Why I am not getting approximate equiprobable states in the following circuit on IBM Q simulator?

Question

I have the following circuit which consists of symmetric modules. I compiled the circuit in IBM Quantum experience backend - ibmq_qasm_simulator, 8192 shots. The result is not equiprobable. Why? Since this is not a real machine ideally I should get same probability of 16.67%.

OPENQASM 2.0;
include "qelib1.inc";

qreg qA[8];
qreg qB[8];
qreg qC[6];
qreg qD[6];
creg c[4];

h qA[2];
h qA[4];
x qA[6];
x qA[7];
x qB[1];
h qB[2];
h qB[4];
x qB[6];
x qB[7];
h qC[0];
h qC[2];
x qC[4];
x qC[5];
h qD[0];
h qD[2];
x qD[4];
x qD[5];
cx qA[2],qA[3];
cx qA[4],qA[5];
h qA[6];
cx qB[2],qB[3];
cx qB[4],qB[5];
h qB[6];
cx qC[0],qC[1];
cx qC[2],qC[3];
h qC[4];
cx qD[0],qD[1];
cx qD[2],qD[3];
h qD[4];
cx qA[6],qA[7];
cx qB[6],qB[7];
cx qC[4],qC[5];
cx qD[4],qD[5];
x qA[0];
ccx qA[6],qA[0],qA[4];
ccx qB[6],qB[0],qB[4];
ccx qA[7],qA[1],qA[5];
ccx qB[7],qB[1],qB[5];
x qA[6];
x qA[7];
x qB[6];
x qB[7];
ccx qA[6],qA[0],qA[2];
ccx qB[6],qB[0],qB[2];
ccx qA[7],qA[1],qA[3];
ccx qB[7],qB[1],qB[3];
cx qA[2],qA[3];
cx qA[4],qA[5];
cx qB[2],qB[3];
cx qB[4],qB[5];
ccx qA[3],qC[4],qC[2];
ccx qB[3],qC[5],qC[3];
x qC[4];
x qC[5];
ccx qA[3],qC[4],qC[0];
id qA[5];
ccx qB[3],qC[5],qC[1];
id qA[5];
cx qC[0],qC[1];
cx qC[2],qC[3];
ccx qA[5],qD[4],qD[2];
ccx qB[5],qD[5],qD[3];
x qD[4];
x qD[5];
ccx qA[5],qD[4],qD[0];
ccx qB[5],qD[5],qD[1];
cx qD[0],qD[1];
cx qD[2],qD[3];
measure qC[1] -> c[3];
measure qC[3] -> c[2];
measure qD[1] -> c[1];
measure qD[3] -> c[0];

Answer 1

You might have an issue in your circuit. I believe the first X gate on line qB1 should actually be on line qB0 to be symmetric with the upper block.

Maybe you can also try to move those X gates just before the two controlled gates as they act on the first and third qubit you measure but not on the second and fourth ones (in descending order).