Emulating the one-dimensional Fermi-Hubbard model by a double chain of   qubits
  The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with XX and ZZ couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the ZZ interaction arises due to an inductive coupling and the XX interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators. 
Jan-Michael Reiner, Michael Marthaler, Jochen Braum\"uller, Martin   Weides, and Gerd Sch\"on
quant-ph cond-mat.mes-hall cond-mat.supr-con