diff --git a/mindquantum/simulator/stabilizer/check_qiskit_clifford.py b/mindquantum/simulator/stabilizer/check_qiskit_clifford.py
new file mode 100644
index 000000000..c6b325482
--- /dev/null
+++ b/mindquantum/simulator/stabilizer/check_qiskit_clifford.py
@@ -0,0 +1,78 @@
+import numpy as np
+from qiskit import *
+from qiskit.quantum_info import Clifford as qsClifford
+#from qiskit.quantum_info import decompose_clifford
+from qiskit.synthesis import synth_clifford_full
+from qiskit.quantum_info import Statevector
+
+def check_qiskit_clifford(num_qubits=2):
+    # generate clifford and try decomposition
+    qc = QuantumCircuit(2)
+    qc.s(0)
+    #qc.cx(0,1)
+    qc.s(1)
+    qc.h(1)
+    qc.cx(0,1)
+    cli = qsClifford(qc)
+    qc_decomp1 = synth_clifford_full(cli, method='AG')
+    qc_decomp2 = synth_clifford_full(cli, method='greedy')
+    qc_decomp3 = synth_clifford_full(cli, method=None) # Bravyi & Maslov (n<=3)
+
+    # check circuit
+    print("original circuit:")
+    print(qc.draw())
+    print("AG decomposition:")
+    print(qc_decomp1.draw())
+    print("greedy decomposition:")
+    print(qc_decomp2.draw())
+    print("Bravyi & Maslov decomposition:")
+    print(qc_decomp3.draw())
+
+    # check tableau
+    cli_decomp1 = qsClifford(qc_decomp1)
+    cli_decomp2 = qsClifford(qc_decomp2)
+    cli_decomp3 = qsClifford(qc_decomp3)
+    assert np.all(cli.tableau==cli_decomp1.tableau)
+    assert np.all(cli.tableau==cli_decomp2.tableau)
+    assert np.all(cli.tableau==cli_decomp3.tableau)
+
+    # check matrix
+    mat0 = get_qiskit_matrix(qc)
+    mat1 = get_qiskit_matrix(qc_decomp1)
+    mat2 = get_qiskit_matrix(qc_decomp2)
+    mat3 = get_qiskit_matrix(qc_decomp3)
+    print(mat0)
+    print(mat1)
+    print(mat2)
+    print(mat3)
+    #assert np.all(mat0==mat1)
+    #assert np.all(mat0==mat2)
+    #assert np.all(mat0==mat3)
+    #assert np.all(mat1==mat2)
+    
+    # check state
+    state0 = Statevector(qc)  # inner product < psi1 | psi2 >
+    state1 = Statevector(qc_decomp1)
+    state2 = Statevector(qc_decomp2)
+    state3 = Statevector(qc_decomp3)
+    print(state0)
+    print(state1)
+    print(state2)
+    print(state3)
+    print(state0.probabilities())
+    print(state1.probabilities())
+    print(state2.probabilities())
+    print(state3.probabilities())
+
+
+def get_qiskit_matrix(qc):
+    # get unitary matrix of quantum circuits
+    backend = BasicAer.get_backend('unitary_simulator')
+    job = backend.run(transpile(qc, backend))
+    return job.result().get_unitary(qc, decimals=6)
+
+
+if __name__=="__main__":
+    check_qiskit_clifford()
+
+
diff --git a/mindquantum/simulator/stabilizer/check_qiskit_expval.py b/mindquantum/simulator/stabilizer/check_qiskit_expval.py
new file mode 100644
index 000000000..0464e4629
--- /dev/null
+++ b/mindquantum/simulator/stabilizer/check_qiskit_expval.py
@@ -0,0 +1,143 @@
+import numpy as np
+from qiskit import *
+from qiskit.quantum_info import Clifford as qsClifford
+#from qiskit.quantum_info import decompose_clifford
+from qiskit.synthesis import synth_clifford_full
+from qiskit.quantum_info import Statevector
+
+def check_qiskit_expval(num_qubits=2):
+    # generate clifford and try expectation on Pauli string
+    qc = QuantumCircuit(2)
+    qc.s(0)
+    #qc.cx(0,1)
+    qc.s(1)
+    qc.h(1)
+    qc.cx(0,1)
+    
+    for i in range(8):
+        x = np.random.randint(6)
+        if   x==0: qc.cx(0,1)
+        elif x==1: qc.cx(1,0)
+        elif x==2: qc.h(0)
+        elif x==3: qc.h(1)
+        elif x==4: qc.s(0)
+        elif x==5: qc.s(1)
+
+    cli = qsClifford(qc)
+    qc_decomp1 = synth_clifford_full(cli, method='AG')
+    qc_decomp2 = synth_clifford_full(cli, method='greedy')
+    qc_decomp3 = synth_clifford_full(cli, method=None) # Bravyi & Maslov (n<=3)
+
+    # check circuit
+    print("original circuit:")
+    print(qc.draw())
+    print("AG decomposition:")
+    print(qc_decomp1.draw())
+    print("greedy decomposition:")
+    print(qc_decomp2.draw())
+    print("Bravyi & Maslov decomposition:")
+    print(qc_decomp3.draw())
+
+    # check tableau
+    cli_decomp1 = qsClifford(qc_decomp1)
+    cli_decomp2 = qsClifford(qc_decomp2)
+    cli_decomp3 = qsClifford(qc_decomp3)
+    assert np.all(cli.tableau==cli_decomp1.tableau)
+    assert np.all(cli.tableau==cli_decomp2.tableau)
+    assert np.all(cli.tableau==cli_decomp3.tableau)
+
+    # check pauli expectation  < psi | P | psi >
+    P = 'ZX'
+    expval0 = get_expval_pauli(cli, pauli=P)
+    expval1 = get_expval_pauli(cli_decomp1, pauli=P)
+    expval2 = get_expval_pauli(cli_decomp2, pauli=P)
+    expval3 = get_expval_pauli(cli_decomp3, pauli=P)
+    assert expval0==expval1
+    assert expval0==expval2
+    assert expval0==expval3
+
+    #expval0p = get_expval_inner(qc, pauli=P)
+    #assert np.abs(expval0 - expval0p)<1e-5
+
+    for P in ['II','IX','IY','IZ',
+              'XI','XX','XY','XZ',
+              'YI','YX','YY','YZ',
+              'ZI','ZX','ZY','ZZ']:
+        expval0 = get_expval_pauli(cli, pauli=P) # by tableau
+        expval0p = get_expval_inner(qc, pauli=P) # by state vector
+        try:
+            assert np.abs(expval0 - expval0p)<1e-5
+        except:
+            print(f"<psi|{P}|psi> Failed!!! exp_tableau={expval0} while exp_state={expval0p}")
+
+
+def apply_pauli(qc, pauli):
+    # apply pauli to quantum circuit
+    qc1 = qc.copy()
+    for ip in range(len(pauli)):
+        if pauli[ip]=='X': qc1.x(ip)
+        elif pauli[ip]=='Y': qc1.y(ip)
+        elif pauli[ip]=='Z': qc1.z(ip)
+    return qc1
+
+def get_expval_inner(qc, pauli):
+    # < psi | P | psi > by inner product
+    qcp = apply_pauli(qc, pauli)
+    psi1 = Statevector(qc)
+    psi2 = Statevector(qcp)
+    return np.round(psi1.inner(psi2).real, decimals=6)
+
+def get_expval_pauli(cli, num_qubits=2, qubits=[0,1], pauli='ZZ'):
+    # < psi | P | psi >
+    #   see: https://github.com/Qiskit/qiskit-aer/blob/main/src/simulators/stabilizer/clifford.hpp#L642
+    if qubits is None:
+        assert len(pauli)==num_qubits
+        qubits = [i for i in range(num_qubits)]
+    n = num_qubits
+    P = np.zeros(2*n, dtype=bool)
+    phase = 0
+    for i in range(len(qubits)):
+        if   pauli[i]=='X': P[qubits[i]]=1
+        elif pauli[i]=='Z': P[qubits[i]+n]=1
+        elif pauli[i]=='Y': P[qubits[i]]=1; P[qubits[i]+n]=1; phase+=1
+
+    stabilizer_table_X = cli.tableau[n:,:n]
+    stabilizer_table_Z = cli.tableau[n:,n:-1]
+    destabilizer_table_X = cli.tableau[:n,:n]
+    destabilizer_table_Z = cli.tableau[:n,n:-1]
+    stabilizer_phase = cli.tableau[n:,-1]
+    destabilizer_phase = cli.tableau[:n,-1]
+
+    for i in range(num_qubits):
+        num_anti = 0
+        for qubit in qubits:
+            if P[qubit+n] and stabilizer_table_X[i,qubit] :
+                num_anti += 1
+            if P[qubit] and stabilizer_table_Z[i,qubit] :
+                num_anti += 1
+        if num_anti%2==1:
+            return 0.0
+
+    PZ = P[n:]
+    for i in range(num_qubits):
+        num_anti = 0
+        for qubit in qubits:
+            if P[qubit+n] and destabilizer_table_X[i,qubit] :
+                num_anti += 1
+            if P[qubit] and destabilizer_table_Z[i,qubit] :
+                num_anti += 1
+        if num_anti%2==0: continue
+
+        phase += 2 * stabilizer_phase[i]
+        for k in range(num_qubits):
+            phase += stabilizer_table_Z[i,k] & stabilizer_table_X[i,k]
+            phase += 2 * (PZ[k] & stabilizer_table_X[i,k])
+            PZ[k] = PZ[k] ^ stabilizer_table_Z[i,k]
+
+    return -1.0 if phase%4 else 1.0
+            
+
+if __name__=="__main__":
+    check_qiskit_expval()
+
+