Parallel Gate Operations Fidelity in a Linear Array of Flip-Flop Qubits

Quantum computers based on silicon are promising candidates for long term universal quantum computation due to the long coherence times of electron and nuclear spin states. Furthermore, the continuous progress of micro- and nano-electronics, also related to the scaling of metal-oxide-semiconductor systems, makes it possible to control the displacement of single dopants thus suggesting their exploitation as qubit holders. Flip-flop qubit is a donor based qubit where interactions between qubits are achievable for distance up to several hundred nanometers. In this work, a linear array of flip-flop qubits is considered and the unwanted mutual qubit interactions due to the simultaneous application of two one-qubit and two two-qubit gates are included in the quantum gate simulations. In particular, by studying the parallel execution of couples of one-qubit gates, namely Rz(-pi 2)$R_z(-\frac{\pi }{2})$ and Rx(-pi 2)$R_x(-\frac{\pi }{2})$, and of couples of two-qubit gate, that is, iSWAP$\sqrt {\text{i}\text{SWAP}}$, a safe inter-qubit distance is found where unwanted qubit interactions are negligible thus leading to parallel gates fidelity up to 99.9%.