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  • Open Access

Shallow instantaneous quantum polynomial-time circuits for generative modeling on noisy intermediate-scale quantum hardware

Oriol Balló-Gimbernat1,2,3,*, Marcos Arroyo-Sánchez1,2,3, Paula García-Molina2, Adan Garriga1, and Fernando Vilariño2,3

  • *Contact author: oriol.ballo@eurecat.org
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Phys. Rev. A 113, 042617 – Published 15 April, 2026

DOI: https://doi.org/10.1103/jcdk-q3xc

Abstract

Generative modeling is one of the most promising applications of quantum machine learning, yet training and deploying quantum generative models (QGMs) on near-term hardware remains effectively intractable due to prohibitive gradient estimation and implementation costs. We propose a resource-efficient approach based on shallow instantaneous quantum polynomial-time (IQP) circuits that circumvents these bottlenecks by leveraging efficient classical training while retaining the guarantee of sampling hardness. To validate this approach, we formalize graph generation as a hierarchy of physical correlations, allowing us to map abstract data features—such as edge density and bipartiteness—directly to the quantum observables required to learn them. We validate our protocol through demonstrations both on real hardware (from 28 to 153 qubits) and simulations (28 qubits). Results show that while global structural features exhibit significant degradation beyond 91 qubits, our models achieve high-precision reproduction of local correlations, even up to 153 qubits. These findings establish shallow IQP circuits as a robust, scalable candidate for generative tasks on current noisy intermediate-scale quantum (NISQ) devices.

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Outline

Information

Phys. Rev. A 113, 042617– Published 15 April, 2026
  • Received 13 November 2025
  • Accepted 12 March 2026
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