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Discovery of connectivity-trainability trade-off of IQP Circuits for Hamiltonian Optimization
Quoc Chuong Nguyen·June 23, 2026
cs.SImath.NAphysics.data-anQuantum Physics
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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.