Experimental demonstration of breakeven for a compact fermionic encoding

Abstract

Solving the Fermi–Hubbard model is a central task in the study of strongly correlated materials. Digital quantum computers can, in principle, be suitable for this purpose, but have so far been limited to quasi-one-dimensional models. This is because of exponential overheads caused by the interplay of noise and the non-locality of the mapping between fermions and qubits. Here we use a trapped-ion quantum computer to experimentally demonstrate that a recently developed local encoding can overcome this problem. In particular, we show that suitable reordering of terms and application of circuit identities—a scheme called corner hopping—substantially reduces the cost of simulating fermionic hopping. This enables the efficient preparation of the ground state of a 6 × 6 spinless Fermi–Hubbard model encoded in 48 physical qubits. We also develop two error mitigation schemes for systems with conserved quantities, based on local postselection and on extrapolation of local observables, respectively. Our results suggest that Fermi–Hubbard models beyond classical simulability can be addressed by digital quantum computers without large increases in gate fidelity.