diff --git a/pyproject.toml b/pyproject.toml
index 4ec4d90..2e13e6b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -28,6 +28,7 @@ dependencies = [
   "numpy",
   "pymanopt==2.0.0",
   "h5py",
+  "bitarray",
   "hydra-core",
   "jax==0.4.26",
   "jaxlib @ https://storage.googleapis.com/jax-releases/cuda12/jaxlib-0.4.26+cuda12.cudnn89-cp311-cp311-manylinux2014_x86_64.whl "
diff --git a/translate.py b/translate.py
new file mode 100644
index 0000000..0365f02
--- /dev/null
+++ b/translate.py
@@ -0,0 +1,133 @@
+import jax.numpy as jnp
+import jax
+import numpy as np
+jax.config.update("jax_enable_x64", True)
+import logging
+import h5py
+import bitarray
+import bitarray.util
+
+def skew(x): return x-x.T
+
+def permuteG(G,Nv):
+    def permutation_order(Nv):
+        match Nv:
+            case 1:
+                order = [8 ,6 , 0,  1, 10,  4,  9,  7,  2,  3, 11,  5]
+            case 2:
+                order = [12, 16,  6, 10,  0,  1, 14, 18,  4,  8, 13, 17,  7, 11,  2,  3, 15, 19,  5,  9]
+            case 3:
+                order = [16, 20, 24,  6, 10, 14,  0,  1, 18, 22, 26,  4,  8, 12, 17, 21, 25, 7, 11, 15,  2,  3, 19, 23, 27,  5,  9, 13]
+            case 4:
+                order = [20, 24, 28, 32,  6, 10, 14, 18,  0,  1, 22, 26, 30, 34,  4,  8, 12, 16, 21, 25, 29, 33,  7, 11, 15, 19,  2,  3, 23, 27, 31, 35,  5,  9,13, 17]
+            case 5:
+                order = [24, 28, 32, 36, 40,  6, 10, 14, 18, 22,  0,  1,  26, 30, 34, 38, 42,  4,  8, 12, 16, 20, 25, 29, 33, 37, 41,  7, 11, 15, 19, 23,  2,  3,27, 31, 35, 39, 43,  5,  9, 13, 17, 21]
+            case _:
+                raise ValueError("Nv must be 1,2,3,4,5")
+        return np.array(order)
+
+
+    def permutation_matrix(Nv):
+        perm = permutation_order(Nv)
+        M = np.zeros((len(perm),len(perm)))
+        for i in range(len(perm)):
+            M[perm[i],i] = 1.0
+        return M
+    
+    P = permutation_matrix(Nv)
+    return P.T @ G @ P
+
+def getG(T, Nv):
+    def J(Nv): return skew(np.reshape(np.array([int(j-i==1 and np.mod(j+1,2)==0) for i in range(8*Nv+4) for j in range(8*Nv+4)]),(8*Nv+4,8*Nv+4)))
+    
+    optim_G = T.T @ J(Nv) @T
+    return permuteG(optim_G,Nv)
+
+def cor_trans_matrix(cm):
+    N = cm.shape[0] // 2
+    one = np.eye(N)
+    S = np.block([[one,one],[+one*1.0j ,-one*1.0j]])
+    return S.T @ cm @ S
+
+def fiducial_hamiltonian(hρ,hκ):
+    N = hρ.shape[0]
+    dim = 2**N
+    assert hρ.shape[1]==N and hκ.shape[1]==N and hκ.shape[1]==N
+    assert np.linalg.norm(hρ-hρ.T.conj())<1E-10 and np.linalg.norm(hκ + hκ.T) < 1E-10
+    
+    H = np.zeros((2**N,2**N),dtype=np.complex128)
+
+    for i in range(N):
+        for j in range(N):
+            for k in range(2**N):
+                bk = bitarray.util.int2ba(k,length=N)
+                bk.reverse()
+
+                parity = (bk.count(1,i,N) + bk.count(1,j,N)) % 2
+                
+                if bk[i]==0:
+                    if bk[j] == 1:
+                        bk[i] = 1
+                        bk[j] = 0
+                        target = bitarray.util.ba2int(bk)
+                        H[target,k] += hρ[i,j] * (-1)**parity
+                    elif bk[j] == 0:
+                        bk[j] = 1
+                        bk[i] = 1
+                        target = bitarray.util.ba2int(bk)
+                        H[target,k] -= hκ[i,j].conj() * (-1)**parity    
+    return H
+
+def translate(Gamma,Nv):
+    N = Gamma.shape[0]//2
+    
+    trans_h = cor_trans_matrix(-Gamma)
+    
+    hρ = -1.0j*trans_h[0:N,N:2*N].T
+    hκ = 1.0j*trans_h[0:N,0:N]
+    local_h = fiducial_hamiltonian(hρ,hκ)
+    tw,tv = np.linalg.eig(local_h)
+    return tv[:,0]
+
+def paritygate(n):
+    S = np.eye(n)
+    for i in range(n):
+        if bitarray.util.int2ba(i,int(np.ceil(np.log(n)/np.log(2)))).count() %2 !=0: 
+            S[i,i] = -1
+    return S
+
+def fsign(n_list):
+    result = 0
+    for i in range(1,len(n_list)):
+        result += n[i]*sum(n[0:i-1])
+    return (-1)**(result % 2)
+
+def bondgate(Nv):
+    
+    n = np.zeros((Nv,Nv)) # store n_i
+    p = zeros([2 for i =1:Nv]...)
+    for index in ind
+        for i = 1:Nv
+            n[i] = Tuple(index)[i]
+        end
+        n = n.-1
+        p[index] = fsign(n)
+    end
+    return Array(Diagonal(p[:]))
+end
+
+
+
+def main(input_file):
+    with h5py.File(input_file, "r") as fid:
+        Nv = fid["/model/Nv"][()]
+        T = fid["/transformer/T"][0:8*Nv+4,0:8*Nv+4]
+        
+    Gamma = getG(T,Nv)
+    tensor_0 = translate(Gamma,Nv)
+    
+    assert abs(tensor_0[1])< 1E-10 # check parity
+    tensor_1 = np.reshape(tensor_0,(2**Nv,2**Nv,4,2**Nv,2**Nv))
+
+if __name__ == "__main__":
+    main(input_file = "/home/yangqi/jaxgfpeps/data/default.h5")
\ No newline at end of file