Designs of the divider and special multiplier optimizing T and CNOT gates

EPJ Quantum Technology

Table 6 Comparisons of multipliers for $n \ge 3$

Operators	T-count	T-depth	CNOT-count	CNOT-depth	Width
Proposed	$8{n^{2}}{\text{$+$}}9n{\text{-}}12$	$2{n^{2}}{\text{$+$}}3n{\text{$+$}}1$	$11{n^{2}}{\text{$+$}}9n{\text{-}}16$	$4{n^{2}}{\text{$+$}}10n{\text{-}}8$	3n
[23]	$21{n^{2}}{\text{-}}9n{\text{-}}5$	$9{n^{2}}{\text{-}}3n{\text{-}}3$	$23{n^{2}}{\text{-}}12n{\text{-}}4$	$18{n^{2}}{\text{-}}48n{\text{$+$}}30$	4n
[35]	$21{n^{2}}{\text{-}}14$	$9{n^{2}}{\text{-}}3n{\text{-}}3$	$25{n^{2}}{\text{-}}10n{\text{-}}8$	$20{n^{2}}{\text{-}}10n$	4n + 1
[36]	$8{n^{2}}{\text{$+$}}15n{\text{-}}8$	$2{n^{2}}{\text{$+$}}4n$	$15{n^{2}}{\text{$+$}}14n{\text{-}}15$	$8{n^{2}}{\text{$+$}}11n{\text{-}}16$	3n + 1

Operators	T-count	T-depth	CNOT-count	CNOT-depth	Width
Proposed	\(8{n^{2}}{\text{$+$}}9n{\text{-}}12\)	\(2{n^{2}}{\text{$+$}}3n{\text{$+$}}1\)	\(11{n^{2}}{\text{$+$}}9n{\text{-}}16\)	\(4{n^{2}}{\text{$+$}}10n{\text{-}}8\)	3n
[23]	\(21{n^{2}}{\text{-}}9n{\text{-}}5\)	\(9{n^{2}}{\text{-}}3n{\text{-}}3\)	\(23{n^{2}}{\text{-}}12n{\text{-}}4\)	\(18{n^{2}}{\text{-}}48n{\text{$+$}}30\)	4n
[35]	\(21{n^{2}}{\text{-}}14\)	\(9{n^{2}}{\text{-}}3n{\text{-}}3\)	\(25{n^{2}}{\text{-}}10n{\text{-}}8\)	\(20{n^{2}}{\text{-}}10n\)	4n + 1
[36]	\(8{n^{2}}{\text{$+$}}15n{\text{-}}8\)	\(2{n^{2}}{\text{$+$}}4n\)	\(15{n^{2}}{\text{$+$}}14n{\text{-}}15\)	\(8{n^{2}}{\text{$+$}}11n{\text{-}}16\)	3n + 1