Quantum Computation and Simulation using Fermion Pair Registers

Abstract

Quantum gas microscopes provide a powerful toolbox for probing quantum many-body physics. Recently, an exciting progress has been reported on realizing a large-scale quantum register of fermion pairs with a quantum gas microscope, in which tightly localized fermion pairs are used to encode qubits exhibiting long coherence time and robustness against laser intensity noise. In this thesis, we propose and analyze a new approach for quantum computation and simulation, leveraging fermionic particles on optical lattices under quantum gas microscopes. We engineer the SWAP gate and high-fidelity controlled-phase gates by adjusting the fermion hopping as well as the Feshbach interaction between two fermions. These gates, together with previously demonstrated single-qubit rotations, form a universal gate set. Furthermore, by modulating the strength of the Feshbach interaction, one can realize 2D quantum Ising Hamiltonians in a programmable geometry with tunable transverse and longitudinal fields. In addition, we present a sample-efficient protocol to characterize engineered gates and Hamiltonian dynamics by improving classical shadow process tomography to require minimal experimental controls. Our work opens up new opportunities to harness existing ultracold quantum gas techniques for quantum information processing.