Simulating Parity Magnetic Effects with Superconducting Qubits*

A highly tunable diamond energy diagram is constructed with four coupled superconducting qubits. We parametrically modulate their tunable couplers, mapping the momentum space to parameter space and realizing 4D Dirac-like Hamiltonian with fourfold degenerate points. Then we apply an additional pump microwave field to manipulate the energy of tensor monopoles, providing an effective magnetic and pseudo-electric field. By using non-adiabatic response methods we obtain the fractional second Chern number. Combining these elements we obtain the topological current of parity magnetic effect. Our experiments pave the way to explore the higher-dimensional topological states of matter and deepen our understanding of the topological effects.