# Hamiltonian-based Quantum Reinforcement Learning for Neural Combinatorial Optimization

arXiv: https://arxiv.org/abs/2405.07790 · HTML: https://mlsanity.com/paper/2405.07790/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 13 May 2024.

## Placed in

- Deep reinforcement learning methods / [Quantum reinforcement learning](https://mlsanity.com/deeprl/quantum-reinforcement-learning/)

## Builds on (most cited first, 12 of 12)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Quantum Policy Gradient Algorithm with Optimized Action Decoding](https://mlsanity.com/paper/2212.06663/) (2022)
- [VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainability](https://mlsanity.com/paper/2401.11555/) (2024)
- [Equivariant Quantum Graph Circuits](https://mlsanity.com/paper/2112.05261/) (2021)

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

- [Benchmarking Quantum Reinforcement Learning](https://mlsanity.com/paper/2501.15893/) (2025)
- [Dissecting Quantum Reinforcement Learning: A Systematic Evaluation of Key Components](https://mlsanity.com/paper/2511.17112/) (2025)

## Abstract (arXiv)

Advancements in Quantum Computing (QC) and Neural Combinatorial Optimization (NCO) represent promising steps in tackling complex computational challenges. On the one hand, Variational Quantum Algorithms such as QAOA can be used to solve a wide range of combinatorial optimization problems. On the other hand, the same class of problems can be solved by NCO, a method that has shown promising results, particularly since the introduction of Graph Neural Networks. Given recent advances in both research areas, we introduce Hamiltonian-based Quantum Reinforcement Learning (QRL), an approach at the intersection of QC and NCO. We model our ansatzes directly on the combinatorial optimization problem's Hamiltonian formulation, which allows us to apply our approach to a broad class of problems. Our ansatzes show favourable trainability properties when compared to the hardware efficient ansatzes, while also not being limited to graph-based problems, unlike previous works. In this work, we evaluate the performance of Hamiltonian-based QRL on a diverse set of combinatorial optimization problems to demonstrate the broad applicability of our approach and compare it to QAOA.