initial commit

scripts/grraph_state_cuts.py

@@ -0,0 +1,83 @@
+import numpy as np
+from itertools import product, combinations
+
+I=np.array([[1,0],[0,1]],complex)
+X=np.array([[0,1],[1,0]],complex)
+Y=np.array([[0,-1j],[1j,0]],complex)
+Z=np.array([[1,0],[0,-1]],complex)
+paulis=[I,X,Y,Z]
+labels=['I','X','Y','Z']
+
+def kron_all(ops):
+    out=ops[0]
+    for op in ops[1:]: out=np.kron(out,op)
+    return out
+
+def graph_state(n, edges):
+    psi=np.ones(2**n,complex)/np.sqrt(2**n)
+    # basis index bits qubit 0..n-1 as MSB? phase invariant consistent
+    for idx in range(2**n):
+        bits=[(idx>>(n-1-q))&1 for q in range(n)]
+        phase=1
+        for a,b in edges:
+            if bits[a]*bits[b]: phase*=-1
+        psi[idx]*=phase
+    return psi
+
+def corr_tensor(psi,n):
+    coeff={}
+    for inds in product(range(4), repeat=n):
+        op=kron_all([paulis[i] for i in inds])
+        val=np.vdot(psi, op@psi)
+        if abs(val)>1e-9:
+            coeff[inds]=float(np.real_if_close(val))
+    return coeff
+
+def matrix_for_cut(coeff,S,n, source_full=False, target_full=False):
+    Sc=[i for i in range(n) if i not in S]
+    row=[]; col=[]
+    for inds in product(range(4), repeat=len(S)):
+        if all(i==0 for i in inds): continue
+        if source_full and any(i==0 for i in inds): continue
+        row.append(inds)
+    for inds in product(range(4), repeat=len(Sc)):
+        if all(i==0 for i in inds): continue
+        if target_full and any(i==0 for i in inds): continue
+        col.append(inds)
+    M=np.zeros((len(col),len(row))) # target rows, source cols
+    for r,tinds in enumerate(col):
+        for c,sinds in enumerate(row):
+            full=[0]*n
+            for q,ind in zip(S,sinds): full[q]=ind
+            for q,ind in zip(Sc,tinds): full[q]=ind
+            M[r,c]=coeff.get(tuple(full),0.0)
+    return M,row,col
+
+def partial_rho(psi, keep, n):
+    rho=np.outer(psi, psi.conj()).reshape([2]*n*2)
+    trace=[i for i in range(n) if i not in keep]
+    # trace out from high to low axes
+    for q in sorted(trace, reverse=True):
+        rho=np.trace(rho, axis1=q, axis2=q+rho.ndim//2)
+    d=2**len(keep)
+    return rho.reshape(d,d)
+
+n=4
+edges=[(0,1),(1,2),(2,3),(3,0)]
+psi=graph_state(n,edges)
+coeff=corr_tensor(psi,n)
+print('nonzero coeffs', len(coeff))
+for cutname,S in [('adjacent12|34',[0,1]),('diagonal13|24',[0,2]),('adjacent14|23',[0,3])]:
+    M,_,_=matrix_for_cut(coeff,S,n)
+    G,_,_=matrix_for_cut(coeff,S,n,source_full=True,target_full=True)
+    norm=np.linalg.svd(M/3, compute_uv=False).sum()
+    rawn=np.linalg.svd(M, compute_uv=False).sum()
+    gnorm=np.linalg.svd(G/3, compute_uv=False).sum()
+    graw=np.linalg.svd(G, compute_uv=False).sum()
+    print('\n',cutname)
+    print('full normalized',norm,'raw',rawn,'sing',np.linalg.svd(M/3,compute_uv=False))
+    print('genuine normalized',gnorm,'raw',graw,'sing',np.linalg.svd(G/3,compute_uv=False))
+    rho=partial_rho(psi,S,n)
+    print('rho eigen',np.linalg.eigvalsh(rho),'max mixed dist',np.linalg.norm(rho-np.eye(4)/4))
+    # list nonzero stabilizers labels
+    # print rows/cols maybe