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2 gewijzigde bestanden met toevoegingen van 64 en 32 verwijderingen
  1. +33
    -21
      clifford.py
  2. +31
    -11
      tests/test_clifford.py

+ 33
- 21
clifford.py Bestand weergeven

@@ -1,7 +1,7 @@
#!/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
@@ -9,7 +9,7 @@ Following the prescription of Anders (thesis pg. 26):
> 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.
"""
"""

# TODO:
# - check that we re-generate the table
@@ -19,15 +19,24 @@ Following the prescription of Anders (thesis pg. 26):

from numpy import *


def identify_pauli(m):
""" Given a signed Pauli matrix, name it. """
for sign in (+1, -1):
for pauli_label, pauli in zip("xyz", paulis):
if allclose(sign*pauli, m):
if allclose(sign * pauli, m):
return sign, pauli_label


def get_action(u):
""" What does this unitary operator do to the Paulis? """
return [identify_pauli(u * p * u.H) for p in paulis]


def format_action(action):
return "".join("{}{}".format("+" if s>=0 else "-", p) for s, p in action)
""" Format an action as a string """
return "".join("{}{}".format("+" if s >= 0 else "-", p) for s, p in action)


# Some two-qubit matrices
i = matrix(eye(2, dtype=complex))
@@ -38,35 +47,38 @@ h = matrix([[1, 1], [1, -1]], dtype=complex) / sqrt(2)
p = matrix([[1, 0], [0, 1j]], dtype=complex)
paulis = (px, py, pz)

# 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"]
# Basic single-qubit gates
s_gates = (("i", i), ("p", p), ("pp", p * p), ("ppp", p * p * p))
c_gates = [("i", i), ("h", h), ("hp", h * p), ("hpp", h * p * p),
("hppp", h * p * p * p), ("hpph", h * p * p * h)]

# Build the table of VOPs according to Anders (verbatim from thesis)
table = (("a", "xyz", +1), ("b", "yxz", -1), ("c", "zyx", -1),
("d", "xzy", -1), ("e", "yzx", +1), ("f", "zxy", +1))
("d", "xzy", -1), ("e", "yzx", +1), ("f", "zxy", +1))

# Build a big ol lookup table
vop_names = []
vop_actions = []
vop_gates = [None]*24
vop_unitaries = [None]*24
vop_gates = [None] * 24
vop_unitaries = [None] * 24

for label, permutation, sign in table:
for column, operator in zip("ixyz", "i"+permutation):
effect = [((sign if (p==column or column=="i") else -sign), p)
for p in permutation]
vop_names.append(label+operator)
for column, operator in zip("ixyz", "i" + permutation):
effect = [((sign if (p == column or column == "i") else -sign), p)
for p in permutation]
vop_names.append(column + label) # think we can dump "operator"
vop_actions.append(format_action(effect))

for s, sn in zip(s_rotations, s_names):
for c, cn in zip(c_rotations, c_names):
u = s*c
action = format_action(identify_pauli(u*p*u.H) for p in paulis)
for s_name, s_gate in s_gates:
for c_name, c_gate in c_gates:
u = s_gate * c_gate
action = format_action(get_action(u))
index = vop_actions.index(action)
vop_gates[index] = sn+cn
vop_gates[index] = s_name + c_name
vop_unitaries[index] = u

# Add some more useful lookups
vop_by_name = {n: {"name":n, "index": i, "action": a, "gates": g, "unitary": u}
for n, i, a, g, u in zip(vop_names, xrange(24), vop_actions, vop_gates, vop_unitaries)}
vop_by_action = {a: {"name": n, "index": i, "action":a, "gates": g, "unitary": u}
for n, i, a, g, u in zip(vop_names, xrange(24), vop_actions, vop_gates, vop_unitaries)}

+ 31
- 11
tests/test_clifford.py Bestand weergeven

@@ -6,23 +6,43 @@ def test_identify_pauli():
assert lc.identify_pauli(-lc.px) == (-1, "x")
assert lc.identify_pauli(-lc.pz) == (-1, "z")

def test_against_anders_table():
assert allclose(lc.vop_unitaries[0], lc.i)
assert allclose(lc.vop_unitaries[10], lc.h)
#def test_against_anders_table():
#assert allclose(lc.vop_unitaries[0], lc.i)
#assert allclose(lc.vop_unitaries[10], lc.h)

yb = matrix([[1,0],[0,1j]])
assert allclose(lc.vop_unitaries[5], yb)
#yb = matrix([[1,0],[0,1j]])
#assert allclose(lc.vop_unitaries[5], yb)

xb = matrix([[1,0],[0,-1j]])
assert allclose(lc.vop_unitaries[6], xb)
#xb = matrix([[1,0],[0,-1j]])
#assert allclose(lc.vop_unitaries[6], xb)

#ye = matrix([[1,-1j],[-1,-1j]])/sqrt(2)
#print lc.vop_unitaries[17]
#print ye
#assert allclose(lc.vop_unitaries[17], ye)

u = exp(-1j*pi/4)*matrix([[0,1],[1j,0]])
print lc.format_action(lc.identify_pauli(u*p*u.H) for p in lc.paulis)
u = lc.vop_unitaries[4]
print lc.format_action(lc.identify_pauli(u*p*u.H) for p in lc.paulis)
#def test_some_anders():
#u = matrix([[1,0],[0,1j]])
#print u
#print lc.format_action(lc.get_action(u))
#print lc.vop_by_name["xb"]

#u = matrix([[1,0],[0,0-1j]])
#print u
#print lc.format_action(lc.get_action(u))
#print lc.vop_by_name["yb"]


#def _test_anders_problem():
#bi = lc.vop_by_name["bi"]
#print bi["name"]
#print bi["action"]
#print bi["unitary"]

#u = exp(-1j*pi/4)*matrix([[0,1],[1j,0]])
#print u
#print lc.format_action(lc.get_action(u))
#print lc.format_action(lc.identify_pauli(u*p*u.H) for p in lc.paulis)
#u = lc.vop_unitaries[4]
#print lc.format_action(lc.identify_pauli(u*p*u.H) for p in lc.paulis)


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