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Table 4 The optimal TLR scheme obtained by solving the binary linear program for the measurement of the plaquette operator \(\pmb{B_{p}}\) and the six vertex operators \(\pmb{Q_{v}}\) of Figure  5 , following the plaquette swapping method of Ref. [ 28 ]

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

Length of the TLR wire Qubits contained inside the TLR wire
2.52 a.u. \(\alpha_{9}\), \(\alpha_{8}\), \(i_{6}\), \(\alpha_{0}\), \(a_{6}\)
2.84 \(a_{1}\), \(i_{1}\), \(\alpha_{7}\), \(\alpha_{8}\), \(\alpha_{9}\)
4.04 \(\alpha_{7}\), \(\alpha_{9}\), \(i_{4}\), \(i_{3}\), \(a_{3}\)
4.30 \(\alpha_{9}\), \(\alpha_{7}\), \(a_{5}\), \(i_{5}\), \(a_{4}\)
2.44 \(i_{1}\), \(\alpha_{7}\), \(\alpha_{6}\), \(i_{6}\), \(a_{6}\)
2.15 \(i_{2}\), \(\alpha_{1}\), \(i_{1}\), \(a_{1}\)
2.15 \(i_{3}\), \(\alpha_{2}\), \(i_{2}\), \(a_{2}\)
3.04 \(\alpha_{7}\), \(\alpha_{9}\), \(i_{2}\), \(a_{2}\)
2.15 \(i_{5}\), \(\alpha_{4}\), \(i_{4}\), \(a_{4}\)
1.63 \(i_{5}\), \(\alpha_{5}\), \(i_{6}\), \(a_{5}\)
1.15 \(i_{4}\), \(\alpha_{3}\), \(a_{3}\)
0.58 \(i_{3}\), \(\alpha_{3}\)
  1. In particular, all the two-qubit couplings of \(\mathcal{P}_{\mathrm{swapping}}\) in Table 3 are realized: there are no more than five TQs in each TLR, and each TQ couples to maximally four TLRs.