Simulation Codes and Experimental Data for "Enhanced Maximum Independent Set Preparation with Rydberg Atoms Guided by the Spectral Gap"

Simulation Codes and Data for "Enhanced Maximum Independent Set Preparation with Rydberg Atoms Guided by the Spectral Gap" MATLAB CodesSimulation_Code_for_Standard_Schedule.m : Simulation Code for Standard Schedule of Rydberg Adiabatic Quantum Computing (AQC). [Input: 1) Quasi_1D_Chain_N10__Graph_Data.mat (Quasi-1D Chain Graph $Q_{1D, 10}$'s Information Data), 2) Standard_Pulse_Schedule_Omegas_and_deltas_T_05us.mat (Standard AQC Schedule Data for the adiabatic duration T=5.0 μs) / Output: Simulation_Output_of_Standard_Schedule_for_N_10_Atoms.mat (Simulation Result of the Standard AQC Schedule for the Quasi-1D Chain Graph $Q_{1D, 10}$)] Calculation_Code_for_ADGLB_Pulse_Schedule_Construction.m : Calculation Code for Adjusted Detuning for Ground-Energy Leakage Blockade (ADGLB)'s Laser Detuning Schedule [Input: Simulation_Output_of_Standard_Schedule_for_N_10_Atoms.mat (Simulation Result of the Standard AQC Schedule for the Quasi-1D Chain Graph $Q_{1D, 10}$ and the adiabatic duration T=5.0 μs) / Output: ADGLB AQC Schedule Data for the Quasi-1D Chain Graph $Q_{1D, 10}$, the adiabatic duration T=5.0 μs and the Power exponent j=1.0, 1.5, 1.8, 2.0 1) $j=1.0$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_10_over_10_th_Order.mat 2) $j=1.5$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_15_over_10_th_Order.mat 3) $j=1.8$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_18_over_10_th_Order.mat 4) $j=2.0$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_20_over_10_th_Order.mat] Simulation_Code_for_ADGLB_Schedule.m : Simulation Code for the ADGLB Schedule of Rydberg Rydberg AQC [Input: 1) Quasi_1D_Chain_N10__Graph_Data.mat (Quasi-1D Chain Graph $Q_{1D, 10}$'s Information Data) 2) ADGLB AQC Schedule Data for the Quasi-1D Chain Graph $Q_{1D, 10}$ and the Power exponent j=1.0, 1.5, 1.8, 2.0 / Output: Simulation Result of the ADGLB AQC Schedule for the Quasi-1D Chain Graph $Q_{1D, 10}$, the adiabatic duration T=5.0 μs and the Power exponent j=1.0, 1.5, 1.8, 2.0 {Input2 / Output}-pair: 1) $j=1.0$: {ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_10_over_10_th_Order.mat / Simulation_Output_of_ADGLB_Schedule_for_N_Atoms10_and_Power_Order_10_over_10_th_Order.mat} 2) $j=1.5$: {ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_15_over_10_th_Order.mat / Simulation_Output_of_ADGLB_Schedule_for_N_Atoms10_and_Power_Order_15_over_10_th_Order.mat} 3) $j=1.8$: {ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_18_over_10_th_Order.mat / Simulation_Output_of_ADGLB_Schedule_for_N_Atoms10_and_Power_Order_18_over_10_th_Order.mat} 4) $j=2.0$: {ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_20_over_10_th_Order.mat / Simulation_Output_of_ADGLB_Schedule_for_N_Atoms10_and_Power_Order_20_over_10_th_Order.mat}] MATLAB Simulation Input / Output Data Input DataQuasi_1D_Chain_N10__Graph_Data.mat : Quasi-1D Chain $Q_{1D, 10}$'s Graph Information Data including belows 1) a_edge_dist [unit: μm]: Distance between two adjacent atoms (= 8.0 μm), 2) nOfQubits: Numer of Nodes N (=10), 3) Graph_ind_list: The list of the index "Graph_ind" for the graphs [For $Q_{1D, 10}$, Graph_ind=1], 4) G: the MATLAB Cell variable of the MATLAB Graph object [G{10, 1}: $Q_{1D, 10}$], 5) G_Adj{N,Graph_ind}: the MATLAB Cell variable consisting of the Adjacency matrix for the graph G{N,Graph_ind}, 6) G_coord_XYZ{N,Graph_ind} [Unit: μm]: the MATLAB Cell variable of the x, y, z-coordinates of the atoms for the graph G{N,Graph_ind}, 7) HP(N,Graph_ind): the Hardness Parameter $HP = R_{|MIS|-1}/(|MIS|·R_{|MIS|})$ of the graph G{N,Graph_ind} [where |MIS|: the size of Maximum Independent Set (MIS) and $R_k$: the number of independent sets of size k], 8) MIS_nodes_list{N,Graph_ind}: MIS Solutions of the graph G{N,Graph_ind}, Standard_Pulse_Schedule_Omegas_and_deltas_T_05us.mat : Standard AQC Schedule Data for the adiabatic duration T=5.0 μs including belows 1) dt & dtt: Sampling period 1 & 2 [dt=1.0 ns & dtt=dt/2], 2) T_end [Unit: sec]: Total adiabatic evolution time $T$ (i.e. Adiabatic duration), 3) t & tt [Unit: sec]: Time vector t=0:dt:T_end & tt=0:dtt:T_end, 4) anneal_tt: Length of the Time vector tt, 5) ramp_time [Unit: sec]: the Ramp time $t_r$(=0.5 μs), 6) rise_time_index_t & rise_time_index_tt: Rabi frequency Rising end point at each Time vector t & tt 7) fall_time_index_t & fall_time_index_tt: Rabi frequency Falling starting point at each Time vector t & tt 8) Delta_init_2pi_1MHz_unit & Delta_final_2pi_1MHz_unit [Unit: 2π × 1 MHz]: Initial and Final values of the Laser detuning schedule (both for "Standard" and "ADGLB"), 9) Omegas [Unit: 1 MHz] & Omega_peak0_2pi_1MHz_unit [Unit: 2π × 1 MHz]: Rabi frequency Schedule as a function of Time vector tt, 10) Deltas [Unit: 1 MHz]: Laser Detuning Schedule as a function of Time vector tt 11) phi_t [Unit: 1 rad]: Laser phase ADGLB AQC Schedule Data for the Quasi-1D Chain Graph $Q_{1D, 10}$, the adiabatic duration T=5.0 μs and the Power exponent j=1.0, 1.5, 1.8, 2.0 which include belows 1) Standard_Schedule_Simulation_Output_File_name: Standard AQC simulation output source of the Laser detuning schedule for Standard AQC, "Deltas_2pi_1MHz_unit_Standard_Schedule" used as the input of ADGLB Scheduling. 2) Standard_Pulse_Schedule_Data_filename: Standard AQC Schedule Data for the simulation output "Standard_Schedule_Simulation_Output_File_name", 3) ADGLB_Power_order: ADGLB Power exponent $j$, 4) dtt_min_QuEra_Aquila [Unit: sec]: Time-resolution 0.05 μs of QuEra Aquila Machine, 5) dtt_min_QuEra_Aquila_Resol_in_tt: the Ratio between "dtt_min_QuEra_Aquila" and "dtt" [i.e., dtt_min_QuEra_Aquila_Resol_in_tt = dtt_min_QuEra_Aquila/dtt (= 100)], 6) D_H2_MIS{N,Graph_ind} [Unit: 2π × 1 MHz] & D_H2_MIS_gap_min(N,Graph_ind) [Unit: 2π × 1 MHz] & tt_D_H2_MIS_gap_min [Unit: sec] & D_H2_MIS_gap_min_ind(N,Graph_ind): The Spectral gap ΔE01 (=E1-E0) & the minimum spectral gap gmin = mint∈[0,1] ΔE01(t) & the time-point tmin of gmin & the gmin point at the D_H2_MIS{N,Graph_ind}, resepectively [where E0,1: the ground- and first excited-state energy], 7) Deltas_2pi_1MHz_unit_ADGLB_Schedule{N,Graph_ind} [Unit: 2π × 1 MHz]: ADGLB Scheduling of Laser Detuning for the graph G{N,Graph_ind} as a function of Time vector tt, 8) Deltas_2pi_1MHz_unit_ADGLB_Schedule_for_QuEra_Aquila{N,Graph_ind} [Unit: 2π × 1 MHz]: ADGLB Scheduling of Laser Detuning for the graph G{N,Graph_ind} as the input of the QuEra Aquila Machine (Laser Detuning resolution: 0.2 MHz), 9) tt_QuEra_Aquila [Unit: sec] & tt_QuEra_Aquila_ind: Time vector for the QuEra Aquila Machine and their elements' point at the Time vector "tt", 10) Num_of_Slice_for_QuEra_Aquila_Delta_Sweep: the length of the Laser detuning sweep interval at "tt_QuEra_Aquila" i) $j=1.0$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_10_over_10_th_Order.mat ii) $j=1.5$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_15_over_10_th_Order.mat iii) $j=1.8$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_18_over_10_th_Order.mat iv) $j=2.0$: ADGLB_Pulse_Schedule_Omegas_and_deltas_for_N_10_T_05us_with_Power_Order_20_over_10_th_Order.mat Output DataSimulation_Output_of_Standard_Schedule_for_N_10_Atoms.mat: Standard AQC simulation output including belows 1) Quasi_1D_Chain_Graph_Data_filename: the Graph Information Datafile of the graph using for the Standard AQC Simulation, 2) diagrho_test1_1{N,Graph_ind}: "Ground- and First excited-state" Population's time-evolution of the Standard AQC Schedule Simulation, 3) diagrho_test1_2{N,Graph_ind} & diagrho_test1_2_result{N,Graph_ind}: Time-evolution of the Population for the "atomic state basis {|g⟩, |r⟩}⊗N [where |g⟩(=|0⟩) & |r⟩(=|1⟩): Atomic ground- and Rydberg states]" resulted from "diagrho_test1_1" & its final value from the Standard Schedule AQC Simulation, 4) Graph_ind: the index of the graph, 5) Deltas_2pi_1MHz_unit_Standard_Schedule{N,Graph_ind} [Unit: 2π × 1 MHz]: Standard Schedule of Laser Detuning for the graph G{N,Graph_ind} as a function of Time vector tt, 6) P_MIS_Sol & P_MIS_Sol_final & P_MIS_Sol_final_sum: Time-evolution & Final values & Total sum o