Toward Generative Quantum Utility via Correlation-Complexity Map
This work addresses the challenge of identifying domains where quantum generative models can be practically useful, which is an incremental step toward advancing generative quantum utility.
The paper tackles the problem of determining when real-world data distributions are suitable for quantum generative models by proposing a Correlation-Complexity Map as a diagnostic tool, and demonstrates its utility by applying it to classical turbulence data, achieving competitive distributional alignment with fewer training snapshots compared to classical models like RBM and DCGAN.
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.