Numerical Optimization of Two-Qubit Gates in Silicon Flip-Flop Qubit Arrays under Electrical Control

Abstract:Silicon-based donor flip-flop qubits offer a promising path toward scalable, fault-tolerant quantum computing by combining the long coherence times of nuclear spins with fast, fully electrical control and long-range dipole-dipole coupling between qubits. However, realizing high-fidelity entangling operations in this platform remains challenging. The entangling interaction is intrinsically coupled to electron orbital dynamics, which can lead to leakage into non-computational states and unwanted phase accumulation. Furthermore, in multi-qubit architectures, residual dipolar couplings from spectator qubits distort the effective interaction landscape. In this work, we employ a numerical simulation framework, FlipFlopQSim, that models the spin-orbital dynamics of interacting flip-flop qubits to extract effective logical operations from realistic electrical control pulses. Using Makhlin invariants, we map the entangling landscape generated by electrically controlled dipole-dipole interactions and identify operating regions locally equivalent to canonical two-qubit gates, such as $\sqrt{iSWAP}$ and $iSWAP$. We then optimize the control parameters of physically realizable, electrically driven $R_z$ rotations to implement the necessary local corrections and maximize composite gate fidelity. Finally, we scale our analysis to multi-qubit registers with various geometries and connectivity patterns to evaluate spectator-induced distortions. Our results demonstrate that high-fidelity entangling operations cannot be optimized in isolation; rather, they require a co-design approach that simultaneously optimizes pulse control, local phase compensation, and physical device geometry. This work provides a robust numerical framework for assessing the scalability of electrically controlled silicon quantum processors and outlines key design principles for robust multi-qubit gate implementation.

13 pages, 6 figures. The numerical simulator "FlipFlopQSim" developed for this work and used to generate the results presented in this article is publicly available at DOI: https://doi.org/10.5281/zenodo.21669875

arXiv:2607.29123 [quant-ph]

(or arXiv:2607.29123v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.29123 arXiv-issued DOI via DataCite (pending registration)