Parallel Gate Fidelity of Flip-Flop Qubits in Small 1D- and 2D-Arrays in a Noisy Environment

The long coherence time of donor atom nuclear spin states and of its bounded electron in ${}^{28}\mathrm{Si}$ can be exploited to define a qubit. This work is focused on a type of donor- and quantum dot-based qubit, the flip-flop (FF) qubit, that leverages antiparallel electron-nuclear spin states of a ${}^{31}P$ donor atom controlled by an electric field. It can provide long-range inter-qubit interactions in the order of some hundreds of nanometers, thus relaxing the common constraints and tolerances on inter-qubit distances in donor-based qubits. Simulation results of linear array (LA) and square array (SA) of four FF qubits are presented to study the effect of noise, idle qubits, and simultaneous gating (parallel gating) on gate fidelity. The impact of noise and qubit mutual coupling for both considered types of array are presented and the obtained fidelity results are compared.