Table A1.

Numerical simulation details of scalability test on randomly generated quantum circuits with $d=2$. $N_{\mathrm{PQC}}$ denotes the input states number in our variational method, and $N_{\mathrm{SQPT}}$ denotes the input states number in SQPT.

n	d	${\mathit{N}}_{\mathbf{PQC}}$	${\mathit{N}}_{\mathbf{SQPT}}$	# of Paras.	Max. ${\mathit{F}}_{\mathbf{avg}}$	Max. Accuracy
2	3	3	16	24	$99.99\%$	$99.99\%$
3	4	6	64	45	$99.99\%$	$99.99\%$
4	5	8	256	72	$99.99\%$	$99.99\%$
5	6	12	1024	105	$99.99\%$	$99.99\%$
6	7	35	4096	144	$99.99\%$	$99.99\%$
7	8	55	$\mathrm{16,384}$	189	$99.99\%$	$99.99\%$
8	8	120	$\mathrm{65,536}$	216	$99.99\%$	$99.99\%$