanity.com/paper/1308.0971/) (2013)
- [Quantum-inspired algorithms in practice](https://mlsanity.com/paper/1905.10415/) (2019)
- [Community Discovery in Dynamic Networks: a Survey](https://mlsanity.com/paper/1707.03186/) (2017)
- [Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra](https://mlsanity.com/paper/2011.04125/) (2020)
- [Quantum Hamiltonian Descent](https://mlsanity.com/paper/2303.01471/) (2023)
- [Different approaches to community detection](https://mlsanity.com/paper/1712.06468/) (2017)
- [Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding](https://mlsanity.com/paper/2401.08550/) (2024)
- [Quantum-Inspired Evolutionary Algorithms for Feature Subset Selection: A Comprehensive Survey](https://mlsanity.com/paper/2407.17946/) (2024)
- [QHDOPT: A Software for Nonlinear Optimization with Quantum Hamiltonian Descent](https://mlsanity.com/paper/2409.03121/) (2024)

## Built on by (most cited first, 1 of 1)

- [Quantum Optimization via Gradient-Based Hamiltonian Descent](https://mlsanity.com/paper/2505.14670/) (2025)

## Abstract (arXiv)

We present a quantum-inspired algorithm that utilizes Quantum Hamiltonian Descent (QHD) for efficient community detection. Our approach reformulates the community detection task as a Quadratic Unconstrained Binary Optimization (QUBO) problem, and QHD is deployed to identify optimal community structures. We implement a multi-level algorithm that iteratively refines community assignments by alternating between QUBO problem setup and QHD-based optimization. Benchmarking shows our method achieves up to 5.49% better modularity scores while requiring less computational time compared to classical optimization approaches. This work demonstrates the potential of hybrid quantum-inspired solutions for advancing community detection in large-scale graph data.