# Multilevel Combinatorial Optimization Across Quantum Architectures

arXiv: https://arxiv.org/abs/1910.09985 · HTML: https://mlsanity.com/paper/1910.09985/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2204.13751/) (2022)
- [QAOA-GPT: Efficient Generation of Adaptive and Regular Quantum Approximate Optimization Algorithm Circuits](https://mlsanity.com/paper/2504.16350/) (2025)
- [QAdaPrune: Adaptive Parameter Pruning For Training Variational Quantum Circuits](https://mlsanity.com/paper/2408.13352/) (2024)
- [Large Scale Diverse Combinatorial Optimization: ESPN Fantasy Football Player Trades](https://mlsanity.com/paper/2111.02859/) (2021)
- [Towards Practical Explainability with Cluster Descriptors](https://mlsanity.com/paper/2210.10662/) (2022)
- [QArchSearch: A Scalable Quantum Architecture Search Package](https://mlsanity.com/paper/2310.07858/) (2023)
- [Neural Architecture Search Algorithms for Quantum Autoencoders](https://mlsanity.com/paper/2509.15451/) (2025)
- [DQAOA-GPT: AI-Accelerated Distributed Quantum Optimization for Combinatorial Problems](https://mlsanity.com/paper/2607.20225/) (2026)
- [Surrogate Modeling via Factorization Machine and Ising Model with Enhanced Higher-Order Interaction Learning](https://mlsanity.com/paper/2507.01389/) (2025)

## Abstract (arXiv)

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave's quantum annealer and IBM's gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution.