%Experimentally reconstructed process matrices of the implemented gates shown in Fig.S4.
%The maximum-likelihood technique was used for performing quantum process tomography.
%
%\chi_9: U = 1/sqrt(2)*(I + iZ) 
U_exp(:,:,1) =[
   0.4817 + 0.0000i   0.0346 + 0.0435i   0.0973 - 0.0449i  -0.0054 - 0.2656i;
   0.0346 - 0.0435i   0.0699 + 0.0000i   0.0184 + 0.0126i  -0.0698 + 0.0521i;
   0.0973 + 0.0449i   0.0184 - 0.0126i   0.0596 + 0.0000i   0.0401 + 0.0544i;
  -0.0054 + 0.2656i  -0.0698 - 0.0521i   0.0401 - 0.0544i   0.4993 + 0.0000i];

%\chi_10: U = 1/sqrt(2)*(I - iZ)
U_exp(:,:,2) =[
   0.5692 + 0.0000i   0.0075 - 0.1106i   0.0379 - 0.0448i  -0.0032 + 0.2624i;
   0.0075 + 0.1106i   0.1187 + 0.0000i  -0.0030 + 0.0143i  -0.0146 + 0.0575i;
   0.0379 + 0.0448i  -0.0030 - 0.0143i   0.0335 + 0.0000i  -0.0044 - 0.0693i;
  -0.0032 - 0.2624i  -0.0146 - 0.0575i  -0.0044 + 0.0693i   0.4091 + 0.0000i];

%\chi_11: U = 1/sqrt(2)*(X  + Z)
U_exp(:,:,3) =[
   0.0101 + 0.0000i   0.0013 + 0.0359i   0.0066 - 0.0127i   0.0338 - 0.0097i;
   0.0013 - 0.0359i   0.3300 + 0.0000i  -0.0532 - 0.0446i  -0.1434 - 0.3509i;
   0.0066 + 0.0127i  -0.0532 + 0.0446i   0.0313 + 0.0000i   0.0315 + 0.0624i;
   0.0338 + 0.0097i  -0.1434 + 0.3509i   0.0315 - 0.0624i   0.6328 + 0.0000i];

%Note: the following recontructed process matrix is also shown in Fig.5 in the main text.
%\chi_12: U = 1/sqrt(2)*(X + iZ)
U_exp(:,:,4) =[
   0.1468 + 0.0000i  -0.0124 + 0.0344i   0.0260 + 0.0678i   0.0306 - 0.0951i;
  -0.0124 - 0.0344i   0.5355 + 0.0000i  -0.0184 - 0.0540i   0.3009 - 0.0766i;
   0.0260 - 0.0678i  -0.0184 + 0.0540i   0.0951 + 0.0000i  -0.0288 - 0.0236i;
   0.0306 + 0.0951i   0.3009 + 0.0766i  -0.0288 + 0.0236i   0.3014 + 0.0000i];