Hadfield, S. et al. From the quantum approximate        optimization algorithm to a quantum alternating operator        Ansatz. Algorithms 12, 34 (2019).      
        Article MathSciNet                Google Scholar      
        Cook, J., Eidenbenz, S. & Brtschi, A. The quantum        alternating operator Ansatz on maximum k-Vertex cover. In        IEEE International Conference on Quantum Computing and        Engineering QCE20, 8392 (2020). https://doi.org/10.1109/QCE49297.2020.00021.      
        Wang, Z., Rubin, N. C., Dominy, J. M. & Rieffel, E. G.        XY mixers: Analytical and numerical results        for the quantum alternating operator ansatz. Phys. Rev.        A 101, 012320 (2020).      
        Article        ADS MathSciNet        CAS         Google Scholar      
        Farhi, E., Goldstone, J. & Gutmann, S. A Quantum        Approximate Optimization Algorithm. arXiv preprint (2014).        https://doi.org/10.48550/arXiv.1411.4028.      
        Farhi, E., Goldstone, J. & Gutmann, S. A Quantum        Approximate Optimization Algorithm Applied to a Bounded        Occurrence Constraint Problem. arXiv preprint (2015).        https://doi.org/10.48550/arXiv.1412.6062.      
        Farhi, E., Goldstone, J., Gutmann, S. & Sipser, M. Quantum        computation by adiabatic evolution. arXiv preprint (2000).        https://doi.org/10.48550/arXiv.quant-ph/0001106.      
        Kadowaki, T. & Nishimori, H. Quantum annealing in the        transverse ising model. Phys. Rev. E 58,        53555363 (1998).      
        Article ADS CAS         Google Scholar      
        Das, A. & Chakrabarti, B. K. Quantum annealing and analog        quantum computation. Rev. Mod. Phys. 80, 1061        (2008).      
        Article        ADS MathSciNet                Google Scholar      
        Hauke, P., Katzgraber, H. G., Lechner, W., Nishimori, H. &        Oliver, W. D. Perspectives of quantum annealing: methods        and implementations. Rep. Prog. Phys. 83,        054401 (2020).      
        Article ADS CAS PubMed                Google Scholar      
        Yarkoni, S., Raponi, E., Bck, T. & Schmitt, S. Quantum        annealing for industry applications: Introduction and        review. Rep. Prog. Phys. 85, 104001 (2022).      
        Article ADS MathSciNet                Google Scholar      
        Morita, S. & Nishimori, H. Mathematical foundation of        quantum annealing. J. Math. Phys. 49, 125210        (2008).      
        Article ADS MathSciNet                Google Scholar      
        Santoro, G. E. & Tosatti, E. Optimization using quantum        mechanics: Quantum annealing through adiabatic evolution.        J. Phys. A: Math. Gen. 39, R393 (2006).      
        Article        ADS MathSciNet        CAS         Google Scholar      
        Finnila, A. B., Gomez, M., Sebenik, C., Stenson, C. & Doll,        J. D. Quantum annealing: A new method for minimizing        multidimensional functions. Chem. Phys. Lett.        219, 343348 (1994).      
        Article        ADS CAS         Google Scholar      
        Johnson, M. W. et al. Quantum annealing with manufactured        spins. Nature 473, 194198 (2011).      
        Article ADS CAS PubMed                Google Scholar      
        Lanting, T. et al. Entanglement in a quantum annealing        processor. Phys. Rev. X 4, 021041 (2014).      
                Google Scholar      
        Boixo, S., Albash, T., Spedalieri, F. M., Chancellor, N. &        Lidar, D. A. Experimental signature of programmable quantum        annealing. Nat. Commun. 4, 2067 (2013).      
        Article ADS PubMed                Google Scholar      
        King, A. D. et al. Coherent quantum annealing in a        programmable 2000-qubit Ising chain. Nat. Phys.        18, 13241328 (2022).      
        Article        CAS         Google Scholar      
        Chow, J. M. et al. Simple all-microwave entangling gate for        fixed-frequency superconducting qubits. Phys. Rev.        Lett. 107, 080502 (2011).      
        Article        ADS PubMed                Google Scholar      
        Chamberland, C., Zhu, G., Yoder, T. J., Hertzberg, J. B. &        Cross, A. W. Topological and subsystem codes on low-degree        graphs with flag qubits. Phys. Rev. X 10,        011022 (2020).      
        CAS         Google Scholar      
        Tasseff, B. et al. On the emerging potential of quantum        annealing hardware for combinatorial optimization. arXiv        preprint (2022). https://doi.org/10.48550/arXiv.2210.04291.      
        Sanders, Y. R. et al. Compilation of fault-tolerant quantum        heuristics for combinatorial optimization. PRX        Quantum 1, 020312 (2020).      
        Article                Google Scholar      
        Lotshaw, P. C. et al. Scaling quantum approximate        optimization on near-term hardware. Sci. Rep.        12, 12388 (2022).      
        Article        ADS CAS PubMed        PubMed        Central         Google Scholar      
        Albash, T. & Lidar, D. A. Demonstration of a scaling        advantage for a quantum annealer over simulated annealing.        Phys. Rev. X 8, 031016 (2018).      
        CAS         Google Scholar      
        King, A. D. et al. Scaling advantage over path-integral        Monte Carlo in quantum simulation of geometrically        frustrated magnets. Nat. Commun. 12, 1113        (2021).      
        Article        ADS CAS PubMed        PubMed        Central         Google Scholar      
        Farhi, E. & Harrow, A. W. Quantum supremacy through the        quantum approximate optimization algorithm. arXiv preprint        (2019). https://doi.org/10.48550/arXiv.1602.07674.      
        Brady, L. T., Baldwin, C. L., Bapat, A., Kharkov, Y. &        Gorshkov, A. V. Optimal protocols in quantum annealing and        quantum approximate optimization algorithm problems.        Phys. Rev. Lett. 126, 070505 (2021).      
        Article        ADS MathSciNet        CAS PubMed                Google Scholar      
        Willsch, M., Willsch, D., Jin, F., De Raedt, H. &        Michielsen, K. Benchmarking the quantum approximate        optimization algorithm. Quantum Inf. Process.        19, 197 (2020).      
        Article        ADS MathSciNet                Google Scholar      
        Sack, S. H. & Serbyn, M. Quantum annealing initialization        of the quantum approximate optimization algorithm.        Quantum 5, 491 (2021).      
        Article                Google Scholar      
        Golden, J., Brtschi, A., Eidenbenz, S. & OMalley, D.        Numerical Evidence for Exponential Speed-up of QAOA over        Unstructured Search for Approximate Constrained        Optimization. In IEEE International Conference on        Quantum Computing and Engineering QCE23, 496505        (2023). https://doi.org/10.1109/QCE57702.2023.00063.      
        Golden, J., Brtschi, A., OMalley, D. & Eidenbenz, S. The        Quantum Alternating Operator Ansatz for Satisfiability        Problems. In IEEE International Conference on Quantum        Computing and Engineering QCE23, 307312 (2023).        https://doi.org/10.1109/QCE57702.2023.00042.      
        Binkowski, L., Komann, G., Ziegler, T. & Schwonnek, R.        Elementary Proof of QAOA Convergence. arXiv preprint        (2023). https://doi.org/10.48550/arXiv.2302.04968.      
        Lubinski, T. et al. Optimization Applications as Quantum        Performance Benchmarks. arXiv preprint (2024). https://doi.org/10.48550/arXiv.2302.02278.      
        Pelofske, E., Golden, J., Brtschi, A., OMalley, D. &        Eidenbenz, S. Sampling on NISQ Devices: Whos the Fairest        One of All?. In IEEE International Conference on        Quantum Computing and Engineering QCE21, 207217        (2021). https://doi.org/10.1109/qce52317.2021.00038.      
        Ushijima-Mwesigwa, H. et al. Multilevel combinatorial        optimization across quantum architectures. ACM Trans.        Quantum Comput. 2, 1:11:29 (2021).      
        Article MathSciNet                Google Scholar      
        Streif, M. & Leib, M. Comparison of QAOA with quantum and        simulated annealing. arXiv preprint (2019). https://doi.org/10.48550/arXiv.1901.01903.      
        Pelofske, E., Brtschi, A. & Eidenbenz, S. Quantum        Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems        on NISQ Computers. In International Conference on High        Performance Computing ISC HPC23, 240258 (2023).        https://doi.org/10.1007/978-3-031-32041-5_13.      
        Suau, A. et al. Single-Qubit Cross Platform Comparison of        Quantum Computing Hardware. In IEEE International        Conference on Quantum Computing and Engineering QCE23,        13691377 (2023). https://doi.org/10.1109/QCE57702.2023.00155.      
        Pagano, G. et al. Quantum approximate optimization of the        long-range ising model with a trapped-ion quantum        simulator. Proc. Natl. Acad. Sci. 117,        2539625401 (2020).      
        Article ADS MathSciNet        CAS PubMed        PubMed        Central         Google Scholar      
        Weidenfeller, J. et al. Scaling of the quantum approximate        optimization algorithm on superconducting qubit based        hardware. Quantum 6, 870 (2022).      
        Article                Google Scholar      
        Harrigan, M. P. et al. Quantum approximate optimization of        non-planar graph problems on a planar superconducting        processor. Nat. Phys. 17, 332336 (2021).      
        Article        CAS         Google Scholar      
        Herman, D. et al. Constrained optimization via quantum Zeno        dynamics. Commun. Phys. 6, 219 (2023).      
        Article                Google Scholar      
        Niroula, P. et al. Constrained quantum optimization for        extractive summarization on a trapped-ion quantum computer.        Sci. Rep. 12, 17171 (2022).      
        Article        ADS CAS PubMed        PubMed        Central         Google Scholar      
        Zhou, L., Wang, S.-T., Choi, S., Pichler, H. & Lukin, M. D.        Quantum approximate optimization algorithm: Performance,        mechanism, and implementation on near-term devices.        Phys. Rev. X 10, 021067 (2020).      
        CAS         Google Scholar      
        Basso, J., Farhi, E., Marwaha, K., Villalonga, B. & Zhou,        L. The quantum approximate optimization algorithm at high        depth for maxcut on large-girth regular graphs and the        Sherrington-Kirkpatrick Model. In 17th Conference on the        Theory of Quantum Computation, Communication and        Cryptography TQC22 (2022). https://doi.org/10.4230/LIPICS.TQC.2022.7.      
        Wang, Z., Hadfield, S., Jiang, Z. & Rieffel, E. G. Quantum        approximate optimization algorithm for MaxCut: A fermionic        view. Phys. Rev. A 97, 022304 (2018).      
        Article        ADS CAS         Google Scholar      
        Crooks, G. E. Performance of the quantum approximate        optimization algorithm on the maximum cut problem. arXiv        preprint (2018). https://doi.org/10.48550/arXiv.1811.08419.      
        Guerreschi, G. G. & Matsuura, A. Y. QAOA for Max-Cut        requires hundreds of qubits for quantum speed-up. Sci.        Rep. 9, 6903 (2019).      
        Article        ADS CAS PubMed        PubMed        Central         Google Scholar      
        Marwaha, K. Local classical MAX-CUT algorithm outperforms        p=2 QAOA on high-girth regular graphs.        Quantum 5, 437 (2021).      
        Article                Google Scholar      
        Hastings, M. B. Classical and quantum bounded depth        approximation algorithms. Quantum Inf. Comput.        19, 11161140 (2019).      
        MathSciNet                Google Scholar      
        Saleem, Z. H. Max independent set and quantum alternating        operator Ansatz. Int. J. Quantum Inf. 18,        2050011 (2020).      
        Article        MathSciNet                Google Scholar      
        de la Grandrive, P. D. & Hullo, J.-F. Knapsack Problem        variants of QAOA for battery revenue optimisation. arXiv        preprint (2019). https://doi.org/10.48550/arXiv.1908.02210.      
        Farhi, E., Goldstone, J., Gutmann, S. & Zhou, L. The        quantum approximate optimization algorithm and the        Sherrington-Kirkpatrick model at infinite size.        Quantum 6, 759 (2022).      
        Article                Google Scholar      
        Jiang, S., Britt, K. A., McCaskey, A. J., Humble, T. S. &        Kais, S. Quantum annealing for prime factorization. Sci.        Rep. 8, 17667 (2018).      
        Article        ADS PubMed        PubMed        Central         Google Scholar      
        Ji, X., Wang, B., Hu, F., Wang, C. & Zhang, H. New advanced        computing architecture for cryptography design and analysis        by D-Wave quantum annealer. Tsinghua Sci. Technol.        27, 751759 (2022).      
        Article                Google Scholar      
        Dridi, R. & Alghassi, H. Prime factorization using quantum        annealing and computational algebraic geometry. Sci.        Rep. 7, 43048 (2017).      
        Article ADS CAS PubMed        PubMed        Central         Google Scholar      
        Peng, W. et al. Factoring larger integers with fewer qubits        via quantum annealing with optimized parameters. Sci.        China Phys., Mech. Astron. 62, 60311 (2019).      
        Article        ADS         Google Scholar      
        Warren, R. H. Factoring on a quantum annealing computer.        Quantum Inf. Comput. 19, 252261 (2019).      
        MathSciNet                Google Scholar      
        Titiloye, O. & Crispin, A. Quantum annealing of the graph        coloring problem. Discret. Optim. 8, 376384        (2011).      
        Article        MathSciNet                Google Scholar      
        Kwok, J. & Pudenz, K. Graph coloring with quantum        annealing. arXiv preprint (2020). https://doi.org/10.48550/arXiv.2012.04470.      
See the article here:
Short-depth QAOA circuits and quantum annealing on higher-order ising models | npj Quantum Information - Nature.com