# Qubit-efficient Variational Quantum Algorithms for Image Segmentation

arXiv: https://arxiv.org/abs/2405.14405 · HTML: https://mlsanity.com/paper/2405.14405/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 10 of 10)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [FVP: Fourier Visual Prompting for Source-Free Unsupervised Domain Adaptation of Medical Image Segmentation](https://mlsanity.com/paper/2304.13672/) (2023)
- [CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes](https://mlsanity.com/paper/2303.16202/) (2023)
- [Q-Seg: Quantum Annealing-Based Unsupervised Image Segmentation](https://mlsanity.com/paper/2311.12912/) (2023)
- [GCS-Q: Quantum Graph Coalition Structure Generation](https://mlsanity.com/paper/2212.11372/) (2022)
- [BILP-Q: Quantum Coalition Structure Generation](https://mlsanity.com/paper/2204.13802/) (2022)
- [Graph Cut Segmentation Methods Revisited with a Quantum Algorithm](https://mlsanity.com/paper/1812.03050/) (2018)
- [A Quantum Approach for Stochastic Constrained Binary Optimization](https://mlsanity.com/paper/2301.01443/) (2023)

## Built on by (most cited first, 6 of 6)

- [Quantum Artificial Intelligence: A Brief Survey](https://mlsanity.com/paper/2408.10726/) (2024)
- [Quantum-enhanced unsupervised image segmentation for medical images analysis](https://mlsanity.com/paper/2411.15086/) (2024)
- [Benefiting from Quantum? A Comparative Study of Q-Seg, Quantum-Inspired Techniques, and U-Net for Crack Segmentation](https://mlsanity.com/paper/2410.10713/) (2024)
- [Toward Quantum Utility in Finance: A Robust Data-Driven Algorithm for Asset Clustering](https://mlsanity.com/paper/2509.07766/) (2025)
- [Quantum-Assisted Correlation Clustering](https://mlsanity.com/paper/2509.03561/) (2025)
- [QINA: Quantum-Inspired Nonlinear Adapters for Pretrained Vision Models](https://mlsanity.com/paper/2609.29592/) (2026)

## Abstract (arXiv)

Quantum computing is expected to transform a range of computational tasks beyond the reach of classical algorithms. In this work, we examine the application of variational quantum algorithms (VQAs) for unsupervised image segmentation to partition images into separate semantic regions. Specifically, we formulate the task as a graph cut optimization problem and employ two established qubit-efficient VQAs, which we refer to as Parametric Gate Encoding (PGE) and Ancilla Basis Encoding (ABE), to find the optimal segmentation mask. In addition, we propose Adaptive Cost Encoding (ACE), a new approach that leverages the same circuit architecture as ABE but adopts a problem-dependent cost function. We benchmark PGE, ABE and ACE on synthetically generated images, focusing on quality and trainability. ACE shows consistently faster convergence in training the parameterized quantum circuits in comparison to PGE and ABE. Furthermore, we provide a theoretical analysis of the scalability of these approaches against the Quantum Approximate Optimization Algorithm (QAOA), showing a significant cutback in the quantum resources, especially in the number of qubits that logarithmically depends on the number of pixels. The results validate the strengths of ACE, while concurrently highlighting its inherent limitations and challenges. This paves way for further research in quantum-enhanced computer vision.