A universal and efficient fermionic variational quantum simulator

We design a universal framework for fermionic quantum hardware that runs efficient variational algorithms to simulate generic many-body systems beyond the hardware's native interactions. Our theoretical and numerical analysis shows that one can compute the ground-state properties of target Hamiltonians with a fixed total relative error in a time that is independent of the system size, offering an exponential speedup over naïve classical algorithms. We provide theory and evidence that this holds for energy, as well as more intricate physical observables in three qualitatively distinct models – the repulsive Hubbard model; a Hubbard model augmented with nearest-neighbor attractive interactions, which introduces the phenomenon of pairing; and the Hofstadter-Hubbard model, which introduces a gauge field and fractional quantum Hall physics. This work demonstrates the usefulness fermionic quantum hardware for practical quantum simulations of fermionic many-body systems.