Theoretical approximation ratios for Warm-Started QAOA on 3-regular max-cut instances at depth p=1
We generalize Farhi et al.’s 0.6924-approximation result technique of the Max-Cut Quantum Approximate Optimization Algorithm (QAOA) on 3-regular graphs to obtain provable lower bounds on the approximation ratio for warm-started QAOA. Given a tilt angle θ, we consider warm-starts where the initial st...
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| Vydáno v: | Theoretical computer science Ročník 1059; s. 115571 |
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Elsevier B.V
04.01.2026
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| ISSN: | 0304-3975 |
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| Abstract | We generalize Farhi et al.’s 0.6924-approximation result technique of the Max-Cut Quantum Approximate Optimization Algorithm (QAOA) on 3-regular graphs to obtain provable lower bounds on the approximation ratio for warm-started QAOA. Given a tilt angle θ, we consider warm-starts where the initial state is a product state where each qubit position is angle θ away from either the north or south pole of the Bloch sphere; of the two possible qubit positions the position of each qubit is decided by some classically obtained cut encoded as a bitstring b.
We illustrate through plots how the properties of b and the tilt angle θ influence the bound on the approximation ratios of warm-started QAOA. We consider various classical algorithms (and the cuts they produce which we use to generate the warm-start). Our results strongly suggest that there does not exist any choice of tilt angle that yields a (worst-case) approximation ratio that simultaneously beats standard QAOA and the classical algorithm used to create the warm-start. Additionally, we show that at θ=60∘, warm-started QAOA is able to (effectively) recover the cut used to generate the warm-start, thus suggesting that in practice, this value could be a promising starting angle to explore alternate solutions in a heuristic fashion. |
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| AbstractList | We generalize Farhi et al.’s 0.6924-approximation result technique of the Max-Cut Quantum Approximate Optimization Algorithm (QAOA) on 3-regular graphs to obtain provable lower bounds on the approximation ratio for warm-started QAOA. Given a tilt angle θ, we consider warm-starts where the initial state is a product state where each qubit position is angle θ away from either the north or south pole of the Bloch sphere; of the two possible qubit positions the position of each qubit is decided by some classically obtained cut encoded as a bitstring b.
We illustrate through plots how the properties of b and the tilt angle θ influence the bound on the approximation ratios of warm-started QAOA. We consider various classical algorithms (and the cuts they produce which we use to generate the warm-start). Our results strongly suggest that there does not exist any choice of tilt angle that yields a (worst-case) approximation ratio that simultaneously beats standard QAOA and the classical algorithm used to create the warm-start. Additionally, we show that at θ=60∘, warm-started QAOA is able to (effectively) recover the cut used to generate the warm-start, thus suggesting that in practice, this value could be a promising starting angle to explore alternate solutions in a heuristic fashion. |
| ArticleNumber | 115571 |
| Author | Eidenbenz, Stephan Tate, Reuben |
| Author_xml | – sequence: 1 givenname: Reuben orcidid: 0000-0002-9170-8906 surname: Tate fullname: Tate, Reuben email: rtate@lanl.gov – sequence: 2 givenname: Stephan surname: Eidenbenz fullname: Eidenbenz, Stephan email: eidenben@lanl.gov |
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| Cites_doi | 10.22331/q-2022-03-30-678 10.1103/PhysRevLett.125.260505 10.1103/PhysRevA.95.062317 10.22331/q-2021-04-20-437 10.1016/j.jalgor.2004.06.001 10.3390/a12020034 10.1103/PhysRevA.103.042612 10.22331/q-2021-06-17-479 10.1145/502090.502098 10.1007/978-3-031-82697-9_23 10.1103/PhysRevResearch.4.033029 10.1103/PhysRevA.107.062404 10.1109/QCNC64685.2025.00077 10.1145/227683.227684 10.22331/q-2023-09-26-1121 10.1016/S0196-6774(02)00005-6 10.1002/nav.3800090303 10.1137/S0097539705447372 10.22331/q-2021-07-01-491 10.1145/3549554 10.1038/s41534-023-00787-5 10.1038/s41592-019-0686-2 10.1103/PhysRevA.101.012320 10.1145/3584706 |
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| References | Wurtz, Love (bib0017) 2021; 103 Charnes, Cooper (bib0032) 1962; 9 Zhou, Wang, Choi, Pichler, Lukin (bib0013) 2020; 10 Virtanen, Gommers, Oliphant, Haberland, Reddy, Cournapeau, Burovski, Peterson, Weckesser, Bright, van der Walt, Brett, Wilson, Millman, Mayorov, Nelson, Jones, Kern, Larson, Carey, Polat, Feng, Moore, VanderPlas, Laxalde, Perktold, Cimrman, Henriksen, Quintero, Harris, Archibald, Ribeiro, Pedregosa, van Mulbregt, SciPy 1.0 Contributors (bib0031) 2020; 17 Galda, Liu, Lykov, Alexeev, Safro (bib0009) 2021 Wang, Rubin, Dominy, Rieffel (bib0004) 2020; 101 M. Cain, E. Farhi, S. Gutmann, D. Ranard, E. Tang, The QAOA gets stuck starting from a good classical string, (2022). Håstad (bib0028) 2001; 48 Feige, Karpinski, Langberg (bib0026) 2002; 43 Khot, Kindler, Mossel, O’Donnell (bib0024) 2007; 37 Wang, Rubin, Dominy, Rieffel (bib0036) 2020; 101 Karp (bib0022) 2010 Jiang, Rieffel, Wang (bib0008) 2017; 95 Zhu, Tang, Barron, Calderon-Vargas, Mayhall, Barnes, Economou (bib0005) 2022; 4 Bravyi, Kliesch, Koenig, Tang (bib0006) 2020; 125 E. Farhi, J. Goldstone, S. Gutmann, A quantum approximate optimization algorithm, (2014). Tate, Moondra, Gard, Mohler, Gupta (bib0018) 2023; 7 Bärtschi, Eidenbenz (bib0007) 2020 Hadfield, Wang, O’Gorman, Rieffel, Venturelli, Biswas (bib0003) 2019; 12 Egger, Mareček, Woerner (bib0020) 2021; 5 I. Glendinning, Rotations on the Bloch Sphere, 2010. Golden, Bärtschi, O’Malley, Eidenbenz (bib0037) 2021 Sack, Serbyn (bib0010) 2021; 5 R. Tate, S. Eidenbenz, Warm-Started QAOA with Aligned Mixers Converges Slowly Near the Poles of the Bloch Sphere, (2024). Goemans, Williamson (bib0035) 1995; 42 Bravyi, Kliesch, Koenig, Tang (bib0015) 2022; 6 . He, Shaydulin, Chakrabarti, Herman, Li, Sun, Pistoia (bib0030) 2023; 9 Halperin, Livnat, Zwick (bib0025) 2004; 53 Shaydulin, Lotshaw, Larson, Ostrowski, Humble (bib0012) 2023; 4 Tate, Farhadi, Herold, Mohler, Gupta (bib0019) 2023; 4 Khot (bib0023) 2002 E. Farhi, D. Gamarnik, S. Gutmann, The quantum approximate optimization algorithm needs to see the whole graph: A typical case, arXiv preprint (2020). Sack, Medina, Kueng, Serbyn (bib0011) 2023; 107 E. Farhi, J. Goldstone, S. Gutmann, Quantum algorithms for fixed qubit architectures, (2017). Berman, Karpinski (bib0027) 1999 S. Feeney, R. Tate, S. Eidenbenz, The Better Solution Probability Metric: Optimizing QAOA to Outperform its Warm-Start Solution, (2024). Marwaha (bib0016) 2021; 5 Wang (10.1016/j.tcs.2025.115571_bib0004) 2020; 101 Tate (10.1016/j.tcs.2025.115571_bib0019) 2023; 4 Berman (10.1016/j.tcs.2025.115571_bib0027) 1999 Jiang (10.1016/j.tcs.2025.115571_bib0008) 2017; 95 Hadfield (10.1016/j.tcs.2025.115571_bib0003) 2019; 12 Zhu (10.1016/j.tcs.2025.115571_bib0005) 2022; 4 Feige (10.1016/j.tcs.2025.115571_bib0026) 2002; 43 10.1016/j.tcs.2025.115571_bib0029 Bärtschi (10.1016/j.tcs.2025.115571_bib0007) 2020 Bravyi (10.1016/j.tcs.2025.115571_bib0006) 2020; 125 Egger (10.1016/j.tcs.2025.115571_bib0020) 2021; 5 10.1016/j.tcs.2025.115571_bib0034 He (10.1016/j.tcs.2025.115571_bib0030) 2023; 9 Tate (10.1016/j.tcs.2025.115571_bib0018) 2023; 7 10.1016/j.tcs.2025.115571_bib0033 10.1016/j.tcs.2025.115571_bib0014 Virtanen (10.1016/j.tcs.2025.115571_bib0031) 2020; 17 Sack (10.1016/j.tcs.2025.115571_bib0011) 2023; 107 Khot (10.1016/j.tcs.2025.115571_bib0023) 2002 Bravyi (10.1016/j.tcs.2025.115571_bib0015) 2022; 6 Karp (10.1016/j.tcs.2025.115571_bib0022) 2010 Goemans (10.1016/j.tcs.2025.115571_bib0035) 1995; 42 Charnes (10.1016/j.tcs.2025.115571_bib0032) 1962; 9 Sack (10.1016/j.tcs.2025.115571_bib0010) 2021; 5 Wurtz (10.1016/j.tcs.2025.115571_bib0017) 2021; 103 10.1016/j.tcs.2025.115571_bib0001 Golden (10.1016/j.tcs.2025.115571_bib0037) 2021 10.1016/j.tcs.2025.115571_bib0002 10.1016/j.tcs.2025.115571_bib0021 Håstad (10.1016/j.tcs.2025.115571_bib0028) 2001; 48 Zhou (10.1016/j.tcs.2025.115571_bib0013) 2020; 10 Halperin (10.1016/j.tcs.2025.115571_bib0025) 2004; 53 Shaydulin (10.1016/j.tcs.2025.115571_bib0012) 2023; 4 Wang (10.1016/j.tcs.2025.115571_bib0036) 2020; 101 Marwaha (10.1016/j.tcs.2025.115571_bib0016) 2021; 5 Khot (10.1016/j.tcs.2025.115571_bib0024) 2007; 37 Galda (10.1016/j.tcs.2025.115571_bib0009) 2021 |
| References_xml | – volume: 9 start-page: 121 year: 2023 ident: bib0030 article-title: Alignment between initial state and mixer improves QAOA performance for constrained optimization publication-title: npj Quant. Inf. – volume: 4 start-page: 1 year: 2023 end-page: 39 ident: bib0019 article-title: Bridging classical and quantum with SDP initialized warm-starts for QAOA publication-title: ACM Transact. Quant. Comput. – volume: 43 start-page: 201 year: 2002 end-page: 219 ident: bib0026 article-title: Improved approximation of Max-Cut on graphs of bounded degree publication-title: J. Algorith. – volume: 6 start-page: 678 year: 2022 ident: bib0015 article-title: Hybrid quantum-classical algorithms for approximate graph coloring publication-title: Quantum – volume: 4 start-page: 1 year: 2023 end-page: 15 ident: bib0012 article-title: Parameter transfer for quantum approximate optimization of weighted maxcut publication-title: ACM Transact. Quant. Comput. – start-page: 137 year: 2021 end-page: 147 ident: bib0037 article-title: Threshold-based quantum optimization publication-title: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) – volume: 53 start-page: 169 year: 2004 end-page: 185 ident: bib0025 article-title: MAX CUT In cubic graphs publication-title: J. Algorith. – volume: 7 start-page: 1121 year: 2023 ident: bib0018 article-title: Warm-Started QAOA with custom mixers provably converges and computationally beats goemans-Williamson’s Max-Cut at low circuit depths publication-title: Quantum – volume: 4 year: 2022 ident: bib0005 article-title: Adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer publication-title: Phys. Rev. Res. – volume: 125 year: 2020 ident: bib0006 article-title: Obstacles to variational quantum optimization from symmetry protection publication-title: Phys. Rev. Lett. – volume: 48 start-page: 798 year: 2001 end-page: 859 ident: bib0028 article-title: Some optimal inapproximability results publication-title: J. ACM (JACM) – volume: 5 start-page: 491 year: 2021 ident: bib0010 article-title: Quantum annealing initialization of the quantum approximate optimization algorithm publication-title: Quantum – volume: 101 year: 2020 ident: bib0036 article-title: X y mixers: analytical and numerical results for the quantum alternating operator ansatz publication-title: Phys. Rev. A – reference: S. Feeney, R. Tate, S. Eidenbenz, The Better Solution Probability Metric: Optimizing QAOA to Outperform its Warm-Start Solution, (2024). – reference: E. Farhi, J. Goldstone, S. Gutmann, Quantum algorithms for fixed qubit architectures, (2017). – volume: 12 year: 2019 ident: bib0003 article-title: From the quantum approximate optimization algorithm to a quantum alternating operator Ansatz publication-title: Algorithms – reference: M. Cain, E. Farhi, S. Gutmann, D. Ranard, E. Tang, The QAOA gets stuck starting from a good classical string, (2022). – start-page: 200 year: 1999 end-page: 209 ident: bib0027 article-title: On some tighter inapproximability results (extended abstract) publication-title: Automata, Languages and Programming – volume: 5 start-page: 479 year: 2021 ident: bib0020 article-title: Warm-starting quantum optimization publication-title: Quantum – year: 2010 ident: bib0022 article-title: Reducibility Among Combinatorial Problems – start-page: 767 year: 2002 end-page: 775 ident: bib0023 article-title: On the power of unique 2-prover 1-round games publication-title: Proceedings of the Thiry-fourth Annual ACM Symposium on Theory of Computing – volume: 95 year: 2017 ident: bib0008 article-title: Near-optimal quantum circuit for Grover’s unstructured search using a transverse field publication-title: Phys. Rev. A – volume: 37 start-page: 319 year: 2007 end-page: 357 ident: bib0024 article-title: Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? publication-title: SIAM J. Comput. – reference: I. Glendinning, Rotations on the Bloch Sphere, 2010. – volume: 42 start-page: 1115 year: 1995 end-page: 1145 ident: bib0035 article-title: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming publication-title: J. ACM (JACM) – reference: . – reference: E. Farhi, J. Goldstone, S. Gutmann, A quantum approximate optimization algorithm, (2014). – volume: 5 start-page: 437 year: 2021 ident: bib0016 article-title: Local classical MAX-CUT algorithm outperforms publication-title: Quantum – volume: 9 start-page: 181 year: 1962 end-page: 186 ident: bib0032 article-title: Programming with linear fractional functionals publication-title: Naval Res. Logist. Q. – start-page: 171 year: 2021 end-page: 180 ident: bib0009 article-title: Transferability of optimal QAOA parameters between random graphs publication-title: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) – reference: R. Tate, S. Eidenbenz, Warm-Started QAOA with Aligned Mixers Converges Slowly Near the Poles of the Bloch Sphere, (2024). – volume: 101 year: 2020 ident: bib0004 article-title: Mixers: analytical and numerical results for the quantum alternating operator ansatz publication-title: Phys. Rev. A – volume: 103 year: 2021 ident: bib0017 article-title: MaxCut quantum approximate optimization algorithm performance guarantees for publication-title: Phys. Rev. A – volume: 107 year: 2023 ident: bib0011 article-title: Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement publication-title: Phys. Rev. A – reference: E. Farhi, D. Gamarnik, S. Gutmann, The quantum approximate optimization algorithm needs to see the whole graph: A typical case, arXiv preprint (2020). – volume: 17 start-page: 261 year: 2020 end-page: 272 ident: bib0031 article-title: SciPy 1.0: fundamental algorithms for scientific computing in python publication-title: Nat. Method. – start-page: 72 year: 2020 end-page: 82 ident: bib0007 article-title: Grover mixers for QAOA: shifting complexity from mixer design to state preparation publication-title: 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) – volume: 10 year: 2020 ident: bib0013 article-title: Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices publication-title: Phys. Rev. X – volume: 6 start-page: 678 year: 2022 ident: 10.1016/j.tcs.2025.115571_bib0015 article-title: Hybrid quantum-classical algorithms for approximate graph coloring publication-title: Quantum doi: 10.22331/q-2022-03-30-678 – ident: 10.1016/j.tcs.2025.115571_bib0002 – ident: 10.1016/j.tcs.2025.115571_bib0021 – volume: 125 year: 2020 ident: 10.1016/j.tcs.2025.115571_bib0006 article-title: Obstacles to variational quantum optimization from symmetry protection publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.125.260505 – start-page: 767 year: 2002 ident: 10.1016/j.tcs.2025.115571_bib0023 article-title: On the power of unique 2-prover 1-round games – ident: 10.1016/j.tcs.2025.115571_bib0029 – volume: 10 issue: 2 year: 2020 ident: 10.1016/j.tcs.2025.115571_bib0013 article-title: Quantum approximate optimization algorithm: performance, mechanism, and implementation on near-term devices publication-title: Phys. Rev. X – volume: 95 issue: 6 year: 2017 ident: 10.1016/j.tcs.2025.115571_bib0008 article-title: Near-optimal quantum circuit for Grover’s unstructured search using a transverse field publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.95.062317 – volume: 5 start-page: 437 year: 2021 ident: 10.1016/j.tcs.2025.115571_bib0016 article-title: Local classical MAX-CUT algorithm outperforms p=2 QAOA on high-girth regular graphs publication-title: Quantum doi: 10.22331/q-2021-04-20-437 – volume: 53 start-page: 169 issue: 2 year: 2004 ident: 10.1016/j.tcs.2025.115571_bib0025 article-title: MAX CUT In cubic graphs publication-title: J. Algorith. doi: 10.1016/j.jalgor.2004.06.001 – volume: 12 issue: 2 year: 2019 ident: 10.1016/j.tcs.2025.115571_bib0003 article-title: From the quantum approximate optimization algorithm to a quantum alternating operator Ansatz publication-title: Algorithms doi: 10.3390/a12020034 – volume: 103 issue: 4 year: 2021 ident: 10.1016/j.tcs.2025.115571_bib0017 article-title: MaxCut quantum approximate optimization algorithm performance guarantees for p>1 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.103.042612 – start-page: 171 year: 2021 ident: 10.1016/j.tcs.2025.115571_bib0009 article-title: Transferability of optimal QAOA parameters between random graphs – volume: 5 start-page: 479 year: 2021 ident: 10.1016/j.tcs.2025.115571_bib0020 article-title: Warm-starting quantum optimization publication-title: Quantum doi: 10.22331/q-2021-06-17-479 – volume: 48 start-page: 798 issue: 4 year: 2001 ident: 10.1016/j.tcs.2025.115571_bib0028 article-title: Some optimal inapproximability results publication-title: J. ACM (JACM) doi: 10.1145/502090.502098 – ident: 10.1016/j.tcs.2025.115571_bib0033 doi: 10.1007/978-3-031-82697-9_23 – ident: 10.1016/j.tcs.2025.115571_bib0001 – volume: 4 year: 2022 ident: 10.1016/j.tcs.2025.115571_bib0005 article-title: Adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer publication-title: Phys. Rev. Res. doi: 10.1103/PhysRevResearch.4.033029 – year: 2010 ident: 10.1016/j.tcs.2025.115571_bib0022 – volume: 107 issue: 6 year: 2023 ident: 10.1016/j.tcs.2025.115571_bib0011 article-title: Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.107.062404 – ident: 10.1016/j.tcs.2025.115571_bib0034 doi: 10.1109/QCNC64685.2025.00077 – volume: 42 start-page: 1115 issue: 6 year: 1995 ident: 10.1016/j.tcs.2025.115571_bib0035 article-title: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming publication-title: J. ACM (JACM) doi: 10.1145/227683.227684 – volume: 7 start-page: 1121 year: 2023 ident: 10.1016/j.tcs.2025.115571_bib0018 article-title: Warm-Started QAOA with custom mixers provably converges and computationally beats goemans-Williamson’s Max-Cut at low circuit depths publication-title: Quantum doi: 10.22331/q-2023-09-26-1121 – volume: 43 start-page: 201 issue: 2 year: 2002 ident: 10.1016/j.tcs.2025.115571_bib0026 article-title: Improved approximation of Max-Cut on graphs of bounded degree publication-title: J. Algorith. doi: 10.1016/S0196-6774(02)00005-6 – volume: 9 start-page: 181 issue: 3–4 year: 1962 ident: 10.1016/j.tcs.2025.115571_bib0032 article-title: Programming with linear fractional functionals publication-title: Naval Res. Logist. Q. doi: 10.1002/nav.3800090303 – volume: 37 start-page: 319 issue: 1 year: 2007 ident: 10.1016/j.tcs.2025.115571_bib0024 article-title: Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? publication-title: SIAM J. Comput. doi: 10.1137/S0097539705447372 – volume: 101 year: 2020 ident: 10.1016/j.tcs.2025.115571_bib0004 article-title: XY Mixers: analytical and numerical results for the quantum alternating operator ansatz publication-title: Phys. Rev. A – ident: 10.1016/j.tcs.2025.115571_bib0014 – volume: 5 start-page: 491 year: 2021 ident: 10.1016/j.tcs.2025.115571_bib0010 article-title: Quantum annealing initialization of the quantum approximate optimization algorithm publication-title: Quantum doi: 10.22331/q-2021-07-01-491 – volume: 4 start-page: 1 issue: 2 year: 2023 ident: 10.1016/j.tcs.2025.115571_bib0019 article-title: Bridging classical and quantum with SDP initialized warm-starts for QAOA publication-title: ACM Transact. Quant. Comput. doi: 10.1145/3549554 – volume: 9 start-page: 121 issue: 1 year: 2023 ident: 10.1016/j.tcs.2025.115571_bib0030 article-title: Alignment between initial state and mixer improves QAOA performance for constrained optimization publication-title: npj Quant. Inf. doi: 10.1038/s41534-023-00787-5 – volume: 17 start-page: 261 year: 2020 ident: 10.1016/j.tcs.2025.115571_bib0031 article-title: SciPy 1.0: fundamental algorithms for scientific computing in python publication-title: Nat. Method. doi: 10.1038/s41592-019-0686-2 – start-page: 200 year: 1999 ident: 10.1016/j.tcs.2025.115571_bib0027 article-title: On some tighter inapproximability results (extended abstract) – start-page: 72 year: 2020 ident: 10.1016/j.tcs.2025.115571_bib0007 article-title: Grover mixers for QAOA: shifting complexity from mixer design to state preparation – start-page: 137 year: 2021 ident: 10.1016/j.tcs.2025.115571_bib0037 article-title: Threshold-based quantum optimization – volume: 101 issue: 1 year: 2020 ident: 10.1016/j.tcs.2025.115571_bib0036 article-title: X y mixers: analytical and numerical results for the quantum alternating operator ansatz publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.101.012320 – volume: 4 start-page: 1 issue: 3 year: 2023 ident: 10.1016/j.tcs.2025.115571_bib0012 article-title: Parameter transfer for quantum approximate optimization of weighted maxcut publication-title: ACM Transact. Quant. Comput. doi: 10.1145/3584706 |
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| Snippet | We generalize Farhi et al.’s 0.6924-approximation result technique of the Max-Cut Quantum Approximate Optimization Algorithm (QAOA) on 3-regular graphs to... |
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| SubjectTerms | Combinatorial optimization Max-Cut Quantum approximate optimization algorithm Quantum computing |
| Title | Theoretical approximation ratios for Warm-Started QAOA on 3-regular max-cut instances at depth p=1 |
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