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Now calculates a CZ table ... is it correct??!?

master
Pete Shadbolt преди 8 години
родител
ревизия
d8d0aa108a
променени са 4 файла, в които са добавени 48 реда и са изтрити 36 реда
  1. +30
    -20
      cz_table.py
  2. +3
    -0
      qi.py
  3. +9
    -10
      tables.py
  4. +6
    -6
      tests/test_clifford.py

+ 30
- 20
cz_table.py Целия файл

@@ -1,32 +1,42 @@
import qi
import numpy as np
import tables
import tqdm
from tqdm import tqdm
import itertools as it

# TODO: ensure that Constraint 1 is met. i.e.
# if C1 is in Z, choose C1' such that it is in Z
def get_krontable():
table = np.zeros((24,24,4,4), dtype=complex)
for i, j in it.product(range(24), range(24)):
u1 = tables.unitaries[i]
u2 = tables.unitaries[j]
table[i, j, :, :] = np.kron(u1, u2)
return table

table1 = []
table2 = []
def find(bond, c1, c2, z, krontable):
# Figure out the target state
state = qi.bond if bond else qi.nobond
target = qi.cz * krontable[c1, c2] * state

bond = qi.cz * np.kron(qi.plus, qi.plus)
no_bond = np.kron(qi.plus, qi.plus)
# Choose the sets to search over
s1 = z if c1 in z else xrange(24)
s2 = z if c2 in z else xrange(24)

def find(thing, table):
for index, trial in enumerate(table):
for qq in range(16):
if np.allclose(thing, np.exp(2j*np.pi*qq/16.) * trial):
yield index
for bond, c1p, c2p in it.product([0,1], s1, s2):
state = qi.bond if bond else qi.nobond
trial = krontable[c1p, c2p] * state
for phase in range(8):
if np.allclose(target, np.exp(1j * phase * np.pi / 4.) * trial):
return bond, c1p, c2p

for state in bond, no_bond:
for a in tables.unitaries:
for b in tables.unitaries:
state = np.kron(a, b) * state
table1.append(state)
table2.append(qi.cz*state)
raise IndexError

for index, thing in enumerate(table2):
print "{} -> {}".format(index, list(find(thing, table1)))

z = [tables.find(u, tables.unitaries) for u in qi.id, qi.px, qi.pz, qi.ph, qi.ph.H]
krontable = get_krontable()

cz_table = np.zeros((2, 24, 24, 3))
for bond, c1, c2 in tqdm(list(it.product([0,1], range(24), range(24)))):
cz_table[bond, c1, c2] = find(bond, c1, c2, z, krontable)

np.save("cz_table.npy", cz_table)


+ 3
- 0
qi.py Целия файл

@@ -30,3 +30,6 @@ paulis = (px, py, pz)
common_us = id, px, py, pz, ha, ph, sqz, msqz, sqy, msqy, sqx, msqx
names = "identity", "px", "py", "pz", "hadamard", "phase", "sqz", "msqz", "sqy", "msqy", "sqx", "msqx"
by_name = dict(zip(names, common_us))

bond = cz * np.kron(plus, plus)
nobond = np.kron(plus, plus)

+ 9
- 10
tables.py Целия файл

@@ -13,18 +13,18 @@ import cPickle
import qi

# TODO: make this more efficient / shorter
def find_up_to_phase(u):
def find(needle, haystack):
""" Find the index of a given u within a list of unitaries, up to a global phase """
for i, t in enumerate(unitaries):
for i, t in enumerate(haystack):
for phase in range(8):
if np.allclose(t, np.exp(1j * phase * np.pi / 4.) * u):
return i, phase
if np.allclose(t, np.exp(1j * phase * np.pi / 4.) * needle):
return i
raise IndexError


def compose_u(decomposition):
""" Get the unitary representation of a particular decomposition """
us = (elements[c] for c in decomposition)
us = ({"x": qi.sqx, "z": qi.msqz}[c] for c in decomposition)
return np.matrix(reduce(np.dot, us), dtype=complex)


@@ -38,14 +38,15 @@ def construct_tables(filename="tables.cache"):
if os.path.exists(filename):
return cPickle.load(open(filename, "r"))

by_name = {name: find_up_to_phase(u)[0] for name, u in qi.by_name.items()}
by_name = {name: find(u, unitaries) for name, u in qi.by_name.items()}
get_name = {v:k for k, v in by_name.items()}
conjugation_table = [find_up_to_phase(u.H)[0]
conjugation_table = [find(u.H, unitaries)
for i, u in enumerate(unitaries)]
times_table = [[find_up_to_phase(u * v)[0] for v in unitaries]
times_table = [[find(u * v, unitaries) for v in unitaries]
for u in tqdm(unitaries)]
cz_table = None
output = by_name, get_name, conjugation_table, times_table, cz_table

with open(filename, "w") as f:
cPickle.dump(output, f)
return output
@@ -53,7 +54,5 @@ def construct_tables(filename="tables.cache"):
decompositions = ("xxxx", "xx", "zzxx", "zz", "zxx", "z", "zzz", "xxz",
"xzx", "xzxxx", "xzzzx", "xxxzx", "xzz", "zzx", "xxx", "x",
"zzzx", "xxzx", "zx", "zxxx", "xxxz", "xzzz", "xz", "xzxx")
elements = {"x": qi.sqx, "z": qi.msqz}
unitaries = [compose_u(d) for d in decompositions]
by_name, get_name, conjugation_table, times_table, cz_table = construct_tables()


+ 6
- 6
tests/test_clifford.py Целия файл

@@ -14,11 +14,11 @@ def identify_pauli(m):
return sign, pauli_label


def _test_find_up_to_phase():
def _test_find():
""" Test that slightly suspicious function """
assert lc.find_up_to_phase(id) == (0, 0)
assert lc.find_up_to_phase(px) == (1, 0)
assert lc.find_up_to_phase(exp(1j*pi/4.)*ha) == (4, 7)
assert lc.find(id, lc.unitaries) == 0
assert lc.find(px, lc.unitaries) == 1
assert lc.find(exp(1j*pi/4.)*ha, lc.unitaries) == 4

def get_action(u):
""" What does this unitary operator do to the Paulis? """
@@ -38,14 +38,14 @@ def test_we_have_24_matrices():
def test_we_have_all_useful_gates():
""" Check that all the interesting gates are included up to a global phase """
for name, u in qi.by_name.items():
lc.find_up_to_phase(u)
lc.find(u, lc.unitaries)


def _test_group():
""" Test we are really in a group """
matches = set()
for a, b in tqdm(it.combinations(lc.unitaries, 2), "Testing this is a group"):
i, phase = lc.find_up_to_phase(a*b)
i, phase = lc.find(a*b, lc.unitaries)
matches.add(i)
assert len(matches)==24



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