Fig. 9
The \({[3,1,3]}_{1}\) and the resulting logical graphs of the DW2X and DW2000Q devices. a A logical qubit of the \({[3,1,3]}_{1}\) is formed by connecting three qubits in one-half of the unit cell to a single qubit on the other half of the unit cell. The three qubits are called the “data qubits” and the single qubit plays the role of a “penalty qubit.” The data qubits are tied together with the penalty qubit by ferromagnetic couplings to ensure consistent evolution of each of the three data qubits. Each unit cell now contains two logical qubits. b, c Each logical qubit connects to its neighbor in the same cell via the intra-cell couplings and connects to its horizontal or vertical neighbor via the inter-cell couplings. This construction gives rise to a graph of degree \(3\) which is a minor embedding of the Chimera graph. b is the logical graph for the DW2X, c for the DW2000Q. In both graphs, green (red) circle denote operational (inactive) logical qubits. Orange circles denote logical qubits with intact data qubits, but an inactive penalty qubit. The lines denote the active couplings between the operational logical qubits. For each problem size \(L\), we used a subgraph formed by taking an \(L\times L\) square starting from the top left corner.
