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Pete Shadbolt 8 年前
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共有 2 个文件被更改,包括 36 次插入32 次删除
  1. +20
    -5
      clifford.py
  2. +16
    -27
      tests/test_clifford.py

+ 20
- 5
clifford.py 查看文件

@@ -13,17 +13,32 @@ Following the prescription of Anders (thesis pg. 26):

from numpy import *

i = matrix(eye(2, dtype=complex))
def find_up_to_phase(u):
""" Find the index of a given u within a list of unitaries, up to a global phase """
global unitaries
for i, t in enumerate(unitaries):
for phase in range(8):
if allclose(t, exp(1j*phase*pi/4.)*u):
return i, phase
raise IndexError

id = 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)
ha = matrix([[1, 1], [1, -1]], dtype=complex) / sqrt(2)
ph= matrix([[1, 0], [0, 1j]], dtype=complex)

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

conjugation_table = []

for i, u in enumerate(unitaries):
i, phase = find_up_to_phase(u.H)
conjugation_table.append(i)


# TODO:
# - check that we re-generate the table


+ 16
- 27
tests/test_clifford.py 查看文件

@@ -11,14 +11,6 @@ msqx = sqrtm(-1j * lc.px)
paulis = (lc.px, lc.py, lc.pz)


def find_u(u, unitaries):
""" Find the index of a given u within a list of unitaries """
for i, t in enumerate(unitaries):
if allclose(t, u):
return i
return -1


def identify_pauli(m):
""" Given a signed Pauli matrix, name it. """
for sign in (+1, -1):
@@ -27,6 +19,12 @@ def identify_pauli(m):
return sign, pauli_label


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

def get_action(u):
""" What does this unitary operator do to the Paulis? """
return [identify_pauli(u * p * u.H) for p in paulis]
@@ -44,31 +42,22 @@ 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 """
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):
i = find_u(unitary, lc.unitaries)
assert i >= 0
print "{}\t=\tlc.unitaries[{}]".format(name, i)

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):
rotated = [exp(1j * phase * pi / 4.) * unitary for phase in range(8)]
results = [find_u(r, lc.unitaries) for r in rotated]
assert any(x > 0 for x in results)
phase, index = [(i, r) for i, r in enumerate(results) if r>=0][0]
print "exp(1j*{}*pi/4) . {}\t=\tlc.unitaries[{}]".format(phase, name, index)
common_us = lc.id, lc.px, lc.py, lc.pz, lc.ha, lc.ph, sqz, msqz, sqy, msqy, sqx, msqx
for u in common_us:
lc.find_up_to_phase(u)


def test_group():
""" Test we are really in a group """
matches = set()
for a in lc.unitaries:
for b in lc.unitaries:
unitary = a*b
rotated = [exp(1j * phase * pi / 4.) * unitary for phase in range(8)]
results = [find_u(r, lc.unitaries) for r in rotated]
assert len([x for x in results if x>=0])==1
i, phase = lc.find_up_to_phase(a*b)
matches.add(i)
assert len(matches)==24


def test_conjugation_table():
""" Check that the table of Hermitian conjugates is okay """
assert len(set(lc.conjugation_table))==24


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