def test_QubitBra():
assert Qubit(0).dual_class() == QubitBra
assert QubitBra(0).dual_class() == Qubit
assert represent(Qubit(1,1,0), nqubits=3).H ==\
represent(QubitBra(1,1,0), nqubits=3)
assert Qubit(0,1)._eval_innerproduct_QubitBra(QubitBra(1,0)) == Integer(0)
assert Qubit(0,1)._eval_innerproduct_QubitBra(QubitBra(0,1)) == Integer(1)
def test_measure_all():
assert measure_all(Qubit('11')) == [(Qubit('11'), 1)]
state = Qubit('11') + Qubit('10')
assert sorted(measure_all(state)) == sorted([(Qubit('11'), Rational(1,2)),\
(Qubit('10'), Rational(1,2))])
state2 = Qubit('11') / sqrt(5) + 2 * Qubit('00') / sqrt(5)
assert sorted(measure_all(state2)) == sorted([(Qubit('11'), Rational(1,5)), \
(Qubit('00'), Rational(4,5))])
def test_superposition_of_states():
assert qapply(CNOT(0,1)*HadamardGate(0)*(1/sqrt(2)*Qubit('01') + 1/sqrt(2)*Qubit('10'))).expand() == (Qubit('01')/2 + Qubit('00')/2 - Qubit('11')/2 +\
Qubit('10')/2)
assert matrix_to_qubit(represent(CNOT(0,1)*HadamardGate(0)\
*(1/sqrt(2)*Qubit('01') + 1/sqrt(2)*Qubit('10')), nqubits=2))\
== (Qubit('01')/2 + Qubit('00')/2 - Qubit('11')/2 + Qubit('10')/2)
def test_Qubit():
array = [0, 0, 1, 1, 0]
qb = Qubit('00110')
assert qb.flip(0) == Qubit('00111')
assert qb.flip(1) == Qubit('00100')
assert qb.flip(4) == Qubit('10110')
assert qb.dimension == 5
for i in range(5):
assert qb[i] == array[4 - i]
assert len(qb) == 5
qb = Qubit('110')
def test_Qubit():
array = [0, 0, 1, 1, 0]
qb = Qubit('00110')
assert qb.flip(0) == Qubit('00111')
assert qb.flip(1) == Qubit('00100')
assert qb.flip(4) == Qubit('10110')
assert qb.dimension == 5
for i in range(5):
assert qb[i] == array[4 - i]
assert len(qb) == 5
qb = Qubit('110')
def test_Qubit():
array = [0, 0, 1, 1, 0]
qb = Qubit("00110")
assert qb.flip(0) == Qubit("00111")
assert qb.flip(1) == Qubit("00100")
assert qb.flip(4) == Qubit("10110")
assert qb.qubit_values == (0, 0, 1, 1, 0)
assert qb.dimension == 5
for i in range(5):
assert qb[i] == array[4 - i]
assert len(qb) == 5
qb = Qubit("110")
def test_matrix_to_qubits():
qb = Qubit(0, 0, 0, 0)
mat = Matrix([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
assert matrix_to_qubit(mat) == qb
assert qubit_to_matrix(qb) == mat
state = 2 * sqrt(2) * (Qubit(0, 0, 0) + Qubit(0, 0, 1) + Qubit(0, 1, 0) +
Qubit(0, 1, 1) + Qubit(1, 0, 0) + Qubit(1, 0, 1) +
Qubit(1, 1, 0) + Qubit(1, 1, 1))
ones = sqrt(2) * 2 * Matrix([1, 1, 1, 1, 1, 1, 1, 1])
assert matrix_to_qubit(ones) == state.expand()
assert qubit_to_matrix(state) == ones
def test_apply_represent_equality():
gates = [
HadamardGate(int(3 * random.random())),
XGate(int(3 * random.random())),
ZGate(int(3 * random.random())),
YGate(int(3 * random.random())),
ZGate(int(3 * random.random())),
PhaseGate(int(3 * random.random())),
]
circuit = Qubit(
int(random.random() * 2),
int(random.random() * 2),
int(random.random() * 2),
int(random.random() * 2),
int(random.random() * 2),
int(random.random() * 2),
)
for i in range(int(random.random() * 6)):
circuit = gates[int(random.random() * 6)] * circuit
mat = represent(circuit, nqubits=6)
states = qapply(circuit)
state_rep = matrix_to_qubit(mat)
states = states.expand()
state_rep = state_rep.expand()
assert state_rep == states
def test_matrix_to_density():
mat = Matrix([[0, 0], [0, 1]])
assert matrix_to_density(mat) == Density([Qubit('1'), 1])
mat = Matrix([[1, 0], [0, 0]])
assert matrix_to_density(mat) == Density([Qubit('0'), 1])
mat = Matrix([[0, 0], [0, 0]])
assert matrix_to_density(mat) == 0
mat = Matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0]])
assert matrix_to_density(mat) == Density([Qubit('10'), 1])
mat = Matrix([[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
assert matrix_to_density(mat) == Density([Qubit('00'), 1])
def test_matrix_to_density():
mat = Matrix([[0, 0], [0, 1]])
assert matrix_to_density(mat) == Density([Qubit("1"), 1])
mat = Matrix([[1, 0], [0, 0]])
assert matrix_to_density(mat) == Density([Qubit("0"), 1])
mat = Matrix([[0, 0], [0, 0]])
assert matrix_to_density(mat) == 0
mat = Matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0]])
assert matrix_to_density(mat) == Density([Qubit("10"), 1])
mat = Matrix([[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
assert matrix_to_density(mat) == Density([Qubit("00"), 1])
def test_IntQubit():
# issue 9136
iqb = IntQubit(0, nqubits=1)
assert qubit_to_matrix(Qubit('0')) == qubit_to_matrix(iqb)
qb = Qubit('1010')
assert qubit_to_matrix(IntQubit(qb)) == qubit_to_matrix(qb)
iqb = IntQubit(1, nqubits=1)
assert qubit_to_matrix(Qubit('1')) == qubit_to_matrix(iqb)
assert qubit_to_matrix(IntQubit(1)) == qubit_to_matrix(iqb)
iqb = IntQubit(7, nqubits=4)
assert qubit_to_matrix(Qubit('0111')) == qubit_to_matrix(iqb)
assert qubit_to_matrix(IntQubit(7, 4)) == qubit_to_matrix(iqb)
iqb = IntQubit(8)
assert iqb.as_int() == 8
assert iqb.qubit_values == (1, 0, 0, 0)
iqb = IntQubit(7, 4)
assert iqb.qubit_values == (0, 1, 1, 1)
assert IntQubit(3) == IntQubit(3, 2)
#test Dual Classes
iqb = IntQubit(3)
iqb_bra = IntQubitBra(3)
assert iqb.dual_class() == IntQubitBra
assert iqb_bra.dual_class() == IntQubit
iqb = IntQubit(5)
iqb_bra = IntQubitBra(5)
assert iqb._eval_innerproduct_IntQubitBra(iqb_bra) == Integer(1)
iqb = IntQubit(4)
iqb_bra = IntQubitBra(5)
assert iqb._eval_innerproduct_IntQubitBra(iqb_bra) == Integer(0)
raises(ValueError, lambda: IntQubit(4, 1))
raises(ValueError, lambda: IntQubit('5'))
raises(ValueError, lambda: IntQubit(5, '5'))
raises(ValueError, lambda: IntQubit(5, nqubits='5'))
raises(TypeError, lambda: IntQubit(5, bad_arg=True))
def test_QubitBra():
qb = Qubit(0)
qb_bra = QubitBra(0)
assert qb.dual_class() == QubitBra
assert qb_bra.dual_class() == Qubit
qb = Qubit(1, 1, 0)
qb_bra = QubitBra(1, 1, 0)
assert represent(qb, nqubits=3).H == represent(qb_bra, nqubits=3)
qb = Qubit(0, 1)
qb_bra = QubitBra(1, 0)
assert qb._eval_innerproduct_QubitBra(qb_bra) == Integer(0)
qb_bra = QubitBra(0, 1)
assert qb._eval_innerproduct_QubitBra(qb_bra) == Integer(1)
def test_measure_normalize():
a, b = symbols('a b')
state = a * Qubit('110') + b * Qubit('111')
assert measure_partial(state, (0,), normalize=False) ==\
[(a*Qubit('110'), a*a.conjugate()), (b*Qubit('111'),b*b.conjugate())]
assert measure_all(state, normalize=False) ==\
[(Qubit('110'), a*a.conjugate()),(Qubit('111'), b*b.conjugate())]
def test_superposition_of_states():
state = 1 / sqrt(2) * Qubit('01') + 1 / sqrt(2) * Qubit('10')
state_gate = CNOT(0, 1) * HadamardGate(0) * state
state_expanded = Qubit('01') / 2 + Qubit('00') / 2 - Qubit(
'11') / 2 + Qubit('10') / 2
assert qapply(state_gate).expand() == state_expanded
assert matrix_to_qubit(represent(state_gate, nqubits=2)) == state_expanded
def test_superposition_of_states():
state = 1 / sqrt(2) * Qubit("01") + 1 / sqrt(2) * Qubit("10")
state_gate = CNOT(0, 1) * HadamardGate(0) * state
state_expanded = (
Qubit("01") / 2 + Qubit("00") / 2 - Qubit("11") / 2 + Qubit("10") / 2
)
assert qapply(state_gate).expand() == state_expanded
assert matrix_to_qubit(represent(state_gate, nqubits=2)) == state_expanded
def test_measure_normalize():
a, b = symbols("a b")
state = a * Qubit("110") + b * Qubit("111")
assert measure_partial(state, (0,), normalize=False) == [
(a * Qubit("110"), a * a.conjugate()),
(b * Qubit("111"), b * b.conjugate()),
]
assert measure_all(state, normalize=False) == [
(Qubit("110"), a * a.conjugate()),
(Qubit("111"), b * b.conjugate()),
]
def test_QubitBra():
qb = Qubit(0)
qb_bra = QubitBra(0)
assert qb.dual_class() == QubitBra
assert qb_bra.dual_class() == Qubit
qb = Qubit(1, 1, 0)
qb_bra = QubitBra(1, 1, 0)
assert represent(qb, nqubits=3).H == represent(qb_bra, nqubits=3)
qb = Qubit(0, 1)
qb_bra = QubitBra(1,0)
assert qb._eval_innerproduct_QubitBra(qb_bra) == Integer(0)
qb_bra = QubitBra(0, 1)
assert qb._eval_innerproduct_QubitBra(qb_bra) == Integer(1)
def test_eval_trace():
q1 = Qubit('10110')
q2 = Qubit('01010')
d = Density([q1, 0.6], [q2, 0.4])
t = Tr(d)
assert t.doit() == 1
# extreme bits
t = Tr(d, 0)
assert t.doit() == (0.4 * Density([Qubit('0101'), 1]) +
0.6 * Density([Qubit('1011'), 1]))
t = Tr(d, 4)
assert t.doit() == (0.4 * Density([Qubit('1010'), 1]) +
0.6 * Density([Qubit('0110'), 1]))
# index somewhere in between
t = Tr(d, 2)
assert t.doit() == (0.4 * Density([Qubit('0110'), 1]) +
0.6 * Density([Qubit('1010'), 1]))
#trace all indices
t = Tr(d, [0, 1, 2, 3, 4])
assert t.doit() == 1
# trace some indices, initialized in
# non-canonical order
t = Tr(d, [2, 1, 3])
assert t.doit() == (0.4 * Density([Qubit('00'), 1]) +
0.6 * Density([Qubit('10'), 1]))
# mixed states
q = (1 / sqrt(2)) * (Qubit('00') + Qubit('11'))
d = Density([q, 1.0])
t = Tr(d, 0)
assert t.doit() == (0.5 * Density([Qubit('0'), 1]) +
0.5 * Density([Qubit('1'), 1]))
def test_measure_partial():
#Basic test of collapse of entangled two qubits (Bell States)
state = Qubit('01') + Qubit('10')
assert sorted(measure_partial(state, (0,))) ==\
[(Qubit('01'), Rational(1,2)), (Qubit('10'), Rational(1,2))]
assert sorted(measure_partial(state, (0,))) ==\
sorted(measure_partial(state, (1,)))
#Test of more complex collapse and probability calculation
state1 = sqrt(2) / sqrt(3) * Qubit('00001') + 1 / sqrt(3) * Qubit('11111')
assert measure_partial(state1, (0,)) ==\
[(sqrt(2)/sqrt(3)*Qubit('00001') + 1/sqrt(3)*Qubit('11111'), 1)]
assert measure_partial(state1, (1, 2)) == measure_partial(state1, (3, 4))
assert measure_partial(state1, (1,2,3)) ==\
[(Qubit('00001'), Rational(2,3)), (Qubit('11111'), Rational(1,3))]
#test of measuring multiple bits at once
state2 = Qubit('1111') + Qubit('1101') + Qubit('1011') + Qubit('1000')
assert sorted(measure_partial(state2, (0,1,3))) ==\
sorted([(Qubit('1011')/sqrt(2) + Qubit('1111')/sqrt(2), Rational(1,2)), \
(Qubit('1101'), Rational(1,4)), (Qubit('1000'), Rational(1,4))])
assert sorted(measure_partial(state2, (0,))) ==\
sorted([(Qubit('1111')/sqrt(3) + Qubit('1101')/sqrt(3) + Qubit('1011')/sqrt(3), Rational(3,4)),\
(Qubit('1000'), Rational(1,4))])
def test_measure_partial():
# Basic test of collapse of entangled two qubits (Bell States)
state = Qubit("01") + Qubit("10")
assert measure_partial(state, (0,)) == [
(Qubit("10"), S.Half),
(Qubit("01"), S.Half),
]
assert measure_partial(state, long(0)) == [
(Qubit("10"), S.Half),
(Qubit("01"), S.Half),
]
assert measure_partial(state, (0,)) == measure_partial(state, (1,))[::-1]
# Test of more complex collapse and probability calculation
state1 = sqrt(2) / sqrt(3) * Qubit("00001") + 1 / sqrt(3) * Qubit("11111")
assert measure_partial(state1, (0,)) == [
(sqrt(2) / sqrt(3) * Qubit("00001") + 1 / sqrt(3) * Qubit("11111"), 1)
]
assert measure_partial(state1, (1, 2)) == measure_partial(state1, (3, 4))
assert measure_partial(state1, (1, 2, 3)) == [
(Qubit("00001"), Rational(2, 3)),
(Qubit("11111"), Rational(1, 3)),
]
# test of measuring multiple bits at once
state2 = Qubit("1111") + Qubit("1101") + Qubit("1011") + Qubit("1000")
assert measure_partial(state2, (0, 1, 3)) == [
(Qubit("1000"), Rational(1, 4)),
(Qubit("1101"), Rational(1, 4)),
(Qubit("1011") / sqrt(2) + Qubit("1111") / sqrt(2), S.Half),
]
assert measure_partial(state2, (0,)) == [
(Qubit("1000"), Rational(1, 4)),
(
Qubit("1111") / sqrt(3) + Qubit("1101") / sqrt(3) + Qubit("1011") / sqrt(3),
Rational(3, 4),
),
]
def test_measure_all():
assert measure_all(Qubit("11")) == [(Qubit("11"), 1)]
state = Qubit("11") + Qubit("10")
assert measure_all(state) == [(Qubit("10"), S.Half), (Qubit("11"), S.Half)]
state2 = Qubit("11") / sqrt(5) + 2 * Qubit("00") / sqrt(5)
assert measure_all(state2) == [
(Qubit("00"), Rational(4, 5)),
(Qubit("11"), Rational(1, 5)),
]
# from issue #12585
assert measure_all(qapply(Qubit("0"))) == [(Qubit("0"), 1)]
def test_matrix_to_qubits():
assert matrix_to_qubit(Matrix([1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]))\
== Qubit(0,0,0,0)
assert qubit_to_matrix(Qubit(0,0,0,0)) ==\
Matrix([1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0])
assert matrix_to_qubit(sqrt(2)*2*Matrix([1,1,1,1,1,1,1,1])) ==\
(2*sqrt(2)*(Qubit(0,0,0) + Qubit(0,0,1) + Qubit(0,1,0) + Qubit(0,1,1)\
+ Qubit(1,0,0) + Qubit(1,0,1) + Qubit(1,1,0) + Qubit(1,1,1))).expand()
assert qubit_to_matrix(2*sqrt(2)*(Qubit(0,0,0) + Qubit(0,0,1) + Qubit(0,1,0)\
+ Qubit(0,1,1) + Qubit(1,0,0) + Qubit(1,0,1) + Qubit(1,1,0) + Qubit(1,1,1)))\
== sqrt(2)*2*Matrix([1,1,1,1,1,1,1,1])
def test_measure_all():
assert measure_all(Qubit('11')) == [(Qubit('11'), 1)]
state = Qubit('11') + Qubit('10')
assert measure_all(state) == [(Qubit('10'), S.Half), (Qubit('11'), S.Half)]
state2 = Qubit('11') / sqrt(5) + 2 * Qubit('00') / sqrt(5)
assert measure_all(state2) == \
[(Qubit('00'), Rational(4, 5)), (Qubit('11'), Rational(1, 5))]
# from issue #12585
assert measure_all(qapply(Qubit('0'))) == [(Qubit('0'), 1)]
