Figure 7

Scheme of the magnitude of the couplings, \(\pmb{g_{l}}\) , of the superconducting qubits \(\pmb{i,\ldots,j}\) with the transmission line resonator as a function of time for the simulation of fermionic hopping terms. This sketch shows how sequences of rotations and nonlocal multiqubit gates gives place to interactions of the form \(b_{i}^{\dagger}b_{j}+b_{j}^{\dagger}b_{i}\), which can be written in terms of spin operators as \(-(\sigma_{i}^{x}\otimes\sigma_{i+1}^{z}\otimes\cdots\otimes \sigma_{j-1}^{z}\otimes\sigma_{j}^{x}+\sigma_{i}^{y}\otimes \sigma_{i+1}^{z}\otimes \cdots\otimes\sigma_{j-1}^{z}\otimes\sigma_{j}^{y})/2\). Multiqubit gates are marked with red color where all the couplings suffer a frequency modulation [27]. Single-qubit rotations are implemented by coupling a single qubit to the resonator. They are marked with green color for a phase of \(\pi/4\) and with blue for a phase-dependent single-qubit rotation, \(U_{\sigma_{y}}(\phi)\), where the phase ϕ is proportional to the simulated time evolution of the hopping term. Note that all the qubits between sites i and j play a role in this interaction in order to fulfill the Jordan-Wigner mapping.