Quantum Computation and Simulation using Fermion-Pair Registers*

Fermion pairs have recently been shown as a scalable and robust quantum register with long coherent time, providing promising applications for quantum information processing. In this work, we develop schemes for programmable universal quantum computation and quantum many-body simulations based on the quantum register of fermion pairs. We utilize the fermion hopping J to design the SWAP gate, which serves as a prelimary for applying gates between arbitrary two qubits. We engineer an effective Hamiltonian using J and the tunable Feshbach interaction U in a perturbative regime J « U, which can generate the controlled-phase gate with infidelity scaling as (J/U)⁴. By modulating the U term, the platform can be also used for 2D quantum Ising model simulations. To calibrate quantum gates and probe quantum dynamics, we further propose a new shadow process tomography protocol with minimal experimental requirements and high sampling efficiency. Our work opens up a number of new opportunities for quantum computation and simulation with fermion pair registers.