Quantum Approximate Optimization Algorithm

Also known as QAOA

QAOA encodes a discrete optimization problem in a cost Hamiltonian and alternates it with a mixer circuit; a classical optimizer adjusts the circuit parameters to improve the measured solutions. Work explores parameter initialization and transfer, constraint-preserving mixers, problem decomposition, and optimizers such as BFGS and differential evolution. Methods are tested on MaxCut and other graph problems, QUBO instances, routing, and portfolio optimization, using both simulators and quantum hardware. A central tension is that greater expressibility and larger instances can demand deeper, harder-to-optimize circuits, while noise and hardware connectivity can erase gains; practical quantum advantage remains unestablished.

Latest papers

24 papers2 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Learning angles for quantum approximate optimization
Oct 16, 2026Johannes Jakubik, Isabelle Wittmann, Zaheed Gaffoor +5Quantum Approximate Optimization Algorithm Learning to Optimize
IBM Research
Optimization Geometry of QAOA and Variational Quantum Algorithms
Oct 4, 2026Vojtěch Novák, Ivan Zelinka, Silvie Illésová +2Quantum Approximate Optimization Algorithm Variational Quantum Algorithms
Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VSB – Technical University of Ostrava, Ostrava, Czech Republic · IT4Innovations National Supercomputing Center, VSB – Technical University of Ostrava, 708 00 Ostrava, Czech Republic · Department of Informatics and Statistics, Marine Research Institute, Klaipeda University, Klaipeda, Lithuania +3
Adaptive Differential Evolution and Multistart Search for Noisy QAOA Optimization
Sep 19, 2026Vojtěch Novák, Ivan Zelinka, Swagatam Das +1Stochastic Optimization Black-Box Optimization
Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VSB–Technical University of Ostrava, Ostrava, Czech Republic · IT4Innovations National Supercomputing Center, VSB–Technical University of Ostrava, 708 00 Ostrava, Czech Republic · Department of Informatics and Statistics, Marine Research Institute, Klaipeda University, Lithuania +2
When is global evolutionary search useful for variational quantum algorithms? A landscape-first study
Sep 13, 2026Vojtěch Novák, Ivan ZelinkaVariational Quantum Algorithms Evolutionary Optimization
Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VSB - Technical University of Ostrava, Ostrava, Czech Republic · IT4Innovations National Supercomputing Center, VSB - Technical University of Ostrava, 708 00 Ostrava, Czech Republic
RASP-QAOA: Resource-Aware Per-Instance Selection for Exact QAOA Simulation
Aug 6, 2026Chih-Chung HsuAlgorithm Selection Quantum Circuit Simulation
Institute of Smart Industry and Green Energy, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
LC-Implicit-QAOA: Active-Workspace-Capped Exact Objective-and-Gradient Evaluation for Training over Bounded QUBO Light Cones
Aug 6, 2026Chih-Chung HsuQuadratic Unconstrained Binary Optimization Variational Quantum Circuits
Institute of Smart Industry and Green Energy, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
Dynamical Lie Algebras Cannot Describe Shallow QAOA: Cragged Terrains, Barren Plateaus, and Empirical Hardness Models
Aug 4, 2026Harrison Copp, Charlton Li, Anžej Margeta-Cacace +1Barren Plateaus Quantum Approximate Optimization Algorithm
Yale University
DQAOA-GPT: AI-Accelerated Distributed Quantum Optimization for Combinatorial Problems
Jul 22, 2026Seongmin Kim, Abhinav Rijal, Yuri Alexeev +5Distributed Optimization Combinatorial Optimization
National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA · Department of Physics & Astronomy, University of Tennessee, Knoxville, TN, USA · NVIDIA Corporation, Santa Clara, CA, USA +3
COMET: Combinatorial Optimization for Multiplex Editing Targets Via Constraint-Preserving QAOA
Jul 2, 2026Priyansh Singhal, Sumit Maheshwari, Piyush JoshiQuadratic Unconstrained Binary Optimization Constrained Optimization
Independent Researcher India · Microsoft Boston, USA · Department of Computer Science & Engineering IIIT Sri City, India
A Machine-Verified Proof of a Quantum-Optimization Conjecture
Jun 29, 2026Uri Kol, Maor Ben-Shahar, Kfir Sulimany +1Large Language Model-Guided Theorem Proving Quantum Approximate Optimization Algorithm
Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA · MIT Center for Theoretical Physics - a Leinweber Institute, Cambridge, MA 02139, USA · Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Dimensionality Reduction of QAOA Parameter Space with Kernel PCA for Max-Cut
Jun 17, 2026Sidharth Brahmandam, Vayd RamkumarPrincipal Component Analysis Combinatorial Optimization
Naperville North High School · Independent Researcher
Optimality-Preserving Decomposition for Scalable QAOA in Natural-Language-Guided Multi-Drone Assignment
Jun 12, 2026Junyeop Bang, Byongho Lee, Dohyun An +1Multi-Robot Task Allocation Quantum Approximate Optimization Algorithm
Department of Smart Convergence Korea University Republic of Korea · School of Electrical Engineering Korea University Republic of Korea
Benchmarking Quantum Algorithmic Resilience for CVaR Portfolio Optimization: The Expressibility-Coherence Trade-off
Jun 5, 2026Prashik N. Somkuwar, K. Srinivasan, G. RaghavanVariational Quantum Circuits Portfolio Optimization
School of Quantum Technology, Defence Institute of Advanced Technology, Pune, India
Classical State Preparation for Variational Quantum Algorithms via Reinforcement Learning
May 22, 2026Gino Kwun, Dhanvi Bharadwaj, Gokul Subramanian RaviQuantum State Preparation Quantum Approximate Optimization Algorithm
Computer Science and Engineering University of Michigan Ann Arbor, MI 48109, USA
Neural QAOA $^{2}$ : Differentiable Joint Graph Partitioning and Parameter Initialization for Quantum Combinatorial Optimization
May 13, 2026Zubin Zheng, Jiahao Wu, Shengcai LiuGraph Partitioning Quadratic Unconstrained Binary Optimization
Guangdong Provincial Key Labora- tory of Brain-Inspired Intelligent Computation, Department of CSE, SUSTech.
Quantum End-to-End Learning for Contextual Combinatorial Optimization
May 13, 2026Jaehwan Lee, Changhyun KwonCombinatorial Optimization Hybrid Quantum-Classical ML
1KAIST · 2Omelet
SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis
May 11, 2026Sean Feeney, Pooja Rao, Andreas Klappenecker +5AI-Assisted Scientific Research Neuro-Symbolic Reasoning
Department of Computer Science, Texas A&M University, College Station, USA · NVIDIA Corporation, Santa Clara, USA · Computing and Artificial Intelligence Division (CAI-3), Los Alamos National Laboratory, Los Alamos, USA
Optimal FALQON for Quantum Approximate Optimization via Layer-wise Parameter Tuning
May 8, 2026Michael Mancini, Shabnam SodagariQuantum Approximate Optimization Algorithm
Computer Engineering & Computer Science, California State University, Long Beach, CA 90840
Breaking QAOA's Fixed Target Hamiltonian Barrier: A Fully Connected Quantum Boltzmann Machine via Bilevel Optimization
May 8, 2026Jun LiuQuantum Machine Learning Quantum Approximate Optimization Algorithm
School of Economics, Hunan University of Finance and Economics, Changsha 410205, China
Hybrid Quantum Reinforcement Learning with QAOA for Improved Vehicle Routing Optimization
May 2, 2026T. Satyanarayana Murthy, B. Swathi Sowmya, Santhosh Voruganti +3Quantum Machine Learning Combinatorial Optimization
Chaitanya Bharathi Institute of Technology Hyderabad, India
Query-Efficient Quantum Approximate Optimization via Graph-Conditioned Trust Regions
Apr 27, 2026Molena HuynhBlack-Box Optimization Combinatorial Optimization
North Carolina State University
Domain-Aware Hybrid Quantum Learning via Correlation-Guided Circuit Design for Crime Pattern Analytics
Apr 8, 2026Niloy Das, Apurba Adhikary, Sheikh Salman Hassan +4Quantum Machine Learning Hybrid Quantum-Classical ML
Department of Information and Communication Engineering, Noakhali Science and Technology University, Bangladesh · Institute for Imaging, Data, and Communications (IDCOM), The University of Edinburgh, UK · School of Information Science and Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China +2
Quantum-Assisted Optimal Rebalancing with Uncorrelated Asset Selection for Algorithmic Trading Walk-Forward QUBO Scheduling via QAOA
Mar 4, 2026Abraham Itzhak WeinbergAlgorithmic Trading Portfolio Optimization
AI-WEINBERG, AI Experts, Tel Aviv, Israel
QANTIS: A Hardware-Validated Quantum Platform for POMDP Planning and Multi-Target Data Association
Feb 28, 2026Bayram Yüksel Eker, Suayb S. Arslan, Özgür Nazlı +2Partially Observable Markov Decision Processes Multi-Object Tracking
Neura Parse Ltd., London, United Kingdom · Department of Computer Engineering, Boğaziçi University, Istanbul, Turkey · İzmir Ekonomi Üniversitesi, İzmir, Turkey +2

Oct 16, 2026J/K move · Enter open · S save

Learning angles for quantum approximate optimization

Johannes Jakubik, Isabelle Wittmann, Zaheed Gaffoor, Gciniwe Simphiwe Baloyi+4

IBM Research

Quantum Approximate Optimization Algorithm Learning to Optimize Combinatorial Optimization

Open paper AskPDF arXiv

The Quantum Approximate Optimization Algorithm (QAOA) and its variants are leading algorithms to help solve challenging combinatorial optimization problems. QAOA maps these problems to Ising Hamiltonians such that their ground state is the desired solution. Candidate solutions are then drawn from a variational quantum circuit. The performance of QAOA hinges on a set of variational angles. However, finding good angles is an instance-specific and computationally expensive non-convex classical optimization task. Here, we learn the mapping from the problem instance to high-quality QAOA angles. Our learned models replace the per-instance optimization, that we call the solver, with a single forward pass that is several orders of magnitude faster than the solver with a near identical quality. Our models further generalize to unseen topologies such as Barabási-Albert and 2D grid graphs. Experiments on quantum hardware confirm that QAOA samples with angles produced by our open-source models are indistinguishable from solver angles. Crucially, models sensitive to the topology of the problem instance increase the quality of the QAOA angles. Our work amortizes a major bottleneck in QAOA by an up-front data generation and training cost. Importantly, this cost can be amortized over time in settings where many similar problems are optimized on a regular basis, as is often the case in applications for industry.