Sorry that I keep asking questions for the same subject. It is driving me crazy.
I have followed the [5,1,3] stabilizer code circuit designed by Gottesman in page 35 in his paper (also illustrated in my another question). This code has four stabilizer generators $XZZXI$, $IXZZX$, $XIXZZ$, $ZXIXZ$.
The following is a minimal working example in which I only draw the stabilizer generator $IXZZX$,
from qiskit import *
encoded = QuantumRegister(5,'encoded')
stab = QuantumRegister(4,'stab')
syndr = ClassicalRegister(4, 'syndr')
five = QuantumCircuit(encoded)
fiveS = QuantumCircuit(encoded, stab, syndr)
#----------------------------------encode----------------------------------
five.h(encoded[0])
five.h(encoded[1])
five.h(encoded[2])
five.h(encoded[3])
five.z(encoded[0])
five.z(encoded[3])
five.cz(encoded[0],encoded[1])
five.cz(encoded[0],encoded[3])
five.cy(encoded[0],encoded[4])
five.cz(encoded[1],encoded[2])
five.cz(encoded[1],encoded[3])
five.cx(encoded[1],encoded[4])
five.cz(encoded[2],encoded[0])
five.cz(encoded[2],encoded[1])
five.cx(encoded[2],encoded[4])
five.cz(encoded[3],encoded[0])
five.cz(encoded[3],encoded[2])
five.cy(encoded[3],encoded[4])
five.barrier()
#-------------------stabilizer generator IXZZX------------------------------
fiveS.h(stab[1])
fiveS.cx(stab[1],encoded[1])
fiveS.cz(stab[1],encoded[2])
fiveS.cz(stab[1],encoded[3])
fiveS.cx(stab[1],encoded[4])
fiveS.h(stab[1])
fiveS.measure(stab,syndr)
#----------------circuit visualization--------------------
#%matplotlib inline
#(five+fiveS).draw(output='mpl')
counts = execute( five+fiveS, Aer.get_backend('qasm_simulator'), shots=10000).result().get_counts()
print(counts)
Measuring stabilizer generators should return $0000$ but instead I get half $0000$ and half $0010$ (Same results returns when measuring $XIXZZ$, $ZXIXZ$). Where am I wrong?
Question updated
I tried to add all qubits in one quantum register and produce one quantum circuit.
from qiskit import *
stab = QuantumRegister(9,'stab')
syndr = ClassicalRegister(4, 'syndr')
five = QuantumCircuit(stab, syndr)
#----------------------------------encode----------------------------------
five.h(stab[0])
five.h(stab[1])
five.h(stab[2])
five.h(stab[3])
five.z(stab[0])
five.z(stab[3])
five.cz(stab[0],stab[1])
five.cz(stab[0],stab[3])
five.cy(stab[0],stab[4])
five.cz(stab[1],stab[2])
five.cz(stab[1],stab[3])
five.cx(stab[1],stab[4])
five.cz(stab[2],stab[0])
five.cz(stab[2],stab[1])
five.cx(stab[2],stab[4])
five.cz(stab[3],stab[0])
five.cz(stab[3],stab[2])
five.cy(stab[3],stab[4])
five.barrier()
#-------------------stabilizer generator IXZZX------------------------------
five.h(stab[6])
five.cx(stab[6],stab[1])
five.cz(stab[6],stab[2])
five.cz(stab[6],stab[3])
five.cx(stab[6],stab[4])
five.h(stab[6])
five.measure(stab[5],syndr[0])
five.measure(stab[6],syndr[1])
five.measure(stab[7],syndr[2])
five.measure(stab[8],syndr[3])
#----------------circuit visualization--------------------
#%matplotlib inline
#five.draw(output='mpl')
counts = execute( five, Aer.get_backend('qasm_simulator'), shots=10000).result().get_counts()
print(counts)
However, the same happens. The following are my running results.
