def test_flatten_exp():
n1, n2 = 3, 4
H_1 = Gate.random_hermitian(n1)
H_2 = Gate.random_hermitian(n2)
H = H_1 @ Gate.identity(n2) + Gate.identity(n1) @ H_2
op = H.get_flatop()
H_flat = op.do(H)
H_flat = Gate.promote(H_flat)
t = 1.
U_flat = H_flat.evolution_operator(t)
U_1 = H_1.evolution_operator(t)
U_2 = H_2.evolution_operator(t)
U = U_1 @ U_2
U_unflat = op.undo(U_flat)
assert U.is_close(U_unflat)
U_unflat = H.evolution_operator(t)
assert U.is_close(U_unflat)
def test_random():
A = Qu.random((2, 2), 'ud')
A = Gate.random_hermitian(4)
assert A.is_hermitian()
A = Gate.random_unitary(4)
assert A.is_unitary()
def test_tensor_product():
A = Gate((2, 2))
A[0, 0] = 1.
A[0, 1] = 2.
A[1, 0] = 3.
A[1, 1] = 4.
B = Gate((2, 2))
B[0, 0] = 5.
B[0, 1] = 6.
B[1, 0] = 7.
B[1, 1] = 8.
AB = A @ B
for i, j, k, l in genidx((2, 2, 2, 2)):
assert AB[i, j, k, l] == A[i, j] * B[k, l]
AB = AB.contract(1, 2)
for i, j in genidx((2, 2)):
#print i, j, AB[i, j], "=>", sum(A[i, k] * B[k, j] for k in (0, 1))
assert AB[i, j] == sum(A[i, k] * B[k, j] for k in (0, 1))
assert on.shape == (2, )
assert (on @ on).is_close(bits('11'))
c = on @ off
assert c.shape == (2, 2)
c = on @ off @ on @ on
assert c.shape == (2, ) * 4
assert c.is_close(bits('1011'))
for i0 in (0, 1):
for i1 in (0, 1):
for i2 in (0, 1):
for i3 in (0, 1):
r = c[i0, i1, i2, i3]
assert (r != 0.) == ((i0, i1, i2, i3) == (True, False,
True, True))
x = Gate.H.apply(off)
assert x.space == Space((2, ), 'u'), str(x)
y = (Gate.H @ off).contract(1, 2)
assert x.is_close(y)
A = Gate.H @ Gate.I
#print A.shape, A.valence
x = bits('00')
def test_pure():
v = Qu.random((2, ), 'u')
v /= v.norm()
A = v @ ~v
A = Gate.promote(A)
assert is_close(A.trace(), 1.)
assert A.is_pure()
A = 0.5 * Gate.dyads[0] + 0.5 * Gate.dyads[1]
A = Gate.promote(A)
assert is_close(A.trace(), 1.)
assert not A.is_pure()
def test_adjoint():
for A in Gate.I, Gate.X, Gate.Y, Gate.Z, Gate.H:
B = A * ~A
assert B.is_close(Gate.I)
B = ~A * A
assert B.is_close(Gate.I)
A = Qu.random((2, 3), 'ud')
assert (~A).shape == (2, 3)
assert (~A).valence == 'du'
H = ~A * A
assert Gate.promote(H).is_hermitian()
B = Qu.random((4, 2), 'ud')
E = Qu.random((3, 2, 2), 'udu')
u = Qu.random(2, 'u')
v = Qu.random(3, 'd')
for i in range(100):
word = []
for j in range(randint(1, 4)):
word.append(choice((A, B, E, u, v)))
lhs = ~reduce(matmul, word)
rhs = reduce(matmul, [~x for x in word])
assert lhs.space == rhs.space, (lhs.space, rhs.space)
assert lhs.is_close(rhs)
def errop(t):
H = Gate.random_hermitian(2)
U = H.evolution_operator(t)
assert U.is_unitary()
return U
def test_errop(t):
H = Gate.random_hermitian(2)
A = -1.j*t*H
print(A)
for val, vec in A.eigs():
print(val, numpy.exp(val))
print()
U = A.expm()
for val, vec in U.eigs():
print(val)
print()
assert U.is_unitary()
return U
def test_gate_properties():
A = Gate((2, 2))
A[0, 1] = 1.
assert not A.is_unitary()
assert not A.is_hermitian()
for A in Gate.I, Gate.X, Gate.Y, Gate.Z, Gate.H:
assert A.is_unitary()
for A in Gate.I, Gate.X, Gate.Z, Gate.H:
assert A.is_hermitian()
def test_evolve():
t = 1.
H = Gate.random_hermitian(2)
U = H.evolution_operator(t)
W = H.evolution_operator(t / 2)
#print (W*W).shortstr()
assert (W * W).is_close(U)
v = Qu.random(2, 'u')
v.normalize()
#print
w = U * v
#print w.shortstr()
x = W * v
x = W * x
#print x.shortstr()
assert w.is_close(x)