Unconventional geometric quantum computation robust to residual crosstalk in a superconducting circuit

Ongoing advancements in geometric quantum computation, including the continuous refinement of evolution paths and the integration of optimal control techniques, have demonstrated their significant resilience against control errors resulting from imprecise operations. However, as the number of qubits increases with the scaling up of quantum systems, the emergence of residual crosstalk imposes demands on the error tolerance of geometric control. Here, we propose a crosstalk-resistant unconventional geometric quantum computation scheme in a superconducting circuit. This approach significantly broadens the error tolerance of geometric control by leveraging the additional parameter degrees of freedom available in the unconventional geometric process, along with further path optimization. Compared to conventional geometric gates and dynamical Rabi gates, our unconventional geometric gates can exhibit superior crosstalk resistance regardless of the gate type, and still maintain robustness against the main systematic error in superconducting systems. Additionally, our numerical simulations thoroughly evaluate the combined impacts of leakage errors and decoherence, validating the high-fidelity performance of our unconventional geometric gates.