Dataset for Realization of QDA

Section 3 Dataset Description for CDA and QDA Experiments File/Folder Details:All data is available in the main text and supplementary information or at XX. Folder Name: data1 Description: This folder contains two data files in .dat format: “init_state_Psi.dat” and “init_state_Vor.dat”. 1. File Name: init_state_Psi.datData Structure: 32 rows × 16 columns, two-dimensional arrayDescription: This file stores the initial stream function field data generated based on a specific equation, with parameter values as described in the main text. The data corresponds to the stream function field distribution shown in Figure 1(A) of the manuscript. 2. File Name: init_state_Vor.datData Structure: 32 rows × 16 columns, two-dimensional arrayDescription: This file stores the initial vorticity field data obtained via inversion from the initial stream function field (from “init_state_Psi.dat”) using the quasi-geostrophic (QG) model equation (Eq. (1)). This data corresponds to the initial vorticity distribution shown in Figure 1(B) of the manuscript. Folder Name: data2 Description: This folder contains four .dat files: “x_control_Psi.dat”, “xa_cda_Psi_512.dat”, “xa_qda_Psi_512.dat”, and “xtr_Psi.dat”. 1. File Name: x_control_Psi.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription: This file contains control experiment results of 720 QG model simulations using the initial stream function background field as input. It serves as the baseline without data assimilation. Each column represents the stream function field at a time step (512 grid points), which can be reshaped into a 32 × 16 spatial field using the np.reshape() function. The data corresponds to the stream function control time series shown in Figure 2. 2. File Name: xtr_Psi.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription: This file contains the temporal evolution of the true stream function field (from “init_state_Psi.dat”) over 720 QG model integration steps. It is used to evaluate the performance of Classical Data Assimilation (CDA) and Quantum Data Assimilation (QDA). The data format is consistent with “x_control_Psi.dat” and corresponds to the true field evolution shown in Figure 2. 3. File Name: xa_cda_Psi_512.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription: This file contains all stream function fields generated during 120 CDA assimilation cycles (720 time steps). Every six columns constitute a full assimilation cycle: the 1st column is the analysis field, and the 2nd to 6th columns are five forecast steps using the QG model. The data corresponds to the CDA results shown in Figure 2. 4. File Name: xa_qda_Psi_512.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription:This file contains the stream function field sequence generated during 120 QDA assimilation cycles (720 time steps). The structure is identical to that of “xa_cda_Psi_512.dat”. In each group of six columns, the 1st column is the quantum-assimilated analysis field, followed by five QG model forecast steps. The data corresponds to the QDA results shown in Figure 2. Folder Name: data3 Description: This folder contains four .dat files: “x_control_Vor.dat”, “xa_cda_Vor_512.dat”, “xa_qda_Vor_512.dat”, and “xtr_Vor.dat”. 1. File Name: x_control_Vor.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription: This file stores 720 QG model simulations of the initial vorticity background field as control experiments without assimilation. The format is consistent with “x_control_Psi.dat” in data2. The data corresponds to the vorticity control field evolution shown in Figure 3. 2. File Name: xtr_Vor.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription: This file contains the temporal evolution of the true vorticity field (from init_state_Vor.dat) over 720 QG model steps, used to evaluate CDA and QDA. The data corresponds to the true vorticity evolution shown in Figure 3. 3. File Name: xa_cda_Vor_512.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription: This file contains the vorticity field data generated during 120 CDA assimilation cycles (720 time steps). The data supports the CDA vorticity assimilation results presented in Figure 3. 4. File Name: xa_qda_Vor_512.datData Structure: 512 rows × 720 columns, two-dimensional arrayDescription: This file contains the vorticity field sequences produced during 120 QDA assimilation cycles, corresponding to the QDA assimilation performance shown in Figure 3. Folder Name: data4 Description: This folder contains one .xlsx file: “rmse_xa_qda_cda_Psi.xlsx” File Name: rmse_xa_qda_cda_Psi.xlsxData Structure: 720 rows × 8 columns, two-dimensional arrayDescription: This file records the Root Mean Square Error (RMSE) of the stream function analysis fields obtained by CDA and QDA under different observational configurations (8, 32, 128, and 512 observation points). Each column represents the RMSE time series (720 steps) for a specific method-observation pairing, providing a quantitative assessment of assimilation performance. The data supports the RMSE comparison of stream function fields shown in Figure 4. Folder Name: data5 Description: This folder contains one .xlsx file: rmse_xa_qda_cda_Vor.xlsx 1. File Name: rmse_xa_qda_cda_Vor.xlsxData Structure: 720 rows × 8 columns, two-dimensional arrayDescription: This file records the RMSE of the vorticity analysis fields from CDA and QDA under different observational configurations (8, 32, 128, and 512 observation points). Each column corresponds to a time series of RMSE (720 steps) for a specific method and observation point configuration. The data supports the vorticity RMSE comparison shown in Figure 5. Folder Name: data6 Description:This folder contains six .xlsx files: “sub-region_1.xlsx”, “sub-region_2.xlsx”, “sub-region_3.xlsx”, “sub-region_4.xlsx”, “sub-region_5.xlsx”, and “sub-region_6.xlsx”. 1. File Name: sub-region_1.xlsxData Structure: 2000 rows × 3 columns, Excel spreadsheetDescription: This file records quantum optimization data obtained from the optical CIM device during the first data assimilation of the stream function field in the first spatial sub-region. It includes the Hamiltonian values and corresponding evolution times from 2000 consecutive measurement steps recorded over a single continuous operation cycle of the CIM. The data supports the Hamiltonian evolution analysis shown in Figure 7 for sub-region 1. The remaining files (“sub-region_2.xlsx” to “sub-region_6.xlsx”) share the same structure and correspond to quantum optimization results in the other spatial sub-regions.