# Challenges and Opportunities in Quantum Optimization

arXiv: https://arxiv.org/abs/2312.02279 · HTML: https://mlsanity.com/paper/2312.02279/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2023.

## Built on by (most cited first, 30 of 42)

- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [QUASAR: Quantum Assembly Code Generation Using Tool-Augmented LLMs via Agentic RL](https://mlsanity.com/paper/2510.00967/) (2025)
- [Learning for routing: A guided review of recent developments and future directions](https://mlsanity.com/paper/2507.00218/) (2025)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Image Classification with Rotation-Invariant Variational Quantum Circuits](https://mlsanity.com/paper/2403.15031/) (2024)
- [Enhancing variational quantum algorithms by balancing training on classical and quantum hardware](https://mlsanity.com/paper/2503.16361/) (2025)
- [Learning to Learn with Quantum Optimization via Quantum Neural Networks](https://mlsanity.com/paper/2505.00561/) (2025)
- [Demonstration of Efficient Predictive Surrogates for Large-scale Quantum Processors](https://mlsanity.com/paper/2507.17470/) (2025)
- [Variational Quantum Optimization with Continuous Bandits](https://mlsanity.com/paper/2502.04021/) (2025)
- [Quantum Algorithms for Bandits with Knapsacks with Improved Regret and Time Complexities](https://mlsanity.com/paper/2507.04438/) (2025)
- [Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems](https://mlsanity.com/paper/2508.09103/) (2025)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (2024)
- [Efficient measurement of neutral-atom qubits with matched filters](https://mlsanity.com/paper/2504.08170/) (2025)
- [QAOA Parameter Transferability for Maximum Independent Set using Graph Attention Networks](https://mlsanity.com/paper/2504.21135/) (2025)
- [Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential](https://mlsanity.com/paper/2506.03779/) (2025)
- [Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction](https://mlsanity.com/paper/2506.11552/) (2025)
- [Subsampling Factorization Machine Annealing](https://mlsanity.com/paper/2508.08778/) (2025)
- [Quantum Machine Learning for UAV Swarm Intrusion Detection](https://mlsanity.com/paper/2509.01812/) (2025)
- [PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization](https://mlsanity.com/paper/2509.20733/) (2025)
- [Hybrid Quantum-Classical Optimisation of Traveling Salesperson Problem](https://mlsanity.com/paper/2509.26229/) (2025)
- [Replay-buffer engineering for noise-aware quantum circuit optimization](https://mlsanity.com/paper/2604.21863/) (2026)
- [KQFuzz: Knowledge-Guided Fuzzing for Quantum Libraries via Large Language Models](https://mlsanity.com/paper/2607.25647/) (2026)
- [Automatic re-calibration of quantum devices by reinforcement learning](https://mlsanity.com/paper/2404.10726/) (2024)
- [Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketches](https://mlsanity.com/paper/2407.06416/) (2024)
- [Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms](https://mlsanity.com/paper/2501.18432/) (2025)
- [Level Generation with Quantum Reservoir Computing](https://mlsanity.com/paper/2505.13287/) (2025)
- [LLM-QFL: Distilling Large Language Model for Quantum Federated Learning](https://mlsanity.com/paper/2505.18656/) (2025)
- [Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithms](https://mlsanity.com/paper/2506.13865/) (2025)
- [Superconducting Qubit Readout Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2506.15771/) (2025)

## Abstract (arXiv)

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of different approaches for major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions. This work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory - highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains - finance and sustainability - as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.