Compiling the surface code to crossbar spin qubit architectures

Spin qubits in quantum dots provide a promising platform for realizing large-scale quantum processors since they have a small characteristic size of a few tens of nanometers. One difficulty of controlling e.g., a few thousand qubits on a single chip is the large number of control lines. The crossbar control architecture has been proposed to reduce the number of control lines exploiting shared control among the qubits. Here, we compile the surface code cycle to a pulse sequence that can be executed in the crossbar architecture. We decompose the quantum circuits of the stabilizer measurements in terms of native gates of the spin-qubit architecture. We provide a routing and scheduling protocol, and construct a gate voltage pulse sequence for the stabilizer measurement cycle. During this protocol, coherent phase errors can occur on idle qubits, due to the operational constraints of the crossbar architecture. We characterize these crosstalk errors during the stabilizer measurement cycle, and identify an experimentally relevant parameter regime where the crosstalk errors are below the surface code threshold. Our results provide design guidelines for near-term qubit experiments with crossbar architectures.