  We propose and analyze an approach to realize quantum computation and
simulation using fermionic particles under quantum gas microscopes. Our work is
inspired by a recent experimental demonstration of large-scale quantum
registers, where tightly localized fermion pairs are used to encode qubits
exhibiting long coherence time and robustness against laser intensity noise. We
describe how to engineer the SWAP gate and high-fidelity controlled-phase gates
by adjusting the fermion hopping as well as Feshbach interaction strengths.
Combined with previously demonstrated single-qubit rotations, these gates
establish the computational universality of the system. Furthermore, we show
that 2D quantum Ising Hamiltonians with tunable transverse and longitudinal
fields can be efficient simulated by modulating Feshbach interaction strengths.
We present a sample-efficient protocol to characterize engineered gates and
Hamiltonian dynamics based on an improved classical shadow process tomography
that requires minimal experimental controls. Our work opens up new
opportunities to harness existing ultracold quantum gases for quantum
information sciences.
