Fermionic Hamiltonian engineering via local operations

Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible target Hamiltonians from a fixed system Hamiltonian defined by the hardware.

We introduce a new framework for fermionic Hamiltonian engineering based on conjugating free evolution under the system Hamiltonian with sequences of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently via a linear program. By interleaving system evolution with these local unitaries, our method realizes effective time evolution under a broad class of target Hamiltonians with intrinsic robustness to implementation errors. In particular, we demonstrate that arbitrary complex tunnelling amplitudes can be realized, constrained only by the connectivity of the underlying system Hamiltonian. Our approach mitigates challenges such as uncontrolled heating and the demand for high-precision control commonly encountered in Floquet engineering.