QAOAKit: A Toolkit for Reproducible Study, Application, and Verification of the QAOA
Open accessAbstract
Understanding the best known parameters, performance, and systematic behavior of the Quantum Approximate Optimization Algorithm (QAOA) remain open research questions, even as the algorithm gains popularity. We introduce QAOAKit, a Python toolkit for the QAOA built for exploratory research. QAOAKit is a unified repository of preoptimized QAOA parameters and circuit generators for common quantum simulation frameworks. We combine, standardize, and cross-validate previously known parameters for the MaxCut problem, and incorporate this into QAOAKit. We also build conversion tools to use these parameters as inputs in several quantum simulation frameworks that can be used to reproduce, compare, and extend known results from various sources in the literature. We describe QAOAKit and provide examples of how it can be used to reproduce research results and tackle open problems in quantum optimization.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Classes of problems exhibit pronounced parameter concentration of optimal or near-optimal angles.
“On the other hand, there is increasing evidence that classes of problems exhibit pronounced parameter concentration of the optimal or near optimal angles [19], [51], [1], [6], [61], [17], [48], [41]”
From High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices (2023) · cites this paper as [51]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Scikit-learn: Machine Learning in Python
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Müller, A., Nothman, J., Louppe, G., et al. (2012) · arXiv · doi:10.48550/arxiv.1201.0490 · Cited by 71,016 · see citing works
Exploring Network Structure, Dynamics, and Function Using NetworkX
Hagberg, A. A., Schult, D. A., & Swart, P. J. (2008) · Proceedings of the Python in Science Conference · doi:10.25080/tcwv9851 · Cited by 7,477 · see citing works
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587 · cited 1× · see citing works
“Additionally, we can include the classical Goemans–Williamson algorithm [25] in the comparison, with many implementations available.”
MethodA Quantum Approximate Optimization Algorithm
Farhi, E., Goldstone, J., & Gutmann, S. (2014) · arXiv · doi:10.48550/arxiv.1411.4028 · Cited by 1,789 · see citing works
Zhou, L., Wang, S.-T., Choi, S., Pichler, H., & Lukin, M. D. (2020) · Physical Review X · doi:10.1103/physrevx.10.021067 · Cited by 913 · cited 2× · see citing works
“The choice of parameters (commonly referred to as angles) for the QAOA is of central importance to algorithm performance and has been considered extensively in the literature; see, for example, [3]–[5].”
BackgroundMethodFast generation of regular graphs and construction of cages
Meringer, M. (1999) · Journal of Graph Theory · doi:10.1002/(sici)1097-0118(199902)30:2 · Cited by 182 · see citing works
Learning to learn with quantum neural networks via classical neural networksPreprint
Verdon, G., Broughton, M., McClean, J. R., Sung, K. J., Babbush, R., Zhang, J., Neven, H., & Mohseni, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.05415 · Cited by 134 · see citing works
Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems
Khairy, S., Shaydulin, R., Cincio, L., Alexeev, Y., & Balaprakash, P. (2020) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v34i03.5616 · Cited by 117 · see citing works
Self-citationHogg, T., & Portnov, D. (2000) · Information Sciences · doi:10.1016/s0020-0255(00)00052-9 · Cited by 111 · see citing works
Multistart Methods for Quantum Approximate optimization
Shaydulin, R., Safro, I., & Larson, J. (2019) · 2019 IEEE High Performance Extreme Computing Conference (HPEC) · doi:10.1109/hpec.2019.8916288 · Cited by 110 · cited 4× · see citing works
“The choice of parameters (commonly referred to as angles) for the QAOA is of central importance to algorithm performance and has been considered extensively in the literature; see, for example, [3]–[5].”
BackgroundMethodInfluentialSelf-citationMaxCut quantum approximate optimization algorithm performance guarantees for p>1
Wurtz, J., & Love, P. J. (2021) · Physical Review A · doi:10.1103/physreva.103.042612 · Cited by 103 · cited 3× · see citing works
“It was numerically observed in [16] that these fixed angles are close to optimal and so can be a good proxy for QAOA performance at intermediate p.”
BackgroundInfluentialSelf-citationExtremal cuts of sparse random graphs
Dembo, A., Andrea Montanari, A., & Sen, S. (2017) · The Annals of Probability · doi:10.1214/15-aop1084 · Cited by 96 · see citing works
Brandao, F. G. S. L., Broughton, M., Farhi, E., Gutmann, S., & Neven, H. (2018) · arXiv · doi:10.48550/arxiv.1812.04170 · Cited by 88 · see citing works
Optimizing quantum heuristics with meta-learning
Wilson, M., Stromswold, R., Wudarski, F., Hadfield, S., Tubman, N. M., & Rieffel, E. G. (2021) · Quantum Machine Intelligence · doi:10.1007/s42484-020-00022-w · Cited by 79 · see citing works
Optimizing quantum heuristics with meta-learning
Wilson, M., Stromswold, S., Wudarski, F., Hadfield, S., Tubman, N. M., & Rieffel, E. (2019) · arXiv · doi:10.48550/arxiv.1908.03185 · Cited by 77
Transferability of optimal QAOA parameters between random graphs
Galda, A., Liu, X., Lykov, D., Alexeev, Y., & Safro, I. (2021) · 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00034 · Cited by 72 · see citing works
Empirical performance bounds for quantum approximate optimization
Lotshaw, P. C., Humble, T. S., Herrman, R., Ostrowski, J., & Siopsis, G. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03342-3 · Cited by 58 · see citing works
Self-citationEvaluating Quantum Approximate Optimization Algorithm: A Case Study
Shaydulin, R., & Alexeev, Y. (2019) · 2019 Tenth International Green and Sustainable Computing Conference (IGSC) · doi:10.1109/igsc48788.2019.8957201 · Cited by 55 · cited 1× · see citing works
“between similar graph instances; in other words, the optimal parameters from one instance can be transferred to another one [3], [6]–[8], [12], [14], [20].”
BackgroundSelf-citationParameters Fixing Strategy for Quantum Approximate Optimization Algorithm
Lee, X., Saito, Y., Cai, D., & Asai, N. (2021) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00016 · Cited by 34 · see citing works
Reachability Deficits in Quantum Approximate Optimization of Graph Problems
Akshay, V., Philathong, H., Zacharov, I., & Biamonte, J. (2021) · Quantum · doi:10.22331/q-2021-08-30-532 · Cited by 26 · cited 3× · see citing works
“A negative (although weak) relationship between the success probability and average degree is clearly visible in the plots, supporting the findings of [21].”
BackgroundResultInfluentialError Mitigation for Deep Quantum Optimization Circuits by Leveraging Problem Symmetries
Shaydulin, R., & Galda, A. (2021) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00046 · Cited by 24 · cited 1× · see citing works
“For example, the parameters and circuits from QAOAKit have already been used to study error mitigation techniques for the QAOA [26].”
MethodSelf-citationQuantum OptimizationPreprint
Hogg, T., & Portnov, D. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0006090 · Cited by 22 · see citing works
Classical symmetries and QAOAPreprint
Shaydulin, R., Hadfield, S., Hogg, T., & Safro, I. (2020) · arXiv (Cornell University) · Cited by 14 · see citing works
Self-citationThe fixed angle conjecture for QAOA on regular MaxCut graphsPreprint
Wurtz, J., & Lykov, D. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.00677 · Cited by 4 · cited 3× · see citing works
“Additionally, the dataset includes the fixed angles of [14] for all p ≤ 11 and the QAOA cost values evaluated at these angles.”
BackgroundMethodSelf-citationAn explicit vector algorithm for high-girth MaxCut
Thompson, J. K., Parekh, O., & Marwaha, K. (2022) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611977066.17 · Cited by 4 · see citing works
Self-citationEmpirical performance bounds for quantum approximate optimization
Lotshaw, P. C., Humble, T. S., Herrman, R., et al. (2021) · arXiv · doi:10.48550/arxiv.2102.06813
Self-citationParameters Fixing Strategy for Quantum Approximate Optimization Algorithm
Lee, X., Saito, Y., Cai, D., & Asai, N. (2021) · arXiv · doi:10.48550/arxiv.2108.05288
Transferability of optimal QAOA parameters between random graphs
Galda, A., Liu, X., Lykov, D., Alexeev, Y., & Safro, I. (2021) · arXiv · doi:10.48550/arxiv.2106.07531
Classical symmetries and the Quantum Approximate Optimization Algorithm
Shaydulin, R., Hadfield, S., Hogg, T., & Safro, I. (2020) · arXiv · doi:10.48550/arxiv.2012.04713
Self-citationAn explicit vector algorithm for high-girth MaxCut
Thompson, J. K., Parekh, O., & Marwaha, K. (2021) · arXiv · doi:10.48550/arxiv.2108.12477
Self-citation
Flagged first, then by citations
Research works printed but not linked: 1
- [17][17] B. D. McKay and A. Piperno, 'nauty and Traces user's guide (version 2.7),' 2020. [Online]. Available: http://pallini.di.uniroma1.it/Guide.html 19. Machine Learning Research , vol. 12, pp. 2825-2830, 2011. [Online]. Available: 1201.0490 -
Cited by
Sorted by citations
A review on Quantum Approximate Optimization Algorithm and its variants
Blekos, K., Brand, D., Ceschini, A., Chou, C.-H., Li, R.-H., Pandya, K., & Summer, A. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.03.002 · Cited by 444 · see citing works
Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut
Shaydulin, R., Lotshaw, P. C., Larson, J. M., Ostrowski, J., & Humble, T. S. (2023) · ACM Transactions on Quantum Computing · doi:10.1145/3584706 · Cited by 100 · see citing works
“Alldatain this paper is available in the open-source software package QAOAKit [24], and we provide code examples of how our findings can be leveraged in practice [25].”
MethodInfluentialSelf-citationConstrained quantum optimization for extractive summarization on a trapped-ion quantum computer
Niroula, P., Shaydulin, R., Yalovetzky, R., Minssen, P., Herman, D., Hu, S., & Pistoia, M. (2022) · Scientific Reports · doi:10.1038/s41598-022-20853-w · Cited by 59 · see citing works
Self-citationAlignment between initial state and mixer improves QAOA performance for constrained optimization
He, Z., Shaydulin, R., Chakrabarti, S., Herman, D., Li, C., Sun, Y., & Pistoia, M. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00787-5 · Cited by 51 · see citing works
Self-citationQuantum approximate optimization via learning-based adaptive optimization
Cheng, L., Chen, Y., Zhang, S., & Zhang, S. (2024) · Communications Physics · doi:10.1038/s42005-024-01577-x · Cited by 57 · see citing works
Parameter Setting in Quantum Approximate Optimization of Weighted Problems
Sureshbabu, S. H., Herman, D., Shaydulin, R., Basso, J., Chakrabarti, S., Sun, Y., & Pistoia, M. (2024) · Quantum · doi:10.22331/q-2024-01-18-1231 · Cited by 41 · see citing works
“The SK model is given in Equation (72) and has couplings J uv ∼ N (0 , 1). model A natural generalization to consider is a which has couplings J uv ∼ N ( µ, σ 2 ) with arbitrary µ and σ . can More generally, we allow for the bias to be a function of the number of spins, i.e. µ ( N ).”
BackgroundSelf-citationAntunes, B. A., & Hill, D. R. C. (2024) · Computer Science Review · doi:10.1016/j.cosrev.2024.100655 · Cited by 49 · see citing works
Lykov, D., Wurtz, J., Poole, C., Saffman, M. E., Noel, T., & Alexeev, Y. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00718-4 · Cited by 37 · see citing works
“Different ensembles, characterized by different connectivity d and size N , may have different QAOA performance [30; 31].”
BackgroundSelf-citation(2022) · doi:10.1109/saner53432.2022.00148 · Cited by 28 · see citing works
Fast Simulation of High-Depth QAOA Circuits
Lykov, D., Shaydulin, R., Sun, Y., Alexeev, Y., & Pistoia, M. (2023) · Proceedings of the SC '23 Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis · doi:10.1145/3624062.3624216 · Cited by 27 · see citing works
“On the other hand, there exist simulation libraries that focus on the quantum side and delegate the concern of low-level performance to other libraries [18], [19].”
BackgroundMethodSelf-citationAugmenting QAOA Ansatz with Multiparameter Problem-Independent Layer
Chalupnik, M., Melo, H., Alexeev, Y., & Galda, A. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00028 · Cited by 21 · see citing works
“The approximation values for the standard p = 1 and p = 2 QAOA were obtained from the QAOAKit database [59].”
MethodQoncord: A Multi-Device Job Scheduling Framework for Variational Quantum Algorithms
Wang, M., Das, P., & Nair, P. J. (2024) · IEEE/ACM International Symposium on Microarchitecture (MICRO) · doi:10.1109/micro61859.2024.00060 · Cited by 15 · see citing works
“Thorough calibrations on devices are expensive and infrequent [23], [26], [61], [62].”
High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices
Pelofske, E., Bärtschi, A., Golden, J., & Eidenbenz, S. (2023) · 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00064 · Cited by 15 · see citing works
“On the other hand, there is increasing evidence that classes of problems exhibit pronounced parameter concentration of the optimal or near optimal angles [19], [51], [1], [6], [61], [17], [48], [41], which in some cases could lead to scalable heuristics for good angle finding.”
BackgroundSawaya, N. P. D., Schmitz, A. T., & Hadfield, S. (2023) · Quantum · doi:10.22331/q-2023-09-14-1111 · Cited by 16 · see citing works
“In particular, seeking cleaner separations of programming layers is important towards enabling a broad community of practitioners who may not be experts in quantum mechanics or other low-level details [9, 10, 11].”
BackgroundJuliQAOA: Fast, Flexible QAOA Simulation
Golden, J. K., Bärtschi, A., O’Malley, D., Pelofske, E., & Eidenbenz, S. (2023) · International Conference for High Performance Computing, Networking, Storage and Analysis (SC) · doi:10.1145/3624062.3624220 · Cited by 11 · see citing works
Shaydulin, R., & Pistoia, M. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00121 · Cited by 16 · see citing works
Self-citationCharacterizing Error Mitigation by Symmetry Verification in QAOA
Kakkar, A., Larson, J. M., Galda, A., & Shaydulin, R. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00086 · Cited by 11 · see citing works
“For depth d ≤ 3 we use parameters available in QAOAKit [31], and for d > 3 we find them by using exhaustive numerical optimization.”
MethodSelf-citationVariational Quantum Algorithms in the era of Early Fault Tolerance
Dangwal, S., Vittal, S., Seifert, L. M., Chong, F. T., & Ravi, G. S. (2025) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/3695053.3731112 · Cited by 8 · see citing works
“This converts the circuit into a Clifford circuit, enabling efficient classical simulation using stabilizer simulators like Stim [29], as supported by the work of Aaronson and Gottesman [5].”
He, Z., Shaydulin, R., Herman, D., Li, C., Raymond, R., Sureshbabu, S. H., & Pistoia, M. (2024) · doi:10.1145/3676536.3697128 · Cited by 10 · see citing works
“However, instance-specific parameter fine-tuning can still offer meaningful performance gains over directly using instance-independent parameters [63].”
Self-citationRed-QAOA: Efficient Variational Optimization through Circuit Reduction
Wang, M., Fang, B., Li, A., & Nair, P. J. (2024) · International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS) · doi:10.1145/3620665.3640363 · Cited by 6 · see citing works
“This leverages QAOA’s unique property of similar instances having comparable energy land-scapes [10, 26, 27].”
BackgroundQuantum Approximate Optimization Algorithm with Sparsified Phase Operator
Liu, X., Shaydulin, R., & Safro, I. (2022) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce53715.2022.00032 · Cited by 6 · see citing works
“[34] R. Shaydulin, K. Marwaha, J. Wurtz, and P. C. Lotshaw, “QAOAKit: A toolkit for reproducible study, application, and verification of QAOA,” in Second International Workshop on Quantum Computing Software, 2021.”
MethodSelf-citationAccelerating Simulation of Quantum Circuits under Noise via Computational Reuse
Wang, M., Tannu, S., & Nair, P. J. (2025) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/3695053.3730992 · Cited by 5 · see citing works
Kasi, S., Sud, J., Jamieson, K., & Ravi, G. S. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00051 · Cited by 2 · see citing works
Accelerated VQE: Parameter Recycling for Similar Recurring Problem Instances
Rohe, T., Mansky, M. B., Kölle, M., Stein, J., Sünkel, L., & Linnhoff–Popien, C. (2025) · Communications in computer and information science · doi:10.1007/978-3-031-94263-1_5 · Cited by 2 · see citing works
“A dedicated framework for evaluation is available, containing pre-optimised QAOA parameters and circuits for different instances [Shaydulin et al., 2021].”
Wang, H., Alidaee, B., & Sagbansua, L. (2024) · Preprints.org · doi:10.20944/preprints202402.1698.v1 · Cited by 1 · see citing works
Wang, H., Alidaee, B., & Sagbansua, L. (2024) · Preprints.org · doi:10.20944/preprints202402.1698.v2 · Cited by 1 · see citing works
Difference of Convex Algorithm for Warm‐Start Quantum Approximate Optimization Algorithm
Huy, P. N. H., Nguyễn, V. H., & Ta, A. S. (2025) · Advanced Quantum Technologies · doi:10.1002/qute.202400253
Kim, J., & Chung, D. (2026) · IEEE Transactions on Emerging Topics in Computing · doi:10.1109/tetc.2025.3626768 · Cited by 1 · see citing works
“To further support both research and practical implementations of QAOA, a reproducibility toolkit named QAOAKit was introduced [7].”
Jiang, L., Zhang, C., & Chen, F. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00167
“Similar to classical neural network normalization techniques [30], [31], this approach enhances the training quality of QSeer by stabilizing its gradients, and improves the generalization capability of QSeer by mitigating overfitting.”
InfluentialQuantum algorithms for energy management optimization problems
Veshchezerova, M. (2022) · theses.fr (ABES) · doi:10.70675/f0d70a66z3066z4c81z8aa7zf9e72830f940 · Cited by 1 · see citing works
Stealing Variational Secrets from Quantum Clouds: Physical QAOA Parameter Recovery
Delgado, J. L. (2026) · ACM Conference on Post-Quantum and Quantum-based Security · doi:10.1145/3839338.3857276
- Authors
- Shaydulin, R., Marwaha, K., Wurtz, J., & Lotshaw, P. C.
- Affiliations
- Argonne National Laboratory (US)
- University of Chicago (US)
- Tufts University (US)
- Oak Ridge National Laboratory (US)
- Venue
- 2021 IEEE/ACM Second International Workshop on Quantum Computing Software (QCS)
- Publisher
- IEEE
- Published
- 2021-11
- Pages
- 64-71
- OpenAlex
- W3205336365
- Cited by
- 31
- References
- 25
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 10 · 2023: 8 · 2022: 6
- FWCI
- 2.77
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE/ACM International Workshop on Quantum Computing Software (QCS) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (1818914, DE-AC02–06CH11357, 1746045)
- U.S. Department of Energy (DE‐ AC02‐06CH11357, AC02‐06CH11357, 06CH11357, DE-AC02-)
- Defense Advanced Research Projects Agency (HR001120C0068)
- Office of Science (AC02‐06CH11357, DE-AC02, 06CH11357, DE-AC02-06CH11357)
- Advanced Research Projects Agency
- Advanced Scientific Computing Research (DE-AC02-06CH11357)
- Laboratory Directed Research and Development (DE‐AC02‐06CH11357)
- Argonne National Laboratory (DE- AC02-06-CH11357, DE-AC02, AC02–06CH11357, 06CH11357)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- quantum approximate optimization algorithm, MaxCut, quantum circuit generation, reproducibility, quantum optimization, Python library
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
