Transversal Logical Clifford Gates on the Rotated Surface Code with Reconfigurable Neutral Atom Arrays

We propose hardware-efficient schemes for implementing logical h and s gates transversally on the rotated surface code with reconfigurable neutral atom arrays. Our protocol for logical s gates utilizes the time dynamics of the data and ancilla qubits during syndrome extraction (SE). In particular, we move beyond traditional schemes where transversal logical gates take place between two SE rounds and instead embed our fold-transversal logical operation within a single SE round, leveraging the fact that data and ancilla qubits can be morphed into an unrotated surface code state halfway through an SE round. Under circuit noise, we observe that the performance of our s gate protocol is comparable to that of the quantum memory. For logical h gates, we first develop a simple strategy to rotate code patches efficiently with two sets of 2D acousto-optic deflectors (2D-AOD). We also propose a new transversal h gate protocol, based on the same principle as our s gate protocol, to remove the need for an additional set of 2D-AOD. Together with transversal logical cnot gates, our protocols complete a transversal logical Clifford gate set on the rotated surface code and allow for efficient implementation on neutral atom array platforms.