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