Table 5.

Comparison of depth/time complexity of proposed MQCC-optimized against classical CNN.

a Depth complexity of C2Q [12] data encoding (I/O) technique
	${\mathcal{O}}_{\mathrm{I}/\mathrm{O}}\left(2^n\right)={\mathcal{O}}_{\mathrm{I}/\mathrm{O}}\left(N\right)$
b Complexity of proposed technique compared with classical convolutional neural network
MQCC Optimized with MAC-based fully connected layer	MQCC Optimized with ansatz-based fully connected layer	Direct (CPU) [21]	FFT (CPU/GPU) [21,22]	GEMM (GPU) [23,24]
$\begin{array}{c}{\mathcal{O}}_{\mathrm{alg}}\left(2^n)\right.\equiv {\mathcal{O}}_{\mathrm{alg}}\left(N\right)\hfill \\ {\mathcal{O}}_{\mathrm{alg}}+\mathrm{I}/\mathrm{O}\left(2^n+2^n)\right.\equiv \hfill \\ {\mathcal{O}}_{\mathrm{alg}}+\mathrm{I}/\mathrm{O}\left(N\right)\hfill \end{array}$	$\begin{array}{c}{\mathcal{O}}_{\mathrm{alg}}\left(n^2)\right.\equiv {\mathcal{O}}_{\mathrm{alg}}\left({(logN)}^2\right)\hfill \\ {\mathcal{O}}_{\mathrm{alg}}+\mathrm{I}/\mathrm{O}\left(n^2+2^n)\right.\equiv \hfill \\ {\mathcal{O}}_{\mathrm{alg}}+\mathrm{I}/\mathrm{O}\left(N\right)\hfill \end{array}$	$\begin{array}{c}{\mathcal{O}}_{\mathrm{alg}}\left(4^n\right)\equiv \hfill \\ {\mathcal{O}}_{\mathrm{alg}}\left(N^2\right)\hfill \end{array}$	$\begin{array}{c}{\mathcal{O}}_{\mathrm{alg}}\left(n{2}^n\right)\equiv \hfill \\ {\mathcal{O}}_{\mathrm{alg}}\left(NlogN\right)\hfill \end{array}$	$\begin{array}{c}{\mathcal{O}}_{\mathrm{alg}}\left(2^{(n+n_k)}\right)\equiv \hfill \\ {\mathcal{O}}_{\mathrm{alg}}\left(N_{K}N\right)\hfill \end{array}$