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

EPJ Quantum Technology

Table 8 Comparisons of dividers for $n \ge 3$

Operators	T-count	T-depth	CNOT-count	CNOT-depth	Width
Proposed	$8{n^{2}}{\text{$+$}}7n{\text{-}}6$	$2{n^{2}}{\text{$+$}}3n{\text{-}}1$	$11{n^{2}}{\text{$+$}}8n{\text{-}}10$	$4{n^{2}}{\text{$+$}}13n{\text{-}}10$	3n
[36]	$14{n^{2}}{\text{-}}7n{\text{$+$}}1$	$3{n^{2}}{\text{$+$}}2n{\text{-}}1$	$21{n^{2}}{\text{-}}15n{\text{$+$}}7$	$13{n^{2}}{\text{-}}3n{\text{-}}1$	3n
[38]	$14{n^{2}}{\text{$+$}}35n{\text{-}}14$	$6{n^{2}}{\text{$+$}}15n{\text{-}}6$	$20{n^{2}}{\text{$+$}}44n{\text{-}}21$	$13{n^{2}}{\text{$+$}}36n{\text{-}}13$	3n + 2

Operators	T-count	T-depth	CNOT-count	CNOT-depth	Width
Proposed	\(8{n^{2}}{\text{$+$}}7n{\text{-}}6\)	\(2{n^{2}}{\text{$+$}}3n{\text{-}}1\)	\(11{n^{2}}{\text{$+$}}8n{\text{-}}10\)	\(4{n^{2}}{\text{$+$}}13n{\text{-}}10\)	3n
[36]	\(14{n^{2}}{\text{-}}7n{\text{$+$}}1\)	\(3{n^{2}}{\text{$+$}}2n{\text{-}}1\)	\(21{n^{2}}{\text{-}}15n{\text{$+$}}7\)	\(13{n^{2}}{\text{-}}3n{\text{-}}1\)	3n
[38]	\(14{n^{2}}{\text{$+$}}35n{\text{-}}14\)	\(6{n^{2}}{\text{$+$}}15n{\text{-}}6\)	\(20{n^{2}}{\text{$+$}}44n{\text{-}}21\)	\(13{n^{2}}{\text{$+$}}36n{\text{-}}13\)	3n + 2