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Here's a fully compiled version, principles applied in modifying the code has been mentioned in the links above:

ssamp2 = Compile[{{n, _Integer}, {nd, _Integer}}, 
  Partition[Function[xyzw, {{xyzw[[1]] + I xyzw[[2]], 
                             -xyzw[[3]] + I xyzw[[4]]}, 
                            {xyzw[[3]] + I xyzw[[4]], 
                             xyzw[[1]] - I xyzw[[2]]}}]@#/Sqrt@Total[#^2] & /@ 
   Flatten[Transpose@RandomVariate[NormalDistribution[0, 1], {n, nd, 4}], 1], n]]

Here's a fully compiled version, principles applied in modifying the code has been mentioned in the links above:

ssamp2 = Compile[{{n, _Integer}, {nd, _Integer}}, 
  Partition[Function[xyzw, {{xyzw[[1]] + I xyzw[[2]], 
                             -xyzw[[3]] + I xyzw[[4]]}, 
                            {xyzw[[3]] + I xyzw[[4]], 
                             xyzw[[1]] - I xyzw[[2]]}}]@#/Sqrt@Total[#^2] & /@ 
   RandomVariate[NormalDistribution[0, 1], {n nd, 4}], n]]

Here's a fully compiled version, principles applied in modifying the code has been mentioned in the links above:

ssamp2 = Compile[{{n, _Integer}, {nd, _Integer}}, 
  Function[xyzw, {{xyzw[[1]] + I xyzw[[2]], -xyzw[[3]] + I xyzw[[4]]}, {xyzw[[3]] + 
          I xyzw[[4]], xyzw[[1]] - I xyzw[[2]]}}]@#/Sqrt@Total[#^2] & /@ 
   Flatten[Transpose@RandomVariate[NormalDistribution[0, 1], {n, nd, 4}], 1]]

Here's a fully compiled version, principles applied in modifying the code has been mentioned in the links above:

ssamp2 = Compile[{{n, _Integer}, {nd, _Integer}}, 
  Partition[Function[xyzw, {{xyzw[[1]] + I xyzw[[2]], 
                             -xyzw[[3]] + I xyzw[[4]]}, 
                            {xyzw[[3]] + I xyzw[[4]], 
                             xyzw[[1]] - I xyzw[[2]]}}]@#/Sqrt@Total[#^2] & /@ 
   Flatten[Transpose@RandomVariate[NormalDistribution[0, 1], {n, nd, 4}], 1], n]]

Here's a fully compiled version, principles applied in modifying the code has been mentioned in the links above:

ssamp2 = Compile[{{n, _Integer}, {nd, _Integer}}, 
  Function[xyzw, {{xyzw[[1]] + I xyzw[[2]], -xyzw[[3]] + I xyzw[[4]]}, {xyzw[[3]] + 
          I xyzw[[4]], xyzw[[1]] - I xyzw[[2]]}}]@#/Sqrt[Total[#^2]] & /@ 
   Flatten[Transpose@RandomVariate[NormalDistribution[0, 1], {n, nd, 4}], 1]]

Here's a fully compiled version, principles applied in modifying the code has been mentioned in the links above:

ssamp2 = Compile[{{n, _Integer}, {nd, _Integer}}, 
  Function[xyzw, {{xyzw[[1]] + I xyzw[[2]], -xyzw[[3]] + I xyzw[[4]]}, {xyzw[[3]] + 
          I xyzw[[4]], xyzw[[1]] - I xyzw[[2]]}}]@#/Sqrt@Total[#^2] & /@ 
   Flatten[Transpose@RandomVariate[NormalDistribution[0, 1], {n, nd, 4}], 1]]