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

TL;DR

This paper introduces a resource-efficient quantum generative modeling approach using shallow IQP circuits, enabling scalable and high-precision local correlation generation on noisy intermediate-scale quantum hardware.

Contribution

It proposes a novel shallow IQP circuit-based method for quantum generative modeling that balances classical training efficiency with quantum sampling hardness, suitable for NISQ devices.

Findings

High-precision local correlation reproduction up to 153 qubits

Effective on real hardware from 28 to 153 qubits

Structural features degrade beyond 91 qubits

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.