The Jordan-Wigner transformation maps a one-dimensional (1D) 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.
We present a method for calculating the ground state energy of the Fermi-Hubbard model leveraging Rydberg atom processors and sample-based quantum diagonalization (SQD). By exploiting the perturbative relationship between the Fermi-Hubbard and Heisenberg models, the procedure samples from the Heisenberg model as prepared on the Rydberg atom processor, and uses the samples to diagonalize the Fermi-Hubbard model for large U. We include anisotropy and next-nearest-neighbor interactions and discuss the relevant regime for quasi-superconductivity in the 1-dimensional Fermi- Hubbard model. Numerical and experimental results on the Aquila quantum processor are presented for ground state energy calculations as well as the chemical potential. We find that the Heisenberg model sampling in the studied regime is sufficient to converge near to the ground state for up to 56 qubits, and we see a clear advantage of Rydberg atom sampling as opposed to random sampling even with 10x more samples for diagonalization. We also present a gate-based implementation of the gate-based SQD algorithm on IBM Quantum hardware for 56-qubit Hubbard model as a benchmark. Finally, we provide a gap analysis for studying emergent superconductivity using this method.