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Printing out interesting matrices

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Pete Shadbolt 8 年之前
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共有 2 個文件被更改,包括 34 次插入87 次删除
  1. +0
    -58
      new.py
  2. +34
    -29
      tests/test_clifford.py

+ 0
- 58
new.py 查看文件

@@ -1,58 +0,0 @@
from numpy import *
from scipy.linalg import sqrtm

# 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)

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)

#permuters = (i, h*p*h*pz, p*h*p*h, px*p, p*h, p*p*h*pz)
permuters = (i, h, p, h*p, h*p*h, h*p*h*p)
signs = (i, px, py, pz)
unitaries = []
actions = []
for perm in permuters:
for sign in signs:
action = format_action(get_action(sign*perm))
actions.append(action)
unitaries.append(perm*sign)
#print (perm*sign).round(2).reshape(1,4)[0],
print action,
print


assert len(set(actions)) == 24

sqy = sqrtm(1j*py)
msqy = sqrtm(-1j*py)
sqz = sqrtm(1j*pz)
msqz = sqrtm(-1j*pz)
sqx = sqrtm(1j*px)
msqx = sqrtm(-1j*px)
for m in i, px, py, pz, h, p, sqz, msqz, sqy, msqy, sqx, msqx:
if any([allclose(u, m) for u in unitaries]):
print "found it"
else:
if any([allclose(exp(1j*pi*phi/4.)*u, m) for phi in range(8) for u in unitaries]):
print "found up to global phase"
else:
print "lost"


+ 34
- 29
tests/test_clifford.py 查看文件

@@ -2,14 +2,23 @@ import clifford as lc
from numpy import *
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)
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 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):
@@ -17,12 +26,20 @@ def identify_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)
return "".join("{}{}".format("+" if s >= 0 else "-", p) for s, p in action)


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


def test_we_have_all_useful_gates():
@@ -30,27 +47,15 @@ def test_we_have_all_useful_gates():
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)",
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):
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

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)

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