FIG. 7 shows another lattice arrangement 710 with two-dimensional structures comprising dodecagons; one such structure is represented in the dashed box 772. As can be seen from FIG. 7, including by the qubit 774 (represented by a black circle) and its neighboring qubits 776-778 (represented by crossed circles), any individual qubit in the lattice arrangement 710 directly connects to a maximum of three other qubits. Although not separately shown, it is understood that any two qubit gate in the lattice arrangement 710 of FIG. 7 directly connects to a maximum of four other qubits.

FIG. 8 shows another lattice arrangement 810 with two-dimensional structures comprising dodecagons, in which coupling (e.g., control) qubits are positioned on the edges between the other (e.g., target) qubits positioned on the vertices. As can be seen from FIG. 8, including by the qubits 884 and 886, any individual qubit in the lattice arrangement directly connects only to a coupling qubit, e.g., the coupling qubit 888. Thus, the same reduced frequency collision statistics described above with reference to FIGS. 4 and 5 apply to the lattice arrangement 810 of FIG. 8.