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Table 2 Information about 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  2 , following the plaquette reduction method of Ref. [ 9 ]

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. \(a_{6}\), \(\alpha_{0}\), \(i_{6}\), \(\alpha_{6}\), \(i_{1}\)
4.73 \(i_{6}\), \(a_{6}\), \(a_{1}\), \(i_{2}\), \(a_{2}\)
3.15 \(i_{1}\), \(i_{2}\), \(a_{2}\), \(\alpha_{2}\), \(i_{3}\)
4.73 \(i_{2}\), \(i_{3}\), \(\alpha_{3}\), \(i_{4}\), \(a_{3}\)
3.15 \(i_{3}\), \(a_{3}\), \(a_{4}\), \(i_{5}\), \(i_{6}\)
3.15 \(i_{6}\), \(\alpha_{5}\), \(a_{5}\), \(i_{5}\), \(i_{4}\)
1.15 \(i_{1}\), \(\alpha_{1}\), \(a_{1}\)
1.15 \(i_{4}\), \(\alpha_{4}\), \(a_{4}\)
0.58 \(i_{2}\), \(\alpha_{1}\)
0.58 \(i_{5}\), \(\alpha_{4}\)
  1. In particular, all the two-qubit couplings of \(\mathcal{P}_{\mathrm{reduction}}\) in Table 1 are realized: there are no more than five TQs in each TLR, and each TQ couples to maximally four TLRs. A pictorial representation of this TLR scheme and of the arbitrary unit (a.u.) is given in Figure 4.