The name is absent

6.3 Delay evaluation results

6.3.1 Measurement matrix and estimation in subspaces

As mentioned in Section 4.2, due to the existence of ambiguities (path dependen-
cies), it may not be possible to find the variations for all gates in the circuit. In
the other words, the measurement matrix, A, is not necessarily a full-rank ma-
trix. Most often the measurement matrix is ill-conditioned and its singular values
decay rapidly. Figure 6.4 shows singular values of the measurement matrix for
C880 and C499 circuit. The singular values are normalized to have the maximum
value equal to 1. The singular values decay to 10% of the maximum after almost
100 singular values. Note that C432 and C880 have 206 and 353 gates, respec-
tively. The figure also shows the singular value of a random Gaussian matrix. It
is clear that singular values of the measurement matrices (for C499, C800) decay
much faster than the random Gaussian matrix.

Hence, it is not possible to find the variations of all gates. We measured
estimation error in the space of singular values. The estimation error is minimum
at the direction of the singular vector corresponding to the largest singular value
and so on. We say the estimation subspace has dimension n_e, when we project
estimation error to the space of the first n_e singular vectors.

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