Adjusted Detuning for Ground-Energy Leakage Blockade in Maximum Independent Sets with Rydberg atoms

Quantum computing using Rydberg neutral atoms has seen remarkable experimental progress in recent years. Rydberg adiabatic quantum computation (AQC) provides an efficient and practical solution that directly maps many combinatorial optimization problems into the Maximum Independent Set (MIS) problem [1]. A major bottleneck in solving hard MIS instances, particularly those with a large degeneracy ratio between the ground- and first-excited states, is that the minimum spectral energy gap (g_min) decreases super-exponentially with system size N. In these cases, the scaling of the required adiabatic evolution time is given by 1/(g_min)³ [2], making it difficult to reach the optimal MIS solutions within a limited coherence time, due to the inevitable ground-state population leakage. Here, we study the ground-to-excited state dynamics near g_min. For a fixed evolution time, we introduce the Adjusted Detuning for Ground-Energy Leakage Blockade (ADGLB) method, which optimizes the laser detuning sweep by the energy gap to suppress the ground-state population leakage and thereby maximizes the MIS population. We benchmarked this method using k-PXP chains [3], with relatively large hardness parameter (HP) and small g_min for same N. Experiments on the QuEra Aquila machine [4] demonstrated a performance improvement of approximately 40% in MIS accuracy for a k-PXP chain (N=13 , HP=11.4).

 

[1] S. Jeong, M. Kim, M. Hhan, J. Park, and J. Ahn, “Quantum programming of the satisfiability problem with Rydberg atom graphs”, Phys. Rev. Res. 5, 043037 (2023).

[2] S. Jansen, M.-B. Ruskai, and R. Seiler, “Bounds for the adiabatic approximation with applications to quantum computation”, J. Math. Phys. 48, 102111 (2007).

[3] B. F. Schiffer, D. S. Wild, N. Maskara, M. Cain, M. D. Lukin, and R. Samajdar, “Circumventing superexponential runtimes for hard instances of quantum adiabatic optimization”, Phys. Rev. Res. 6, 013271 (2024).

[4] J. Wurtz, A. Bylinskii, B. Braverman, J. Amato-Grill, S. H. Cantu, F. Huber, A. Lukin, F. Liu, P. Weinberg, J. Long, S.-T. Wang, N. Gemelke, and A. Keesling, “Aquila: QuEra's 256-qubit neutral-atom quantum computer”, arXiv:2306.11727, v1, (2023).