Zi-Han Chen

Recent experimental progress on platforms with movable qubits motivates more efficient designs of logical operations by leveraging long-range connectivity. In our recent works, we address two bottleneck issues on the rotated surface code (RSC)—the logical S gate and T state preparation—by proposing a transversal logical S gate protocol (for the first time) and a new magic state cultivation (MSC) protocol (achieving an order of magnitude reduction in spacetime cost compared to the original MSC protocol). Both our protocols leverage the dynamics of circuits to perform desired logical operations efficiently. In our S gate protocol, we move beyond traditional schemes where transversal logical gates take place between syndrome extraction (SE) rounds. Instead, we embed our fold-transversal logical operation within a single SE round by leveraging the time dynamics of data and ancilla qubits during SE. In our MSC protocol, we co-design two types of codes—the RP code, a variant of the surface code on RP^2 (a non-orientable surface), and the SRP code, a self-dual CSS code—with compact circuits bridging between them to tightly knit fault-tolerant gadgets together and maintain high end-to-end efficiency. Our protocols, together with transversal CNOT and H gates, constitute a new way that fully leverages long-range connectivity to perform universal logical operations on the RSC.