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TableĀ 6 Optimal TLR scheme for the set of couplings \(\pmb{\mathcal{P}_{\mathrm{swpapping}}^{0}}\) , i.e., for couplings between qubits in the unit cell 0 and the rest of the lattice

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

Length of the TLR

Qubits contained inside the TLR wire

3.57 a.u.

\(i_{0,6}\), \(\alpha_{0,9}\), \(i_{2,5}\), \(\alpha_{3,7}\), \(i_{3,1}\)

3.15

\(\alpha_{1,9}\), \(\alpha_{1,7}\), \(i_{1,6}\), \(i_{1,5}\), \(\alpha_{0,7}\)

3.48

\(\alpha_{2,7}\), \(\alpha_{2,5}\), \(i_{0,1}\), \(\alpha_{0,9}\), \(i_{0,6}\)

2.52

\(i_{0,5}\), \(\alpha_{4,0}\), \(i_{4,6}\), \(\alpha_{4,8}\), \(\alpha_{4,9}\)

3.80

\(i_{17,1}\), \(i_{6,6}\), \(\alpha_{6,9}\), \(i_{5,1}\), \(i_{0,5}\)

1.44

\(\alpha_{0,8}\), \(\alpha_{0,7}\), \(\alpha_{1,4}\), \(i_{0,1}\)

1.15

\(\alpha_{0,4}\), \(i_{0,5}\), \(\alpha_{0,5}\)

  1. By translating this TLR scheme to the remaining unit cells of the lattice, one obtains an optimal TLR scheme for the entire lattice that avoids doubled TLRs.