The name is absent



Figure 3.6: Gates are not placed on regular grids.

3.3.3 Irregular grid tomography

In practice, gates are not placed on a regular layout grid. Figure 3.6 shows an
example of an IC in which gates are placed on an irregular grid. To address
the irregular placement, we cover the IC with fine regular grids. Then, using
Procedure 1, each gate is assigned to a point on the regular grid. At the first
step of Procedure 1, all the regular grid points are labeled
unmarked, meaning
that none of the regular points is assigned to any gate. In the second step, for
every gate, we find its closest regular point that is
unmarked. Finally, to prevent
multiple selection, we mark the selected regular grid.

Then, we assign auxiliary variables to the points in the fine grid that are not
assigned to any gate. We also modify the measurement matrix
A to be consistent
with the fine regular grids, i.e., for each auxiliary variable, we add an appropriate
zero column to the matrix
A. Since the coefficients of auxiliary variables in the

33



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