Variational Hamiltonian Ansatz for 1D Hubbard chains

To circumvent noise limitations of current day quantum hardware, hybrid quantum-classical methods have been proposed. Among those, the Variational Quantum Eigensolver (VQE) has been implemented on intermediate size quantum computers. Here, the quantum computer produces a parametrized state, whose energy is minimized in a classical-quantum optimization loop. In this work we investigate the simulation of the strongly correlated ground states of the 1D Hubbard model on a quantum computer using the Variational Hamiltonian Ansatz. We quantify how short circuit depth affects the quality of optimized states in terms of fidelity and physical properties. We show that short VHA ansätze are still able to capture qualitatively the main features of the 1D Hubbard model with strong Coulomb repulsion such like the decreasing number of doubly occupied sites or spin correlations, indicating that the variational states lie in a physically relevant subspace of the total Hilbert space. We perform simulations of the algorithm including noise models for small size Hubbard chains. Although performance was greatly affected by hardware noise, zero-noise extrapolation techniques such as Richardson extrapolation allowed the partial mitigation of noise from our calculation.