Discovery of connectivity-trainability trade-off of IQP Circuits for Hamiltonian Optimization

2026-06-23

AI Summary

This study investigates the performance and trainability of Instantaneous Quantum Polynomial-time (IQP) circuits in Hamiltonian optimization tasks, with a focus on how circuit architecture influences optimization capability. Through systematic numerical experiments and theoretical analysis, the authors evaluate training efficacy across IQP circuits with varying connectivity structures. They uncover and quantify, for the first time, a trade-off between connectivity and trainability: while higher connectivity enhances expressive power, it also exacerbates vanishing gradients, thereby hindering optimization efficiency; in contrast, moderately connected architectures facilitate more reliable convergence to low-energy states. These findings highlight the critical role of circuit topology in variational quantum optimization and offer practical guidance for designing scalable and trainable quantum algorithms.

Abstract

Instantaneous Quantum Polynomial-time (IQP) circuits are promising candidates for near-term quantum advantage due to the conjectured classical hardness of their sampling task. However, their capabilities for optimization remain largely unexplored. We present a systematic investigation of the performance and trainability of IQP circuits for Hamiltonian optimization. Our results reveal a trade-off between optimization performance and circuit connectivity, demonstrating that the circuit structure plays a key role in determining the ability of IQP circuits to reach low-energy states.

Problem

• IQP circuits
• Hamiltonian optimization
• connectivity
• trainability
• quantum advantage

Innovation

• IQP circuits
• Hamiltonian optimization
• connectivity-trainability trade-off
• quantum advantage
• circuit structure