# Generative quantum combinatorial optimization by means of a novel conditional generative quantum eigensolver

arXiv: https://arxiv.org/abs/2501.16986 · HTML: https://mlsanity.com/paper/2501.16986/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 28 Jan 2025.

## Builds on (most cited first, 9 of 9)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [PyTorch Distributed: Experiences on Accelerating Data Parallel Training](https://mlsanity.com/paper/2006.15704/) (2020)
- [Input Redundancy for Parameterized Quantum Circuits](https://mlsanity.com/paper/1901.11434/) (2019)

## Built on by (most cited first, 7 of 7)

- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [QAOA-GPT: Efficient Generation of Adaptive and Regular Quantum Approximate Optimization Algorithm Circuits](https://mlsanity.com/paper/2504.16350/) (2025)
- [Generative Quantum-inspired Kolmogorov-Arnold Eigensolver](https://mlsanity.com/paper/2605.04604/) (2026)
- [Quantum Computing and AI: Perspectives on Advanced Automation in Science and Engineering](https://mlsanity.com/paper/2505.10012/) (2025)
- [SMILES-Inspired Transfer Learning for Quantum Operators in Generative Quantum Eigensolver](https://mlsanity.com/paper/2509.19715/) (2025)
- [An LLM System for Autonomous Variational Quantum Circuit Design](https://mlsanity.com/paper/2606.13380/) (2026)
- [Learning to Prepare Molecular Ground States with Transformer Models](https://mlsanity.com/paper/2607.22468/) (2026)

## Abstract (arXiv)

Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying quantum algorithms to real-world problems remains challenging. Hybrid quantum-classical techniques have been explored to bridge this gap, but they often face limitations in expressiveness, trainability, or scalability. In this work, we introduce conditional Generative Quantum Eigensolver (conditional-GQE), a context-aware quantum circuit generator powered by an encoder-decoder Transformer. Focusing on combinatorial optimization, we train our generator for solving problems with up to 10 qubits, exhibiting nearly perfect performance on new problems. By leveraging the high expressiveness and flexibility of classical generative models, along with an efficient preference-based training scheme, conditional-GQE provides a generalizable and scalable framework for quantum circuit generation. Our approach advances hybrid quantum-classical computing and contributes to accelerate the transition toward fault-tolerant quantum computing.