Hybrid quantum-classical analog simulation of two-dimensional Fermi-Hubbard models with neutral atoms

Abstract

We experimentally study the two-dimensional Fermi-Hubbard model using a Rydberg-based quantum processing unit in the analog mode. Our approach avoids encoding directly the original fermions into qubits and instead relies on reformulating the original model onto a system of fermions coupled to spins and then decoupling them in a self-consistent manner. We then introduce the auxiliary spin solver: this hybrid quantum-classical algorithm handles a free-fermion problem, which can be solved efficiently with a few classical resources, and an interacting spin problem, which can be naturally encoded in the analog quantum computer. This algorithm can be used to study both the equilibrium Mott transition as well as non-equilibrium properties of the original Fermi-Hubbard model, highlighting the potential of quantum-classical hybrid approaches to study strongly correlated matter.

Figures (5)

• Figure 1: (a) Sketch of the anisotropic Fermi-Hubbard model and the auxiliary spin mapping: the original interacting spinful Hamiltonian is mapped to a model of spinless fermions coupled to a quantum Ising model. (b) Hybrid quantum-classical solver. A mean-field decoupling is performed on $\tilde{H}_{f-s}$. Then the solver can be used to either solve the ground-state physics through a hybrid quantum-classical loop or to solve the dynamics with the help of the QPU.
• Figure 2: Results for the equilibrium loop. (a) Metal-to-Mott transition in the anisotropic FHM ($t_y=0.65t_x$) using the auxiliary spin mapping and the QPU or DMRG to solve the ground state of the spin problem. The uncertainty area of the DMRG line accounts for a systematic error in the QPU detuning, $\delta_0$. (b)-(e) Variation of the observables and QPU setpoints through the iterative loop of the hybrid quantum-classical solver.
• Figure 3: Dynamics of the quasiparticle weight $Z_\text{bulk}$ after a sudden interaction quench in a square lattices of size $N=6\times 6$. We compare the QPU data with ideal MPS simulations of the QPU Hamiltonian, and also MPS simulations of the noise model. The inset in (c) shows the equilibrium curve of $Z_\text{bulk}$ for the the same $6\times 6$ square lattice, using the purely classical auxiliary-spin method. The values of post-quench $U_f$ in (a)-(c) are indicated as vertical lines.
• Figure S1: Discrepancy between the algorithm using the original auxiliary spin Hamiltonian $H_s$ and its QPU approximation $H_\text{QPU}$. The figure shows the evolution of the bulk quasiparticle weight obtained after 5 iterations loops at each $U/t_x$. Note that here we use the fermionic classical solver and the classical DMRG solver for both $H_s$ and $H_\text{QPU}$.
• Figure S2: Frequency analysis of the quasiparticle weight oscillations from Fig. \ref{['fig:figure3']}. The dashed line represents the smoothed QPU data.