Discovery of connectivity-trainability trade-off of IQP Circuits for Hamiltonian Optimization
The study investigated how circuit connectivity affects Instantaneous Quantum Polynomial-time (IQP) circuits used for Hamiltonian optimization. The results show a trade-off: fully connected circuits offer high expressivity and better optimization performance but suffer from rapid gradient variance and barren plateaus. Single-Z circuits are trainable but lack expressivity, while circular connectivity offers a balanced intermediate performance.