[Paper Review] Toward Generative Quantum Utility via Correlation-Complexity Map

Chen-Yu Liu, Leonardo Placidi+2 more|arXiv (Cornell University)|Mar 6, 2026

Quantum many-body systems0 citations

TL;DR

This paper introduces a Correlation–Complexity Map with two indicators, QCLI and CCI, to diagnose real-world data for compatibility with IQP-type quantum generative models, and demonstrates a turbulence dataset case study with a latent-adaptation IQP generator.

ABSTRACT

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.

Motivation & Objective

• Provide practical indicators to assess whether a real-world dataset aligns with IQP-type generative biases.
• Develop a two-dimensional Correlation–Complexity Map (QCLI vs. CCI) to separate datasets by quantum compatibility and classical complexity.
• Demonstrate the approach on a turbulence dataset and show an efficient latent-adaptation IQP generator.
• Bridge data representations from floats to bits to enable IQP-based generative modeling of continuous data.
• Validate the workflow against classical generative models to argue practical indicators for locating IQP-aligned domains.

Proposed method

• Define Quantum Correlation–Likeness Indicator (QCLI) as the Jensen–Shannon divergence between the dataset’s Walsh–Hadamard order spectrum and a binomial i.i.d. reference.
• Compute Classical Correlation–Complexity Indicator (CCI) as 1 minus the ratio of the optimal Chow–Liu tree’s captured total correlation to the total correlation.
• Use the Correlation–Complexity Map by plotting (I_QCLI, I_CCI) to identify IQP-compatible regimes.
• Provide a theoretical link showing higher I_QCLI reduces irreducible MMD floors for fixed-architecture IQP families under an MMD objective.
• Implement a float-to-bitstring representation to enable IQP modeling of turbulence data, with a latent-parameter adaptation that reuses a compact IQP circuit across time steps.
• Conduct empirical probing of the QCLI–MMD mechanism with datasets generated from order-4 IQP circuits and fixed-architecture learners to illustrate performance under support mismatch.

Experimental results

Research questions

• RQ1 Can QCLI quantify how quantum-compatible a real-world dataset is with IQP-type generators?
• RQ2 Does CCI effectively measure the degree of irreducible high-order dependencies beyond pairwise structure in data?
• RQ3 Does the combination (I_QCLI, I_CCI) meaningfully separate datasets into IQP-compatible versus non-compatible regimes?
• RQ4 Can a latent-adaptation IQP framework efficiently model temporal turbulence data using a fixed core circuit?
• RQ5 Do IQP-based models remain competitive with classical baselines when data and training resources are limited?

Key findings

• The Correlation–Complexity Map yields a two-axis landscape (I_QCLI, I_CCI) that separates datasets by quantum compatibility and classical complexity.
• Classical turbulence data occupy a high-I_QCLI and high-CCI regime, suggesting potential IQP compatibility despite classical complexity.
• An invertible float-to-bitstring representation enables IQP-based generative modeling of turbulence with a small latent block.
• A latent-parameter adaptation enables reusing a compact IQP circuit to generate unseen temporal turbulence snapshots, achieving competitive performance with limited data.
• Compared to RBM and DCGAN baselines, the IQP approach demonstrates strong distributional alignment with substantially fewer training snapshots.