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Training the quantum approximate optimization algorithm without access to a quantum processing unit
Open accessAbstract
In this paper, we eliminate the classical outer learning loop of the quantum approximate optimization algorithm (QAOA) and present a strategy to find good parameters for QAOA based on topological arguments of the problem graph and tensor network techniques. Starting from the observation of the concentration of control parameters of QAOA, we find a way to classically infer parameters which scales polynomially in the number of qubits and exponentially with the depth of the circuit. Using this strategy, the quantum processing unit (QPU) is only needed to sample from the final state of QAOA. This method paves the way for a variation-free version of QAOA and makes QAOA more practical for applications on NISQ devices. We investigate the performance of the proposed approach for the initial assumptions and its resilience with respect to situations where they are not fulfilled. Moreover, we investigate the applicability of our method beyond the scope of QAOA, in improving schedules for quantum annealing.
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“Several other approaches have been identified where the ansatz adaptations happen as a secondary effect, e.g., References [36, 48, 82, 131, 153].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [131]
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“As repeated calls to the quantum computer for updating the parameters are considered a major bottleneck for VQAs in general, Streif and Leib [131] suggested a different approach to QAOA by introducing a technique that avoids the outer loop optimization and therefore repeated calls to get optimal parameters.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [131]
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“The proposed method is based on the features of the according problem graph and makes use of tensor network techniques.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [131]
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“An adaptation to QAOA, which does not require exhaustive access to the quantum processing unit [131], has been used to solve the binary paint shop problem [132].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [131]
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Citations
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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 563
Layerwise learning for quantum neural networks
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Self-citationDiagnosing Barren Plateaus with Tools from Quantum Optimal Control
Larocca, M., Czarnik, P., Sharma, K., Muraleedharan, G., Coles, P. J., & Cerezo, M. (2022) · Quantum · doi:10.22331/q-2022-09-29-824 · Cited by 272
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Wurtz, J., & Love, P. J. (2022) · Quantum · doi:10.22331/q-2022-01-27-635 · Cited by 124
Parameter concentrations in quantum approximate optimization
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“The authors in [23] explain their numerical observation via reverse causal cone i.”
BackgroundMaxCut quantum approximate optimization algorithm performance guarantees for p>1
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Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
Weidenfeller, J., Valor, L. C., Gacon, J., Tornow, C., Bello, L., Woerner, S., & Egger, D. J. (2022) · Quantum · doi:10.22331/q-2022-12-07-870 · Cited by 127
“[78] Michael Streif and Martin Leib, “Training the quantum approximate optimization algorithm without access to a quantum processing unit,” Quantum Sci.”
BackgroundLayer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers
Liu, X., Angone, A., Shaydulin, R., Safro, I., Alexeev, Y., & Cincio, L. (2022) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3140190 · Cited by 78
“The special structure of the QAOA ansatz enables finding high-quality parameters γ , β purely classically in many settings [4], [37], [38] or using very few iterations of the outer-loop optimizer [25], [39], [40].”
BackgroundCircuit Compilation Methodologies for Quantum Approximate Optimization Algorithm
Alam, M., Saki, A. A., & Ghosh, S. (2020) · IEEE/ACM International Symposium on Microarchitecture (MICRO) · doi:10.1109/micro50266.2020.00029 · Cited by 78
“We propose to find optimal QAOA-circuit parameters analytically [45] (or, for small problem size, running the algorithm in simulation) and use these values to compile the QAOA-circuit.”
BackgroundMethodTransferability 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
Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs
Wurtz, J., & Lykov, D. (2021) · Physical Review A · doi:10.1103/physreva.104.052419 · Cited by 83
Variational preparation of finite-temperature states on a quantum computer
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Avoiding barren plateaus via transferability of smooth solutions in a Hamiltonian variational ansatz
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Quantum Optimization: Potential, Challenges, and the Path Forward
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Multilevel Combinatorial Optimization across Quantum Architectures
Ushijima-Mwesigwa, H., Shaydulin, R., Negre, C. F. A., Mniszewski, S. M., Alexeev, Y., & Safro, I. (2021) · ACM Transactions on Quantum Computing · doi:10.1145/3425607 · Cited by 57
A Perspective on Protein Structure Prediction Using Quantum Computers
Doğa, H., Raubenolt, B. A., Cumbo, F., Joshi, J., DiFilippo, F. P., Qin, J., Blankenberg, D. J., & Shehab, O. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00067 · Cited by 67
Quantum Optimization via Four-Body Rydberg Gates
Dlaska, C., Ender, K., Mbeng, G. B., Kruckenhauser, A., Lechner, W., & van Bijnen, R. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.120503 · Cited by 51
Graph neural network initialisation of quantum approximate optimisation
Jain, N., Coyle, B., Kashefi, E., & Kumar, N. (2022) · Quantum · doi:10.22331/q-2022-11-17-861 · Cited by 54
Accelerating Quantum Approximate Optimization Algorithm using Machine Learning
Alam, M., Saki, A. A., & Ghosh, S. (2020) · Design, Automation, and Test in Europe · doi:10.23919/date48585.2020.9116348 · Cited by 46
“Thus, exploring new avenues to improve the performance of QAOA has become an exciting research domain [8]–[13].”
BackgroundQuantum Approximation for Wireless Scheduling
Choi, J., Oh, S., & Kim, J. (2020) · Applied Sciences · doi:10.3390/app10207116 · Cited by 44
“Thus, QAOA is a hybrid quantum-classical optimization algorithm in which proper Hamiltonian design and the discovery of good parameters in a classical optimization loop are key [20,23,24].”
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
“The cost of finding parameters can be significantly reduced by leveraging the apparent problem-instance independence of the optimal QAOA parameters [26, 27].”
BackgroundSolving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach
Weggemans, J. R., Urech, A., Rausch, A., Spreeuw, R. J. C., Boucherie, R. J., Schreck, F., Schoutens, K., Minář, J., & Speelman, F. (2022) · Quantum · doi:10.22331/q-2022-04-13-687 · Cited by 49
Hybrid quantum ResNet for car classification and its hyperparameter optimization
Sagingalieva, A., Kordzanganeh, M., Kurkin, A., Melnikov, A., Kuhmistrov, D., Perelshtein, M. R., Melnikov, A., Skolik, A., & Dollen, D. V. (2023) · Quantum Machine Intelligence · doi:10.1007/s42484-023-00123-2 · Cited by 54
“Research in the industrial context has been largely motivated by noisy intermediate-scale quantum (NISQ) devices [28] – early quantum devices with a small number of qubits and no error correction.”
Applying quantum approximate optimization to the heterogeneous vehicle routing problem
Fitzek, D., Ghandriz, T., Laine, L., Granath, M., & Kockum, A. F. (2024) · Scientific Reports · doi:10.1038/s41598-024-76967-w · Cited by 49
Streif, M., Yarkoni, S., Skolik, A., Neukart, F., & Leib, M. (2021) · Physical Review A · doi:10.1103/physreva.104.012403 · Cited by 41
Self-citationQuantum Approximate Optimization Algorithm Based Maximum Likelihood Detection
Cui, J., Xiong, Y., Ng, S. X., & Hanzo, L. (2022) · IEEE Transactions on Communications · doi:10.1109/tcomm.2022.3185287 · Cited by 47
Sack, S. H., & Egger, D. J. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013223 · Cited by 58
An Efficient Circuit Compilation Flow for Quantum Approximate Optimization Algorithm
Alam, M., Saki, A. A., & Ghosh, S. (2020) · ACM/IEEE Design Automation Conference (DAC) · doi:10.1109/dac18072.2020.9218558 · Cited by 39
“Due to these limitations, a variation-free version of the algorithm (VF-QAOA) has been pursued [2], [7], [9] where the optimal parameters are either found analytically [2], [7] or they are reused among a similar set of problems [9].”
MethodOzaeta, A., van Dam, W., & McMahon, P. L. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac9013 · Cited by 57
“Our analytical formula gives us the ability to analytically optimize the QAOA parameters—this enables one to compute the optimal QAOA parameters classically, and then only run the QAOA on a quantum processor with the optimal set of angles [9].”
Exploiting Symmetry Reduces the Cost of Training QAOA
Shaydulin, R., & Wild, S. M. (2021) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3066275 · Cited by 39
“Here we briefly review the mechanism for doing so; for more details and an in-depth discussion, the reader is referred to [13], [22].”
BackgroundA practitioner’s guide to quantum algorithms for optimisation problems
Symons, B. C. B., Galvin, D., Sahin, E., Alexandrov, V., & Mensa, S. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad00f0 · Cited by 43
“Streif and Leib [67] developed a method of determining optimal parameters for the QAO algorithm that aimed to reduce or even remove the need for a classical optimisation loop.”
MethodAn expressive ansatz for low-depth quantum approximate optimisation
Vijendran, V., Das, A., Koh, D. E., Assad, S. M., & Lam, P. K. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad200a · Cited by 50
GPU-accelerated simulations of quantum annealing and the quantum approximate optimization algorithm
Willsch, D., Willsch, M., Jin, F., Michielsen, K. F. L., & Raedt, H. A. D. (2022) · Computer Physics Communications · doi:10.1016/j.cpc.2022.108411 · Cited by 48
“Ideas that are similar to AQA have been investigated before [17, 21, 22, 46].”
BackgroundLower bounds on circuit depth of the quantum approximate optimization algorithm
Herrman, R., Ostrowski, J., Humble, T. S., & Siopsis, G. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03001-7 · Cited by 35
“B and C depend on the problem of interest and the angles that maximize them can be found using classical preprocessing [12, 21, 22].”
BackgroundLykov, 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
“Recent results, however, suggest that angles may be precomputed on a classical device [16] or transferred from other similar graphs [17].”
BackgroundPolicy Gradient based Quantum Approximate Optimization AlgorithmPreprint
Yao, J., Bukov, M., & Lin, L. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2002.01068 · Cited by 46
Evaluation of QAOA based on the approximation ratio of individual samples
Larkin, J. M., Jonsson, M., Justice, D., & Guerreschi, G. G. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac6973 · Cited by 44
“Along the same lines of avoiding the training phase, recent works propose the use of machine learning techniques [62, 63] or a mix of analytical and numerical results at N → ∞ [64] to identify good parameters.”
Lumia, L., Torta, P., Mbeng, G. B., Santoro, G. E., Ercolessi, E., Burrello, M., & Wauters, M. M. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.020320 · Cited by 36
Quantum algorithms with local particle-number conservation: Noise effects and error correction
Streif, M., Leib, M., Wudarski, F., Rieffel, E. G., & Wang, Z. (2021) · Physical Review A · doi:10.1103/physreva.103.042412 · Cited by 36
“[18] Michael Streif and Martin Leib.”
BackgroundSelf-citationSimilarity-based parameter transferability in the quantum approximate optimization algorithm
Galda, A., Gupta, E., Falla, J., Liu, X., Lykov, D., Alexeev, Y., & Safro, I. (2023) · Frontiers in Quantum Science and Technology · doi:10.3389/frqst.2023.1200975 · Cited by 44
Analytical framework for quantum alternating operator ansätze
Hadfield, S., Hogg, T., & Rieffel, E. G. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/aca3ce · Cited by 36
“This reduced number of necessary qubits and operators for computing expectation values is often called the (reverse) causal cone or lightcone in the literature [42, 53, 68–70], and relates to Lieb-Robinson bounds concerning the speed of propagation of information [71].”
Provable bounds for noise-free expectation values computed from noisy samples
Barron, S. V., Egger, D. J., Pelofske, E., Bärtschi, A., Eidenbenz, S., Lehmkuehler, M., & Woerner, S. (2024) · Nature Computational Science · doi:10.1038/s43588-024-00709-1 · Cited by 25
“In certain cases it might be feasible to determine θ * classically 39–41 and only use the quantum computer to sample good solutions, since evaluating (local) expectation values might be easier than sampling from the full circuit.”
An investigation of IBM quantum computing device performance on combinatorial optimisation problems
Khumalo, M. T., Chieza, H. A., Prag, K., & Woolway, M. (2022) · Neural Computing and Applications · doi:10.1007/s00521-022-07438-4 · Cited by 38
“On the other hand, QAOA using quantum computers to prepare parameters means it uses more quantum functions and exposes the results to more error [34, 58].”
MethodSecure and Reliable Big-Data-Based Decision Making Using Quantum Approach in IIoT Systems
Azzaoui, A. E., Salim, M. M., & Park, J. H. (2023) · Sensors · doi:10.3390/s23104852 · Cited by 26
“…their clients and personalize unique products and commercials for them, which is regarded as the most essential information that almost every smart factory relies on in the era of social platforms. discovery, material research, finance analytics, precision medicine therapies, drug structure [21–23].”
Quantum approximate multi-objective optimization
Kotil, A., Pelofske, E., Riedmüller, S., Egger, D. J., Eidenbenz, S., Koch, T., & Woerner, S. (2025) · Nature Computational Science · doi:10.1038/s43588-025-00873-y · Cited by 42
“For example, as proposed in [26] the expectation values for training QAOA parameters can be evaluated classically.”
Quantum Scheduling for Millimeter-Wave Observation Satellite Constellation
Kim, J., Kwak, Y., Jung, S., & Kim, J. (2021) · IEEE VTS Asia Pacific Wireless Communications Symposium (APWCS) · doi:10.1109/apwcs50173.2021.9548770 · Cited by 24
“…can be shown that the QAOA-based approximation is one of widely known hybrid quantum-classical optimization algorithms where the efficient Hamiltonian design (for quantum approach) and the approximation of efficient hyper-parameters (for conventional optimization approach) are correlated [29], [30].”
BackgroundQuantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem
Palackal, L., Poggel, B., Wulff, M., Ehm, H., Lorenz, J. M., & Mendl, C. B. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00080 · Cited by 24
“Instead of preparing a uniform superposition state | + ⊗ n , a classical solver obtains a solution to the relaxed continuous problem, ˜ x ∈ [0 , 1] n that, once encoded, serves as initial state where the angles are defined by the solution ˜ x by θ i = 2 arcsin √ ˜ x i .”
BackgroundScaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs
Pelofske, E., Bärtschi, A., Cincio, Ł., Golden, J. K., & Eidenbenz, S. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00906-w · Cited by 41
“This technique, often referred to as parameter transfer or parameter concentration , has been shown to be effective, both analytically and numerically, for a number of different problem types [12, 22, 25–33 , 38 ].”
MethodMahroo, R., & Kargarian, A. (2023) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2023.3320872 · Cited by 28
“Various approaches are proposed for optimizing variational parameters, including gradient-based [28] and gradient-free meth-ods [29], [30].”
BackgroundMethodFalla, J., Langfitt, Q., Alexeev, Y., & Safro, I. (2024) · Quantum Machine Intelligence · doi:10.1007/s42484-024-00178-9 · Cited by 30
“OptimalQAOAparameterconcentrationeffectshavebeen reported for several types of graphs on which the MaxCut is formulated, mainly those involving random 3-regular graphs (Brandao et al. 2018; Streif and Leib 2020; Akshay et al. 2021).”
Multilevel Leapfrogging Initialization Strategy for Quantum Approximate Optimization Algorithm
Ni, X., Cai, B., Liu, H., Qin, S., Gao, F., & Wen, Q. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202300419 · Cited by 29
Circuit depth scaling for quantum approximate optimization
Akshay, V., Philathong, H., Campos, E., Rabinovich, D., Zacharov, I., Zhang, X., & Biamonte, J. (2022) · Physical Review A · doi:10.1103/physreva.106.042438 · Cited by 27
Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study
Gemeinhardt, F., Garmendia, A., Wimmer, M., Weder, B., & Leymann, F. (2024) · ACM Computing Surveys · doi:10.1145/3620668 · Cited by 22
“An adaptation to QAOA, which does not require exhaustive access to the quantum processing unit [131], has been used to solve the binary paint shop problem [132].”
BackgroundMethodInfluentialEnergy-Efficient Cluster Head Selection via Quantum Approximate Optimization
Choi, J., Oh, S., & Kim, J. (2020) · Electronics · doi:10.3390/electronics9101669 · Cited by 20
Quantum dropout: On and over the hardness of quantum approximate optimization algorithm
Wang, Z., Zheng, P.-L., Wu, B., & Zhang, Y. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023171 · Cited by 22
Entanglement production and convergence properties of the variational quantum eigensolver
Woitzik, A. J. C., Barkoutsos, P. K., Wudarski, F., Buchleitner, A., & Tavernelli, I. (2020) · Physical Review A · doi:10.1103/physreva.102.042402 · Cited by 20
Alibaba Cloud Quantum Development Platform: Applications to Quantum Algorithm DesignPreprint
Huang, C., Szegedy, M., Zhang, F., Gao, X., Chen, J., & Shi, Y. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.02559 · Cited by 20
“In fact, it is proposed in [16] that the angle sequences for small-cycle-free instances be used directly to completely get rid of the optimization phase, which could be chanllenging on noisy quantum devices.”
BackgroundModular Parity Quantum Approximate Optimization
Ender, K., Messinger, A., Fellner, M., Dlaska, C., & Lechner, W. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.030304 · Cited by 18
Parity Quantum Optimization: Benchmarks
FELLNER, M. J., Ender, K., ter Hoeven, R., & Lechner, W. (2023) · Quantum · doi:10.22331/q-2023-03-17-952 · Cited by 25
“Recent research also indicates parameter concentration in the QAOA protocol which means that good QAOA parameters found for (small) problem instances are also adequate for other, potentially larger instances [7, 8, 24, 25].”
BackgroundChallenges and Opportunities in Quantum Software Architecture
Yue, T., Mauerer, W., Ali, S., & Taibi, D. (2023) · Springer eBooks · doi:10.1007/978-3-031-36847-9_1 · Cited by 17
Miki, T., Okita, R., Shimada, M., Tsukayama, D., & Shirakashi, J. (2022) · AIP Advances · doi:10.1063/5.0077706 · Cited by 16
Quantum k-community detection: algorithm proposals and cross-architectural evaluation
Gemeinhardt, F., Wille, R., & Wimmer, M. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-03239-1 · Cited by 16
Recommending Solution Paths for Solving Optimization Problems with Quantum Computing
Poggel, B., Quetschlich, N., Burgholzer, L., Wille, R., & Lorenz, J. M. (2023) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw59989.2023.00017 · Cited by 16
“As a first recommendation, we choose the QAOA depth such that all qubits can be entangled by the problem Hamiltonian evolution according to a reverse causal cone argument [6], [27].”
BackgroundParameter-setting heuristic for the quantum alternating operator ansatz
Sud, J., Hadfield, S., Rieffel, E. G., Tubman, N. M., & Hogg, T. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023171 · Cited by 17
“The first of these include initializing parameters to be close to parameters informed by previous information or intuition [22–24].”
Multilevel Combinatorial Optimization Across Quantum Architectures
Ushijima‐Mwesigwa, H., Shaydulin, R., Negre, C. F. A., Mniszewski, S. M., Alexeev, Y., & Safro, I. (2019) · TigerPrints (Clemson University) · Cited by 15
Sawaya, N. P. D., Schmitz, A. T., & Hadfield, S. (2023) · Quantum · doi:10.22331/q-2023-09-14-1111 · Cited by 28
“The algorithm parameters may be predetermined by analytic, empirical, or other means [51, 90, 57, 91, 92, 93, 94, 95, 96, 97, 98], or determined variationally using a hybrid quantum-classical search procedure [27].”
MethodProblem-specific classical optimization of Hamiltonian simulation
Mansuroglu, R., Fischer, F., & Hartmann, M. J. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.043035 · Cited by 13
Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering
Zhang, Z., Paredes, R., Sundar, B., Quiroga, D., Kyrillidis, A., Dueñas‐Osorio, L., Pagano, G., & Hazzard, K. R. A. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad895c · Cited by 25
“While parameter clustering has previously been seen in different QAOA variants, these focused on only few-round results [23, 24, 77].”
Lyngfelt, I., & García-Álvarez, L. (2025) · Physical Review A · doi:10.1103/physreva.111.022418 · Cited by 12
Convergence of digitized-counterdiabatic QAOA: circuit depth versus free parameters
Vizzuso, M., Passarelli, G., Cantele, G., & Lucignano, P. (2023) · New Journal of Physics · doi:10.1088/1367-2630/ad1536 · Cited by 13
Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithmsPreprint
Guerreschi, G. G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.07813 · Cited by 25
“The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm designed to find approximate solutions of combinatorial optimzation problems by variationally improving quantum circuits [16–21].”
MethodCapturing Symmetries of Quantum Optimization Algorithms Using Graph Neural Networks
Deshpande, A., & Melnikov, A. A. (2022) · Symmetry · doi:10.3390/sym14122593 · Cited by 11
Approximating under the Influence of Quantum Noise and Compute Power
Thelen, S., Safi, H., & Mauerer, W. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.10291 · Cited by 10
“[4, 11, 16–20]) have been proposed.”
Problem-size-independent angles for a Grover-driven quantum approximate optimization algorithm
Headley, D., & Wilhelm, F. K. (2023) · Physical Review A · doi:10.1103/physreva.107.012412 · Cited by 13
Cadavid, A. G., Montalban, I., Dalal, A., Solano, E., & Hegade, N. N. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.22.054037 · Cited by 9
“There is extensive literature on how PQCs can be trained and modified in order to circumvent those issues [12–14].”
BackgroundGenuine multipartite entanglement in quantum optimization
Santra, G. C., Roy, S. S., Egger, D. J., & Hauke, P. (2025) · Physical Review A · doi:10.1103/physreva.111.022434 · Cited by 15
“In particular, tensor networks may help to obtain good parameters [64].”
ORQVIZ: Visualizing High-Dimensional Landscapes in Variational Quantum AlgorithmsPreprint
Rudolph, M. S., Sim, S., Raza, A., Stęchły, M., McClean, J. R., Anschuetz, E. R., Serrano, L., & Perdomo‐Ortiz, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.04695 · Cited by 19
Beyond quantum annealing: optimal control solutions to maxcut problems
Pecci, G., Wang, R., Torta, P., Mbeng, G. B., & Santoro, G. E. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad60f2 · Cited by 11
Quantifying the impact of precision errors on quantum approximate optimization algorithms
Quiroz, G., Titum, P., Lotshaw, P. C., Lougovski, P., Schultz, K., Dumitrescu, E., & Hen, I. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.023240 · Cited by 16
Challenges for Quantum Software Engineering: An Industrial Application Scenario Perspective
Carbonelli, C., Felderer, M., Jung, M., Lobe, E., Lochau, M., Luber, S. M., Mauerer, W., Ramler, R., Schaefer, I., & Schroth, C. (2024) · Springer eBooks · doi:10.1007/978-3-031-64136-7_12 · Cited by 16
Diagrammatic Analysis for Parameterized Quantum Circuits
Stollenwerk, T., & Hadfield, S. (2023) · Electronic Proceedings in Theoretical Computer Science · doi:10.4204/eptcs.394.15 · Cited by 7
“This phenomena is known, generally, as the lightcone or causal cone rule [20, 21, 27, 45], and is clearly exhibited with the ZX-calculus.”
BackgroundStreif, M., & Leib, M. (2020) · Physical Review A · doi:10.1103/physreva.102.042416 · Cited by 8
“[16] Michael Streif and Martin Leib.”
MethodSelf-citationQuantum 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
Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
Clausen, H. G., Rahman, S. A., Karabacak, Ö., & Wiśniewski, R. (2023) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2023.10.111 · Cited by 6
“, Streif and Leib (2020) for results suggesting such relations).”
BackgroundLarkin, J. M., Jonsson, M., Justice, D., & Guerreschi, G. G. (2020) · arXiv (Cornell University) · Cited by 6
Engineering a Cost Function for Real-world Implementation of a Variational Quantum Algorithm
Premaratne, S., & Matsuura, A. Y. (2020) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce49297.2020.00042 · Cited by 8
“Concentration of optimal parameters has been observed in training with QAOA, which lends credence to the reuse of previously found optimal parameters in subsequent evaluations [2], [19].”
Parallel circuit implementation of variational quantum algorithms
Cattelan, M., Yarkoni, S., & Lechner, W. (2025) · npj Quantum Information · doi:10.1038/s41534-025-00982-6 · Cited by 8
Constant Depth Code Deformations in the Parity Architecture
Messinger, A., Fellner, M., & Lechner, W. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00022 · Cited by 5
Miki, T., Tsukayama, D., Okita, R., Shimada, M., & Shirakashi, J. (2022) · IEEE International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale (3M-NANO) · doi:10.1109/3m-nano56083.2022.9941666 · Cited by 3
Restricted global optimization for QAOA
Gleißner, P., Kruse, G., & Roßkopf, A. (2024) · APL Quantum · doi:10.1063/5.0189374 · Cited by 3
“This includes the concepts from [10, 17, 27] where this strategy is successfully demonstrated.”
BackgroundMethodInfluentialChoco-Q: Commute Hamiltonian-based QAOA for Constrained Binary Optimization
Xiang, D., Jiang, Q., Lu, L., Tan, S., & Yin, J. (2025) · IEEE International Symposium on High-Performance Computer Architecture (HPCA) · doi:10.1109/hpca61900.2025.00031 · Cited by 4
“Since QAOA can be deployed on current noisy quantum devices, it has been studied and optimized from different aspects, such as compilation [3], parameter initialization [45], parameter updating [42], and distributed version [4].”
Krüger, T., & Mauerer, W. (2025) · Quantum · doi:10.22331/q-2025-11-06-1903 · Cited by 7
“In 2020, Streif and Leib [84] observed a clustering of optimal parameters when training qaoa circuits for random Max-Cut instances, which inspired them to propose training qaoa without quantum hardware access.”
InfluentialAn Efficient QAOA via a Polynomial QPU-Needless Approach
Chicano, F., Dahi, Z. A., & Luque, G. (2023) · Genetic and Evolutionary Computation Conference Companion (GECCO Companion) · doi:10.1145/3583133.3596409 · Cited by 3
Measurement-Based Quantum Approximate Optimization
Stollenwerk, T., & Hadfield, S. (2024) · IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum · doi:10.1109/ipdpsw63119.2024.00183 · Cited by 9
“…algorithm performance will depend on the finding high-quality circuit parameters to begin with, and we emphasize that in different cases parameters may be found through analytic [40], numeric [4], or average-case [41] techniques, among others, though parameter setting remains challenging generally.”
BackgroundA Monte Carlo Tree Search approach to QAOA: finding a needle in the haystack
Agirre, A., van Nieuwenburg, E., & Wauters, M. M. (2025) · New Journal of Physics · doi:10.1088/1367-2630/adc765 · Cited by 7
“The crucial modification to MCTS aims at exploiting the parameter concentration and regularity inherent in many optimal QAOA schedules [27, 48–50].”
Missing Puzzle Pieces in the Performance Landscape of the Quantum Approximate Optimization Algorithm
Wybo, E., & Leib, M. (2025) · Quantum · doi:10.22331/q-2025-10-22-1892 · Cited by 15
Self-citationPredict and Conquer: Navigating Algorithm Trade-Offs with Quantum Design Automation
Thelen, S., & Mauerer, W. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00071 · Cited by 4
“[6], [7], [30]–[34]).”
Quantifying the advantages of applying quantum approximate algorithms to portfolio optimisation
Yuan, H., Long, C. K., Lepage, H. V., & Barnes, C. H. W. (2026) · Quantum Science and Technology · doi:10.1088/2058-9565/ae4a48 · Cited by 2
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 3
“The performance of QAOA relies on the choice of parameters ( ⃗γ, ⃗β ) , and techniques for parameter optimization are in many cases highly non-trivial [45]–[54].”
Metadata
- Authors
- Streif, M., & Leib, M.
- Affiliations
- Volkswagen Group (Germany) (DE)
- Corresponding author
- Streif, Michael
- Leib, Martin
- Venue
- Quantum Science and Technology
- Publisher
- IOP Publishing
- Published
- 2020-05-12
- Volume
- 5
- Issue
- 3
- Pages
- 034008
- ISSN
- 2058-9565 (ISSN-L)
- OpenAlex
- W2969876173
- Cited by
- 125
- References
- 41
- Citations by year
- 2026: 8 · 2025: 16 · 2024: 23 · 2023: 24 · 2022: 26 · 2021: 15 · 2020: 11
- FWCI
- 7.40
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Quantum Science and Technology (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Unions Horizon 2020 (828826)
- 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, tensor networks, NISQ devices, variational quantum algorithms, hybrid quantum-classical optimization
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