Extended Data Fig. 3: Measurement-based topological state preparation.

a, Experimental protocol used for measurement-based preparation of the topological state. First, a ZXXZ toric-code state is prepared on one data qubit sublattice (black circles) using ancilla qubits (blue circles). After midcircuit measurement and feedfoward, this prepares the ZXXZ toric-code state. The weight-four ZXXZ operators are then extended to weight-6 operators with parallel controlled-Y (CY) operations with a fresh data qubit sublattice originally in \(| 0\rangle \) (green circles). In the case that the ZZ link (where the CY gates were applied) are +1, this weight-6 operator is equal to the plaquette operators W_p. This sequence indeed ensures that these ZZ operators are all +1, owing to the propagation of the single-qubit Z stabilizer on the green qubit sublattice through the CY operation, which results in the weight-2 ZZ stabilizers. b, Implementation of the encoding steps in parallel across the full array. The top row of ancillas also performs gates with the bottom row of data qubits. c, Experimental layout, with gate orientation and an example plaquette shown, and ancilla qubit motions for preparing the ZXXZ surface code state on one half of the data qubits. We perform the periodic ancilla measurement step first, such that all other qubits are still in \(| 0\rangle \) and do not experience most of the Rydberg gate errors. d, Atom positions for midcircuit readout and feedfoward, with an example feedforward pattern applied (indicated by orange circles). The midcircuit image is analyzed, and then based on our decoding algorithm, an FPGA outputs a series of digital TTLs which determine which atoms have a local Raman gate applied. e, Data qubit positions for the parallel controlled-Y (CY) operation, completing the state preparation sequence. The sublattice denoted by black circles gets picked up by AOD traps and shifted to the left to perform the parallel CY. This sublattice then remains in AOD traps for the Floquet circuit.