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Table 1 We list the set \(\pmb{\mathcal{P}_{\mathrm{reduction}}}\) of all the two-qubit couplings required to measure the plaquette p and the six vertex operators of Figure  2 , following the plaquette reduction method of Ref. [ 9 ]

From: Methodology for bus layout for topological quantum error correcting codes

Primary qubit Qubits to which the primary qubit couples
\(\alpha_{0}\) \(i_{6}\)
\(a_{1}\) \(a_{6}\), \(i_{1}\), \(i_{2}\), \(i_{6}\), \(\alpha_{1}\)
\(a_{2}\) \(i_{1}\), \(i_{2}\), \(i_{3}\), \(i_{6}\), \(\alpha_{2}\)
\(a_{3}\) \(i_{2}\), \(i_{3}\), \(i_{4}\), \(i_{6}\), \(\alpha_{3}\)
\(a_{4}\) \(i_{3}\), \(i_{4}\), \(i_{5}\), \(i_{6}\), \(\alpha_{4}\)
\(a_{5}\) \(i_{4}\), \(i_{5}\), \(i_{6}\), \(\alpha_{5}\)
\(a_{6}\) \(a_{1}\), \(i_{1}\), \(i_{2}\), \(i_{6}\), \(\alpha_{6}\)
\(i_{1}\) \(a_{1}\), \(a_{2}\), \(a_{6}\), \(i_{2}\), \(i_{3}\), \(i_{6}\), \(\alpha_{1}\), \(\alpha_{6}\)
\(i_{2}\) \(a_{1}\), \(a_{2}\), \(a_{6}\), \(i_{1}\), \(i_{3}\), \(i_{4}\), \(i_{6}\), \(\alpha_{1}\), \(\alpha_{2}\)
\(i_{3}\) \(a_{2}\), \(a_{3}\), \(a_{4}\), \(i_{1}\), \(i_{2}\), \(i_{4}\), \(i_{5}\), \(i_{6}\), \(\alpha_{2}\), \(\alpha_{3}\)
\(i_{4}\) \(a_{3}\), \(a_{4}\), \(a_{5}\), \(i_{2}\), \(i_{3}\), \(i_{5}\), \(i_{6}\), \(\alpha_{3}\), \(\alpha_{4}\)
\(i_{5}\) \(a_{4}\), \(a_{5}\), \(i_{3}\), \(i_{4}\), \(i_{6}\), \(\alpha_{4}\), \(\alpha_{5}\)
\(i_{6}\) \(\alpha_{0}\), \(a_{1}\), \(a_{2}\), \(a_{3}\), \(a_{4}\), \(a_{5}\), \(a_{6}\), \(i_{1}\), \(i_{2}\), \(i_{3}\), \(i_{4}\), \(i_{5}\), \(\alpha_{5}\), \(\alpha_{6}\)
\(\alpha_{1}\) \(a_{1}\), \(i_{1}\), \(i_{2}\)
\(\alpha_{2}\) \(a_{2}\), \(i_{2}\), \(i_{3}\)
\(\alpha_{3}\) \(a_{3}\), \(i_{3}\), \(i_{4}\)
\(\alpha_{4}\) \(a_{4}\), \(i_{4}\), \(i_{5}\)
\(\alpha_{5}\) \(a_{5}\), \(i_{5}\), \(i_{6}\)
\(\alpha_{6}\) \(a_{6}\), \(i_{1}\), \(i_{6}\)
  1. The data and ancillary qubits are labeled according to the notation of Figure 2.