# TableÂ 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 FigureÂ  2 , following the plaquette reduction method of Ref. [9]

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 TableÂ 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 FigureÂ 4.