We propose and validate a framework for analog simulation of the Heisenberg spin model using a circuit-quantum-electrodynamics (circuit-QED) platform. To this end, we develop an $f$-deformed boson representation of the $SU(2)$ algebra, which includes the Holstein–Primakoff and Dyson–Maleev transformations as special cases. While this representation is generally non-Hermitian, for spin-$1/2$ systems, we introduce a procedure to circumvent this limitation, showing that the mapping yields the extended Bose-Hubbard (EBH) Hamiltonian. For the experimental realization of this EBH model, we design a scalable circuit-QED architecture based on an engineered Josephson junction array. Numerical simulations confirm that the microwave photon dynamics in this simulator accurately reproduces the original spin dynamics. Our work establishes an experimentally accessible method for investigating complex quantum spin dynamics in a highly controllable bosonic setting.

Close

PrevNext

View figure in article

• Circuit quantum electrodynamics
• Quantum simulation
• Spin dynamics
• Josephson junctions
• Bose-Hubbard model
• Exact diagonalization
• Heisenberg model
• Microwave techniques