Phase-Sensitive Measurements on a Fermi-Hubbard Quantum Processor

Fermionic quantum processors are a promising platform for quantum simulation of correlated fermionic matter. In this work, we study a hardware-efficient protocol for measuring complex expectation values of the time-evolution operator, commonly referred to as Loschmidt echoes, with fermions in an optical superlattice. We analyze the algorithm for the Fermi-Hubbard model at half-filling as well as at finite doping. The method relies on global quench dynamics and short imaginary time evolution, the latter being realized by architecture-tailored pulse sequences starting from a product state of plaquettes. Our numerical results show that complex Loschmidt echoes can be efficiently obtained for large many-body states over a broad spectral range. This allows one to measure spectral properties of the Fermi-Hubbard model, such as the local density of states, and paves the way for the study of finite-temperature properties in current fermionic quantum simulators.