Fig. 3: Topological surface code and toric code states using mobile ancilla qubit arrays.
From: A quantum processor based on coherent transport of entangled atom arrays
a, Graph state realizing the surface code. Left: the circuit depicts formation of the graph state by use of mobile ancilla qubits; each move corresponds to performing a CZ gate with a neighbouring data qubit (illustrated in box). The logical |+⟩L state is created upon projective measurement of the ancilla qubits in the X basis. Right: stabilizers and logical operators of the code. b, Measured X-plaquette and Z-star stabilizers of the resultant surface code, along with logical operators with and without error detection (implemented in postselection). c, Implementation of the toric code. Top: graph state realizing the two logical-qubit product state \({|+\rangle }_{L}^{(1)}{|+\rangle }_{L}^{(2)}\) of the toric code upon projective measurement of the ancilla qubits in the X basis. Bottom: images showing the movement steps implemented in creating and measuring the toric code state (Supplementary Video 1). The blue shading in the final image represents a local rotation on the data qubit zone. d, Measured X-plaquette and Z-star stabilizers, along with logical operators for the two logical qubits with and without error detection (implemented in postselection).
