We propose a Correlation-Complexity Map as a practical diagnostic tool for determining when real-world data distributions are structurally aligned with IQP-type quantum generative models. Characterized by two complementary indicators: (i) a Quantum Correlation-Likeness Indicator (QCLI), computed from the dataset's correlation-order (Walsh-Hadamard/Fourier) power spectrum aggregated by interaction order and quantified via Jensen-Shannon divergence from an i.i.d. binomial reference; and (ii) a Classical Correlation-Complexity Indicator (CCI), defined as the fraction of total correlation not captured by the optimal Chow-Liu tree approximation, normalized by total correlation. We provide theoretical support by relating QCLI to a support-mismatch mechanism, for fixed-architecture IQP families trained with an MMD objective, higher QCLI implies a smaller irreducible approximation floor. Using the map, we identify the classical turbulence data as both IQP-compatible and classically complex (high QCLI/high CCI). Guided by this placement, we use an invertible float-to-bitstring representation and a latent-parameter adaptation scheme that reuses a compact IQP circuit over a temporal sequence by learning and interpolating a low-dimensional latent trajectory. In comparative evaluations against classical models such as Restricted Boltzmann Machine (RBM) and Deep Convolutional Generative Adversarial Networks (DCGAN), the IQP approach achieves competitive distributional alignment while using substantially fewer training snapshots and a small latent block, supporting the use of QCLI/CCI as practical indicators for locating IQP-aligned domains and advancing generative quantum utility.

翻译：我们提出了一种关联-复杂性映射作为实用诊断工具，用于判断现实世界数据分布是否在结构上与IQP型量子生成模型对齐。该映射通过两个互补指标表征：(i) 量子关联相似性指标，通过数据集的关联阶（沃尔什-哈达玛/傅里叶）功率谱按相互作用阶聚合计算，并利用与独立同分布二项参考分布的Jensen-Shannon散度进行量化；(ii) 经典关联复杂性指标，定义为未被最优Chow-Liu树近似捕获的总关联比例，并以总关联归一化。我们通过将QCLI与支持集失配机制关联提供理论支持：对于采用MMD目标训练的固定架构IQP族，较高的QCLI意味着更小的不可约近似下限。利用该映射，我们识别出经典湍流数据同时具备IQP兼容性与经典复杂性（高QCLI/高CCI）。基于此定位，我们采用可逆浮点-比特串表示和隐参数自适应方案，通过学习并插值低维隐轨迹，在时间序列上复用紧凑的IQP电路。在与经典模型（如受限玻尔兹曼机和深度卷积生成对抗网络）的比较评估中，IQP方法在使用显著更少训练快照和小型隐模块的条件下，实现了具有竞争力的分布对齐效果，这支持了QCLI/CCI作为定位IQP对齐领域和推进生成式量子效用的实用指标。