From 19c91f39895ba6c54e1b3dd464b7136084cdf83c Mon Sep 17 00:00:00 2001
From: Pete Shadbolt <pete.shadbolt@gmail.com>
Date: Thu, 25 Feb 2016 19:40:00 +0000
Subject: [PATCH] Nearly there ...

---
 local_cliffords.py            | 55 ++++++++++++++++++++---------------
 tests/test_local_cliffords.py |  9 ++++++
 tests/test_vops.py            |  5 ----
 3 files changed, 41 insertions(+), 28 deletions(-)
 create mode 100644 tests/test_local_cliffords.py
 delete mode 100644 tests/test_vops.py

diff --git a/local_cliffords.py b/local_cliffords.py
index 8c0b905..cb98c3b 100644
--- a/local_cliffords.py
+++ b/local_cliffords.py
@@ -1,44 +1,53 @@
+ #!/usr/bin/python
+# -*- coding: utf-8 -*-
+
+""" 
+Generates and enumerates the 24 elements of the local Clifford group
+Following the prescription of Anders (thesis pg. 26):
+> Table 2.1: The 24 elements of the local Clifford group. The row index (here called the “sign symbol”) shows how the operator
+> U permutes the Pauli operators σ = X, Y, Z under the conjugation σ = ±UσU† . The column index (the “permutation
+> symbol”) indicates the sign obtained under the conjugation: For operators U in the I column it is the sign of the permutation
+> (indicated on the left). For elements in the X, Y and Z columns, it is this sign only if the conjugated Pauli operator is the one
+> indicated by the column header and the opposite sign otherwise.
+""" 
+
 from numpy import *
 
+# Some two-qubit matrices
+i = matrix(eye(2, dtype=complex))
 px = matrix([[0, 1], [1, 0]], dtype=complex)
 py = matrix([[0, -1j], [1j, 0]], dtype=complex)
 pz = matrix([[1, 0], [0, -1]], dtype=complex)
-i = matrix(eye(2, dtype=complex))
 h = matrix([[1, 1], [1, -1]], dtype=complex) / sqrt(2)
 p = matrix([[1, 0], [0, 1j]], dtype=complex)
+paulis = (px, py, pz)
 
-s_set = [i, p, p*p, p*p*p]
-c_set = [i, h, h*p, h*p*p, h*p*p*p, h*p*p*h]
+# More two-qubit matrices
+s_rotations = [i, p, p*p, p*p*p]
+s_names = ["i", "p", "pp", "ppp"]
+c_rotations = [i, h, h*p, h*p*p, h*p*p*p, h*p*p*h]
+c_names = ["i", "h", "hp", "hpp", "hppp", "hpph"]
 
 def identify_pauli(m):
+    """ Given a signed Pauli matrix, name it. """
     for sign in [+1, -1]:
-        for label, pauli in zip("XYZ", (px, py, pz)):
+        for label, pauli in zip("xyz", paulis):
             if allclose(sign*pauli, m):
                 return "{}{}".format("+" if sign>0 else "-", label)
 
-for p in px, py, pz:
-    for sign in [+1, -1]:
-        print identify_pauli(sign*p)
+def get_action(u):
+    """ Get the action of a Pauli matrix on three qubits """
+    return tuple(identify_pauli(u*p*u.H) for p in paulis)
+
 
 
-print py
-print h*px*h.H
-print h*py*h.H
-print h*pz*h.H
 
-#names = []
-#matrices = []
-#for s, s_name in zip(s_set, s_names):
-    #for c, c_name in zip(c_set, c_names):
-        #names.append(s_name+c_name)
-        #matrices.append(s*c)
+if __name__ == '__main__':
+    permutations = ["xyz", "yxz", "zyx", "xzy", "yzx", "zxy"]
 
-#print " ".join(names)
-#print len(names)
 
-#for m in matrices:
-    # print (m/abs(amax(m))).round(0).reshape(4)
-    #print average(abs(array((m/abs(amax(m))).round(0).reshape(4).tolist()[0])))
+    #for s, sn in zip(s_rotations, s_names):
+        #for c, cn in zip(c_rotations, c_names):
+            #print sn, "\t", cn, "\t", get_action(s*c)
 
 
-    
diff --git a/tests/test_local_cliffords.py b/tests/test_local_cliffords.py
new file mode 100644
index 0000000..e88c890
--- /dev/null
+++ b/tests/test_local_cliffords.py
@@ -0,0 +1,9 @@
+import local_cliffords as lc
+
+def test_identify_pauli():
+    assert lc.identify_pauli(lc.px) == "+x"
+    assert lc.identify_pauli(-lc.px) == "-x"
+    assert lc.identify_pauli(-lc.pz) == "-z"
+
+def test_get_action():
+    assert lc.get_action(lc.i) == ("+x", "+y", "+z")
diff --git a/tests/test_vops.py b/tests/test_vops.py
deleted file mode 100644
index 6282e7a..0000000
--- a/tests/test_vops.py
+++ /dev/null
@@ -1,5 +0,0 @@
-from vops import *
-
-def test_vops():
-    a = LocCliffOp("hadamard")
-