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Table 3 The set \(\pmb{\mathcal{P}_{\mathrm{swapping}}}\) of all the two-qubit couplings required to measure the plaquette p and the six vertex operators of Figure  5 , following the plaquette swapping method of Ref. [ 28 ]

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

Primary Qubit

Qubits to which the primary qubit couples




\(i_{1}\), \(i_{2}\), \(\alpha_{1}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(i_{2}\), \(i_{3}\), \(\alpha_{2}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(i_{3}\), \(i_{4}\), \(\alpha_{3}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(i_{4}\), \(i_{5}\), \(\alpha_{4}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(i_{5}\), \(i_{6}\), \(\alpha_{5}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(i_{1}\), \(i_{6}\), \(\alpha_{6}\), \(\alpha_{7}\), \(\alpha_{8}\), \(\alpha_{9}\)


\(a_{1}\), \(a_{6}\), \(i_{2}\), \(i_{6}\), \(\alpha_{1}\), \(\alpha_{6}\), \(\alpha_{7}\), \(\alpha_{8}\), \(\alpha_{9}\)


\(a_{1}\), \(a_{2}\), \(i_{1}\), \(i_{3}\), \(\alpha_{1}\), \(\alpha_{2}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(a_{2}\), \(a_{3}\), \(i_{2}\), \(i_{4}\), \(\alpha_{2}\), \(\alpha_{3}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(a_{3}\), \(a_{4}\), \(i_{3}\), \(i_{5}\), \(\alpha_{3}\), \(\alpha_{4}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(a_{4}\), \(a_{5}\), \(i_{4}\), \(i_{6}\), \(\alpha_{4}\), \(\alpha_{5}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(a_{5}\), \(a_{6}\), \(i_{1}\), \(i_{5}\), \(\alpha_{5}\), \(\alpha_{6}\), \(\alpha_{7}\), \(\alpha_{8}\), \(\alpha_{9}\)


\(a_{1}\), \(i_{1}\), \(i_{2}\)


\(a_{2}\), \(i_{2}\), \(i_{3}\)


\(a_{3}\), \(i_{3}\), \(i_{4}\)


\(a_{4}\), \(i_{4}\), \(i_{5}\)


\(a_{5}\), \(i_{5}\), \(i_{6}\)


\(a_{6}\), \(i_{1}\), \(i_{6}\)


\(a_{1}\), \(a_{2}\), \(a_{3}\), \(a_{4}\), \(a_{5}\), \(a_{6}\), \(i_{1}\), \(i_{2}\), \(i_{3}\), \(i_{4}\), \(i_{5}\), \(i_{6}\), \(\alpha_{8}\), \(\alpha_{9}\)


\(a_{6}\), \(i_{1}\), \(i_{6}\), \(\alpha_{7}\), \(\alpha_{9}\)


\(\alpha_{0}\), \(a_{1}\), \(a_{2}\), \(a_{3}\), \(a_{4}\), \(a_{5}\), \(a_{6}\), \(i_{1}\), \(i_{2}\), \(i_{3}\), \(i_{4}\), \(i_{5}\), \(i_{6}\), \(\alpha_{7}\), \(\alpha_{8}\)

  1. The data and ancillary qubits are labeled according to the notation of Figure 5.