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Pete Shadbolt 8 jaren geleden
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3 gewijzigde bestanden met toevoegingen van 41 en 28 verwijderingen
  1. +32
    -23
      local_cliffords.py
  2. +9
    -0
      tests/test_local_cliffords.py
  3. +0
    -5
      tests/test_vops.py

+ 32
- 23
local_cliffords.py Bestand weergeven

@@ -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)



+ 9
- 0
tests/test_local_cliffords.py Bestand weergeven

@@ -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")

+ 0
- 5
tests/test_vops.py Bestand weergeven

@@ -1,5 +0,0 @@
from vops import *

def test_vops():
a = LocCliffOp("hadamard")


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