# Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems

arXiv: https://arxiv.org/abs/1911.11071 · HTML: https://mlsanity.com/paper/1911.11071/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2019.

## Built on by (most cited first, 30 of 31)

- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation](https://mlsanity.com/paper/2211.08737/) (2022)
- [Quantum Neural Network Compression](https://mlsanity.com/paper/2207.01578/) (2022)
- [Exploration of Quantum Neural Architecture by Mixing Quantum Neuron Designs](https://mlsanity.com/paper/2109.03806/) (2021)
- [QUILT: Effective Multi-Class Classification on Quantum Computers Using an Ensemble of Diverse Quantum Classifiers](https://mlsanity.com/paper/2309.15056/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Optimizing Quantum Variational Circuits with Deep Reinforcement Learning](https://mlsanity.com/paper/2109.03188/) (2021)
- [Reinforcement Learning for Variational Quantum Circuits Design](https://mlsanity.com/paper/2409.05475/) (2024)
- [Reinforcement Learning Assisted Recursive QAOA](https://mlsanity.com/paper/2207.06294/) (2022)
- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [Quantum Optimization for Training Quantum Neural Networks](https://mlsanity.com/paper/2103.17047/) (2021)
- [SEQUENT: Towards Traceable Quantum Machine Learning using Sequential Quantum Enhanced Training](https://mlsanity.com/paper/2301.02601/) (2023)
- [Variational Quantum Neural Networks (VQNNS) in Image Classification](https://mlsanity.com/paper/2303.05860/) (2023)
- [Quantum approximate optimization via learning-based adaptive optimization](https://mlsanity.com/paper/2303.14877/) (2023)
- [Learning To Optimize Quantum Neural Network Without Gradients](https://mlsanity.com/paper/2304.07442/) (2023)
- [Quantum Architecture Search with Unsupervised Representation Learning](https://mlsanity.com/paper/2401.11576/) (2024)
- [Multifidelity Reinforcement Learning with Control Variates](https://mlsanity.com/paper/2206.05165/) (2022)
- [QuAnt: Quantum Annealing with Learnt Couplings](https://mlsanity.com/paper/2210.08114/) (2022)
- [SLIQ: Quantum Image Similarity Networks on Noisy Quantum Computers](https://mlsanity.com/paper/2309.15259/) (2023)
- [CHARME: A chain-based reinforcement learning approach for the minor embedding problem](https://mlsanity.com/paper/2406.07124/) (2024)
- [Neural Simulated Annealing](https://mlsanity.com/paper/2203.02201/) (2022)
- [AutoQC: Automated Synthesis of Quantum Circuits Using Neural Network](https://mlsanity.com/paper/2210.02766/) (2022)
- [Meta-Learning for Quantum Optimization via Quantum Sequence Model](https://mlsanity.com/paper/2512.05058/) (2025)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (2024)
- [Investigating Quantum Circuit Designs Using Neuro-Evolution](https://mlsanity.com/paper/2602.03840/) (2026)
- [Evaluating the Performance of a D-Wave Quantum Annealing System for Feature Subset Selection in Software Defect Prediction](https://mlsanity.com/paper/2410.16469/) (2024)
- [Query-Efficient Quantum Approximate Optimization via Graph-Conditioned Trust Regions](https://mlsanity.com/paper/2604.24803/) (2026)
- [RASP-QAOA: Resource-Aware Per-Instance Selection for Exact QAOA Simulation](https://mlsanity.com/paper/2608.05646/) (2026)

## Abstract (arXiv)

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.