Pete Shadbolt преди 8 години
родител
ревизия
6a4354aab8
променени са 3 файла, в които са добавени 61 реда и са изтрити 137 реда
  1. +8
    -82
      clifford.py
  2. +0
    -10
      tests/test_against_anders_thesis.py
  3. +53
    -45
      tests/test_clifford.py

+ 8
- 82
clifford.py Целия файл

@@ -11,97 +11,23 @@ Following the prescription of Anders (thesis pg. 26):
> indicated by the column header and the opposite sign otherwise.
"""

# TODO:
# - check that we re-generate the table
# - do conjugation
# - do times table
# - write tests

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

# 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))
permutations = (i, h, p, h*p, h*p*h, h*p*h*p)
signs = (i, px, py, pz)
unitaries = [p*s for p in permutations for s in signs]

# Build a big ol lookup table
vop_names = []
vop_actions = []
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(column + label) # think we can dump "operator"
vop_actions.append(format_action(effect))

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] = 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)}

names, unitaries = [], []
for c_name, c_gate in c_gates:
for s_name, s_gate in s_gates:
names.append(s_name+c_name)
unitaries.append(s_gate * c_gate)
print s_gate * c_gate.round(2)
print

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)
h = matrix([[1, 1], [1, -1]], dtype=complex) / sqrt(2)
p = matrix([[1, 0], [0, 1j]], dtype=complex)

#for m in i, px, py, pz:
#print any([allclose(x, m) for x in unitaries])
# TODO:
# - check that we re-generate the table
# - do conjugation
# - do times table
# - write tests


+ 0
- 10
tests/test_against_anders_thesis.py Целия файл

@@ -36,13 +36,3 @@ anders = [
ir2 * matrix([[1,-1],[-1j,-1j]], dtype=complex),
]


def test_everything():
for i, (a, b) in enumerate(zip(lc.vop_actions, anders)):
a2 = lc.format_action(lc.get_action(b))
if i %4==0:
print
print "({} {})".format(a, a2),
#if not any([allclose(a, x) for x in anders]):
#print lc.vop_gates[i], "is not in {anders}"


+ 53
- 45
tests/test_clifford.py Целия файл

@@ -1,48 +1,56 @@
import clifford as lc
from numpy import *

def test_identify_pauli():
assert lc.identify_pauli(lc.px) == (1, "x")
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)

#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)

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

#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)
from scipy.linalg import sqrtm

sqy = sqrtm(1j*lc.py)
msqy = sqrtm(-1j*lc.py)
sqz = sqrtm(1j*lc.pz)
msqz = sqrtm(-1j*lc.pz)
sqx = sqrtm(1j*lc.px)
msqx = sqrtm(-1j*lc.px)
paulis = (lc.px, lc.py, lc.pz)

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):
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)


def test_we_have_all_useful_gates():
""" Check that all the interesting gates are included up to a global phase """
names = "i", "px", "py", "pz", "h", "p"
unitaries = lc.i, lc.px, lc.py, lc.pz, lc.h, lc.p
for name, unitary in zip(names, unitaries):
foundit = False
for i, clifford in enumerate(lc.unitaries):
if allclose(clifford, unitary):
foundit = True
print "{}\t=\tlc.unitaries[{}]".format(name, i)
assert foundit

names = "sqrt(ix)", "sqrt(-ix)", "sqrt(iy)", "sqrt(-iy)", "sqrt(iz)", "sqrt(-iz)",
unitaries = sqz, msqz, sqy, msqy, sqx, msqx
for name, unitary in zip(names, unitaries):
foundit = False
for phase in range(8):
for i, clifford in enumerate(lc.unitaries):
if allclose(exp(1j*phase*pi/4.)*clifford, unitary):
foundit = True
print "{}\t=\texp({} . i . pi/4).lc.unitaries[{}]".format(name, phase, i)
assert foundit


def test_we_have_24_matrices():
""" Check that we have 24 unique actions on the Bloch sphere """
actions = set(tuple(get_action(u)) for u in lc.unitaries)
assert len(set(actions)) == 24


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