def test_1031_subs():
t, x, y, z = sp.symbols("t x y z")
q_sym = QHStates([QH([t, x, y, x * y * z])])
q_z = q_sym.subs({t: 1, x: 2, y: 3, z: 4})
print("t x y xyz sub 1 2 3 4: ", q_z)
assert q_z.equals(QHStates([QH([1, 2, 3, 24])]))
def test_1130_identity():
I2 = QHStates().identity(2, operator=True)
print("Operator Idenity, diagonal 2x2", I2)
assert I2.qs[0].equals(QH().q_1())
assert I2.qs[1].equals(QH().q_0())
I2 = QHStates().identity(2)
print("Idenity on 2 state ket", I2)
assert I2.qs[0].equals(QH().q_1())
assert I2.qs[1].equals(QH().q_1())
def test_1305_Lorentz_next_rotation():
with pytest.raises(ValueError):
QHStates.Lorentz_next_rotation(qs_1234, q2_states)
next_rot: QHStates = QHStates.Lorentz_next_rotation(qs_1234, qs_1324)
print("next_rotation: ", next_rot)
assert math.isclose(next_rot.qs[0].t, 0)
assert math.isclose(next_rot.qs[1].t, 0)
assert math.isclose(next_rot.norm_squared().qs[0].t, 2)
assert not next_rot.qs[0].equals(next_rot.qs[1])
def test_1305_Lorentz_next_boost():
with pytest.raises(ValueError):
QHStates.Lorentz_next_boost(qs_1234, q2_states)
next_boost: QHStates = QHStates.Lorentz_next_boost(qs_1234, qs_1324)
print("next_boost: ", next_boost)
assert next_boost.qs[0].t != 0
assert next_boost.qs[1].t != 0
assert next_boost.norm_squared().qs[0].t != 1
assert not next_boost.qs[0].equals(next_boost.qs[1])
boosted_square = q2_states.rotation_and_or_boost(next_boost).square()
q2_states_square = q2_states.square()
assert math.isclose(q2_states_square.qs[0].t, boosted_square.qs[0].t)
def test_1140_product():
assert b.product(o).equals(
QHStates([QH([10, 0, 0, 0]),
QH([20, 0, 0, 0]),
QH([30, 0, 0, 0])]))
assert b.product(k).equals(QHStates([QH([32, 0, 0, 0])]))
assert b.product(o).product(k).equals(QHStates([QH([320, 0, 0, 0])]))
assert b.product(b).equals(
QHStates([QH([1, 0, 0, 0]),
QH([4, 0, 0, 0]),
QH([9, 0, 0, 0])]))
assert o.product(k).equals(
QHStates([QH([40, 0, 0, 0]),
QH([50, 0, 0, 0]),
QH([60, 0, 0, 0])]))
assert o.product(o).equals(QHStates([QH([100, 0, 0, 0])]))
assert k.product(k).equals(
QHStates([QH([16, 0, 0, 0]),
QH([25, 0, 0, 0]),
QH([36, 0, 0, 0])]))
assert k.product(b).equals(
QHStates([
QH([4, 0, 0, 0]),
QH([5, 0, 0, 0]),
QH([6, 0, 0, 0]),
QH([8, 0, 0, 0]),
QH([10, 0, 0, 0]),
QH([12, 0, 0, 0]),
QH([12, 0, 0, 0]),
QH([15, 0, 0, 0]),
QH([18, 0, 0, 0]),
]))
def test_1304_rotation_and_or_boost():
q1_sq = Q_states.square()
beta = 0.003
gamma = 1 / math.sqrt(1 - beta**2)
h = QHStates([QH([gamma, gamma * beta, 0, 0])])
q_z = Q_states.rotation_and_or_boost(h)
q_z2 = q_z.square()
print("q1_sq: ", q1_sq)
print("boosted: ", q_z)
print("boosted squared: ", q_z2)
assert round(q_z2.qs[0].t, 5) == round(q1_sq.qs[0].t, 5)
def test_1038_q_j():
qj = QHStates().q_j(2.0, 3)
print("qj(3): ", qj)
assert qj.dim == 3
assert qj.qs[0].y == 2.0
def test_1037_q_i():
qi = QHStates().q_i(2.0, 3)
print("qi(3): ", qi)
assert qi.dim == 3
assert qi.qs[0].x == 2.0
def test_1036_q_1():
q1 = QHStates().q_1(2.0, 3)
print("q1(3): ", q1)
assert q1.dim == 3
assert q1.qs[0].t == 2.0
def test_1035_q_0():
q0 = QHStates().q_0(3)
print("q0(3): ", q0)
assert q0.dim == 3
def test_1430_inverse():
q_z = P_states.inverse()
print("inverse: ", q_z)
assert q_z.equals(QHStates([QH([0, -0.16, 0.12, 0])]))
def test_1302_triple_product():
q_z = Q_states.triple_product(P_states, Q_states)
print("triple product: ", q_z)
assert q_z.equals(QHStates([QH([-2, 124, -84, 8])]))
def test_1125_trace():
trace = v1123.op(2, 2).trace()
print("trace: ", trace)
assert trace.equals(QHStates([q_4]))
def test_1312_square():
ns = q_1_q_i.square()
ns.print_state("q_1_q_i square")
assert ns.equals(QHStates([q_1, q_n1]))
def test_1305_bracket():
bracket1234 = QHStates().bracket(q_1234,
QHStates().identity(4, operator=True),
q_1234)
print("bracket <1234|I|1234>: ", bracket1234)
assert bracket1234.equals(QHStates([QH([34, 0, 0, 0])]))
def test_1303_rotate():
q_z = Q_states.rotate(QHStates([q_i]))
print("rotate: ", q_z)
assert q_z.equals(QHStates([QH([1, -2, 3, 4])]))
def test_1039_q_k():
qk = QHStates().q_k(2.0, 3)
print("qk(3): ", qk)
assert qk.dim == 3
assert qk.qs[0].z == 2.0
def test_1039_q_random():
qr = QHStates().q_random(-2, 2, dim=3)
print("qk(3): ", qr)
assert qr.dim == 3
assert qr.qs[0].z != qr.qs[0].t
def test_1230_product_AOpB():
AOpB = A.product(Op).product(B)
print("A Op B: ", AOpB)
assert AOpB.equals(QHStates([QH([0, 22, 11, 0])]))
def test_1315_norm_squared():
ns = q_1_q_i.norm_squared()
ns.print_state("q_1_q_i norm squared")
assert ns.equals(QHStates([QH([2, 0, 0, 0])]))
def test_1301_divide_by():
q_z = Q_states.divide_by(Q_states)
print("divide_by: ", q_z)
assert q_z.equals(QHStates([q_1]))
def test_1150_product_AA():
Aket = deepcopy(A).ket()
AA = A.product(Aket)
print("<A|A>: ", AA)
assert AA.equals(QHStates([QH([17, 0, 0, 0])]))
def test_1318_norm_squared_of_vector():
ns = q_1_q_i.norm_squared_of_vector()
ns.print_state("q_1_q_i norm squared of vector")
assert ns.equals(QHStates([q_1]))
def test_1290_product_AOp4iB():
AOp4iB = A.product(Op4i).product(B)
print("A* Op4i B: ", AOp4iB)
assert AOp4iB.equals(QHStates([QH([-9, 24, 0, 8])]))
q_2 = QH([2, 0, 0, 0])
q_n2 = QH([-2, 0, 0, 0])
q_3 = QH([3, 0, 0, 0])
q_n3 = QH([-3, 0, 0, 0])
q_4 = QH([4, 0, 0, 0])
q_5 = QH([5, 0, 0, 0])
q_6 = QH([6, 0, 0, 0])
q_10 = QH([10, 0, 0, 0])
q_n5 = QH([-5, 0, 0, 0])
q_7 = QH([7, 0, 0, 0])
q_8 = QH([8, 0, 0, 0])
q_9 = QH([9, 0, 0, 0])
q_n11 = QH([-11, 0, 0, 0])
q_21 = QH([21, 0, 0, 0])
q_n34 = QH([-34, 0, 0, 0])
v3: QHStates = QHStates([q_3])
v1123: QHStates = QHStates([q_1, q_1, q_2, q_3])
v3n1n21: QHStates = QHStates([q_3, q_n1, q_n2, q_1])
v9: QHStates = QHStates([q_1, q_1, q_2, q_3, q_1, q_1, q_2, q_3, q_2])
v9i: QHStates = QHStates([
QH([0, 1, 0, 0]),
QH([0, 2, 0, 0]),
QH([0, 3, 0, 0]),
QH([0, 4, 0, 0]),
QH([0, 5, 0, 0]),
QH([0, 6, 0, 0]),
QH([0, 7, 0, 0]),
QH([0, 8, 0, 0]),
QH([0, 9, 0, 0]),
])
vv9 = v9.add(v9i)