# TableÂ 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 FigureÂ  5 , following the plaquette swapping method of Ref. [28]

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 TableÂ 3 are realized: there are no more than five TQs in each TLR, and each TQ couples to maximally four TLRs.