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.第3节 经典数据同化（Classical Data Assimilation, CDA）与量子数据同化（Quantum Data Assimilation, QDA）实验数据集说明 文件/文件夹说明：所有数据可在正文、补充材料中获取，或于XX处获取。 文件夹名称：data1 说明：该文件夹包含2个.dat格式数据文件："init_state_Psi.dat"与"init_state_Vor.dat"。 1. 文件名称：init_state_Psi.dat 数据结构：32行×16列二维数组 说明：该文件存储基于特定方程生成的初始流函数场数据，参数取值详见正文。其对应稿件图1(A)中的流函数场分布。 2. 文件名称：init_state_Vor.dat 数据结构：32行×16列二维数组 说明：该文件存储通过准地转（quasi-geostrophic, QG）模型方程（式(1)），由初始流函数场（源自"init_state_Psi.dat"）反演得到的初始涡度场数据。其对应稿件图1(B)中的初始涡度分布。 文件夹名称：data2 说明：该文件夹包含4个.dat格式文件："x_control_Psi.dat"、"xa_cda_Psi_512.dat"、"xa_qda_Psi_512.dat"与"xtr_Psi.dat"。 1. 文件名称：x_control_Psi.dat 数据结构：512行×720列二维数组 说明：该文件包含以初始流函数背景场为输入的720次准地转模型模拟的对照实验结果，作为无数据同化的基准对照组。每一列对应一个时间步的流函数场（共512个网格点），可通过np.reshape()函数重塑为32×16的空间场。其对应稿件图2中的流函数对照时间序列。 2. 文件名称：xtr_Psi.dat 数据结构：512行×720列二维数组 说明：该文件包含由"init_state_Psi.dat"生成的真实流函数场，经过720次准地转模型积分后的时间演化序列，用于评估经典数据同化（CDA）与量子数据同化（QDA）的性能。数据格式与data2中的"x_control_Psi.dat"一致，对应稿件图2中的真实场演化过程。 3. 文件名称：xa_cda_Psi_512.dat 数据结构：512行×720列二维数组 说明：该文件包含120次经典数据同化循环（共720个时间步）中生成的全部流函数场数据。每6列构成一个完整的同化循环：第1列为分析场，第2至6列为5次准地转模型预报步。其对应稿件图2中的经典数据同化结果。 4. 文件名称：xa_qda_Psi_512.dat 数据结构：512行×720列二维数组 说明：该文件包含120次量子数据同化循环（共720个时间步）中生成的流函数场序列，数据结构与"xa_cda_Psi_512.dat"完全一致。每6列一组中，第1列为量子同化分析场，后续5列为准地转模型预报步。其对应稿件图2中的量子数据同化结果。 文件夹名称：data3 说明：该文件夹包含4个.dat格式文件："x_control_Vor.dat"、"xa_cda_Vor_512.dat"、"xa_qda_Vor_512.dat"与"xtr_Vor.dat"。 1. 文件名称：x_control_Vor.dat 数据结构：512行×720列二维数组 说明：该文件存储以初始涡度背景场为输入的720次准地转模型模拟结果，作为无同化的对照实验，数据格式与data2中的"x_control_Psi.dat"一致。其对应稿件图3中的涡度对照场演化过程。 2. 文件名称：xtr_Vor.dat 数据结构：512行×720列二维数组 说明：该文件包含由"init_state_Vor.dat"生成的真实涡度场，经过720次准地转模型积分后的时间演化序列，用于评估CDA与QDA的性能。其对应稿件图3中的真实涡度演化过程。 3. 文件名称：xa_cda_Vor_512.dat 数据结构：512行×720列二维数组 说明：该文件包含120次经典数据同化循环（共720个时间步）中生成的涡度场数据，支撑稿件图3中的经典数据同化涡度结果。 4. 文件名称：xa_qda_Vor_512.dat 数据结构：512行×720列二维数组 说明：该文件包含120次量子数据同化循环中生成的涡度场序列，对应稿件图3中的量子数据同化涡度同化结果。 文件夹名称：data4 说明：该文件夹包含1个.xlsx格式文件："rmse_xa_qda_cda_Psi.xlsx"。 文件名称：rmse_xa_qda_cda_Psi.xlsx 数据结构：720行×8列二维数组 说明：该文件记录了经典数据同化（CDA）与量子数据同化（QDA）在不同观测配置（8、32、128及512个观测点）下得到的流函数分析场的均方根误差（Root Mean Square Error, RMSE）。每一列对应一种方法-观测组合的均方根误差时间序列（共720个时间步），用于定量评估同化性能。其支撑稿件图4中的流函数场均方根误差对比结果。 文件夹名称：data5 说明：该文件夹包含1个.xlsx格式文件："rmse_xa_qda_cda_Vor.xlsx"。 文件名称：rmse_xa_qda_cda_Vor.xlsx 数据结构：720行×8列二维数组 说明：该文件记录了CDA与QDA在不同观测配置（8、32、128及512个观测点）下得到的涡度分析场的均方根误差（RMSE）。每一列对应一种方法与观测点配置的均方根误差时间序列（共720个时间步）。其支撑稿件图5中的涡度均方根误差对比结果。 文件夹名称：data6 说明：该文件夹包含6个.xlsx格式文件："sub-region_1.xlsx"、"sub-region_2.xlsx"、"sub-region_3.xlsx"、"sub-region_4.xlsx"、"sub-region_5.xlsx"与"sub-region_6.xlsx"。 1. 文件名称：sub-region_1.xlsx 数据结构：2000行×3列Excel电子表格 说明：该文件记录了首个空间子区域的流函数场首次数据同化过程中，从光学相干伊辛机（CIM）设备获取的量子优化数据，包含在CIM单次连续运行周期内记录的2000次连续测量步骤的哈密顿量值与对应的演化时间。其支撑稿件图7中首个子区域的哈密顿量演化分析。其余文件（"sub-region_2.xlsx"至"sub-region_6.xlsx"）数据结构一致，分别对应其余5个空间子区域的量子优化结果。