Inverse designed Hamiltonians for perfect state transfer and remote entanglement generation, and applications in superconducting qubits

Hamiltonian inverse engineering enables the design of protocols for specific quantum evolutions or target state preparation. Perfect state transfer (PST) and remote entanglement generation are notable examples, as they serve as key primitives in quantum information processing. However, Hamiltonians obtained through conventional methods often lack robustness against noise. Assisted by inverse engineering, we begin with a noise-resilient energy spectrum and construct a class of Hamiltonians, referred to as the dome model, that significantly improves the system's robustness against noise, as confirmed by numerical simulations. This model introduces a tunable parameter $m$ that modifies the energy-level spacing and gives rise to a well-structured Hamiltonian. It reduces to the conventional PST model at $m=0$ and simplifies to a SWAP model involving only two end qubits in the large-$m$ regime. To address the challenge of scalability, we propose a cascaded strategy that divides long-distance PST into multiple consecutive PST steps. Our work is particularly suited for demonstration on superconducting qubits with tunable couplers, which enable rapid and flexible Hamiltonian engineering, thereby advancing the experimental potential of robust and scalable quantum information processing.