article published yes Stefan Sack author dd622248-f6e0-11ea-865d-ce382a1c81a50000-0001-5400-8508 Raimel A Medina Ramos author CE680B90-D85A-11E9-B684-C920E66974250000-0002-5383-2869 Richard Kueng author Maksym Serbyn author 47809E7E-F248-11E8-B48F-1D18A9856A870000-0002-2399-5827 MaSe department Non-Ergodic Quantum Matter: Universality, Dynamics and Control project The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of p layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization, the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic initializations exist, an analytical understanding and performance guarantees for large p remain evasive.We introduce a greedy initialization of QAOA which guarantees improving performance with an increasing number of layers. Our main result is an analytic construction of 2p + 1 transition states—saddle points with a unique negative curvature direction—for QAOA with p + 1 layers that use the local minimum of QAOA with p layers. Transition states connect to new local minima, which are guaranteed to lower the energy compared to the minimum found for p layers. We use the GREEDY procedure to navigate the exponentially increasing with p number of local minima resulting from the recursive application of our analytic construction. The performance of the GREEDY procedure matches available initialization strategies while providing a guarantee for the minimal energy to decrease with an increasing number of layers p. https://research-explorer.ista.ac.at/download/13125/13131/2023_PhysRevA_Sack.pdf application/pdfno American Physical Society2023 eng 2469-9926 2469-9934 2209.01159 00101692710001210.1103/physreva.107.062404 1076 https://research-explorer.ista.ac.at/record/17208 https://research-explorer.ista.ac.at/record/14622 Sack, Stefan, Raimel A Medina Ramos, Richard Kueng, and Maksym Serbyn. “Recursive Greedy Initialization of the Quantum Approximate Optimization Algorithm with Guaranteed Improvement.” <i>Physical Review A</i>. American Physical Society, 2023. <a href="https://doi.org/10.1103/physreva.107.062404">https://doi.org/10.1103/physreva.107.062404</a>. Sack, Stefan, et al. “Recursive Greedy Initialization of the Quantum Approximate Optimization Algorithm with Guaranteed Improvement.” <i>Physical Review A</i>, vol. 107, no. 6, 062404, American Physical Society, 2023, doi:<a href="https://doi.org/10.1103/physreva.107.062404">10.1103/physreva.107.062404</a>. Sack, S., Medina Ramos, R. A., Kueng, R., &#38; Serbyn, M. (2023). Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement. <i>Physical Review A</i>. American Physical Society. <a href="https://doi.org/10.1103/physreva.107.062404">https://doi.org/10.1103/physreva.107.062404</a> S. Sack, R.A. Medina Ramos, R. Kueng, M. Serbyn, Physical Review A 107 (2023). Sack S, Medina Ramos RA, Kueng R, Serbyn M. 2023. Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement. Physical Review A. 107(6), 062404. Sack S, Medina Ramos RA, Kueng R, Serbyn M. Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement. <i>Physical Review A</i>. 2023;107(6). doi:<a href="https://doi.org/10.1103/physreva.107.062404">10.1103/physreva.107.062404</a> S. Sack, R. A. Medina Ramos, R. Kueng, and M. Serbyn, “Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement,” <i>Physical Review A</i>, vol. 107, no. 6. American Physical Society, 2023. 131252023-06-07T06:57:32Z2026-10-05T22:31:10Z