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count respectively. The quantum cost of DFT design as designed by an earlier DFT
method [4] and that by the proposed technique are shown in columns 4 and 5 respec-
tively. For the circuits with a small number of 1-CNOT gates, our overhead is much
less than that in [4]. In addition, the proposed universal test set detects all SMGF, all
PMGFs, and all detectable RGF for all the gates in the circuit including those in the
additional circuit in contrast to the earlier method [4] where the first order PMGF in the
extra gate may remain undetectable. Further, in the earlier work [4], a replica of every
gate was needed in order to make the circuit easily testable, and thus, the overhead had
a uniform pattern. In contrast, in the proposed method, the quantum cost of the each
additional gate depends on the number of control inputs of the original gate; thus, the
overhead strongly depends on the circuit structure.
5Conluion
We have proposed a novel DFT technique for a reversible circuit to make it testable with
a universal test set of length (
n
+2). Our design offers significantly reduced quantum
cost for most of the benchmark circuits compared to earlier approaches [4].
Acknowledgement.
The work was partly supported by CSIR grant (ref.-22(0590)/12/
EMR II) and UGC MRP grant (ref.-41/620/2012(SR)).
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