Fig. 1

Experimental scheme for the realization of the lattice Hamiltonian. a States \(\left| 2 \right\rangle\) and \(\left| 1 \right\rangle\) of a transmon are used as the energy levels of an artificial spin-1/2 particle, whose three components may be denoted by the three Pauli matrices σ̂_1,2,3. \(\left| 0 \right\rangle\) is chosen as an ancillary level to probe the eigenvalues of a Hamiltonian. Microwaves with various frequencies, phases, and amplitudes are applied for the construction of a semimetal Hamiltonian and circuit QED readout, respectively. The detail of the qubit manipulation can be found in the supplementary. b The constructed Hamiltonian is implemented by modulating the microwave amplitude, frequency, and phase, mapping to the momentum space of a square lattice