def test_104_check_a_b(self):
for aaa in [pi / 6, pi / 3, pi, pi + pi / 3, pi + pi / 6]:
q = Qubits.create(1, [(0, cos(aaa)), (1, sin(aaa))])
assert self.check_a_b(q, aaa) == True
q = Qubits.create(1, [(0, -sin(aaa)), (1, cos(aaa))])
assert self.check_a_b(q, aaa) == False
def test_07_controlled_x_general(self):
for ix in range(20):
a, b, c, d = self.random_unit_vector(4)
q = Qubits.create(2, [(0, a), (1, b), (2, c), (3, d)])
target = Qubits.create(2, [(0, a), (1, b), (2, d), (3, c)])
print "before", q
self.controlled_x_general(q)
print "after", q
self.assert_qubits(q, target)
def test_06_controlled_x(self):
"""// Task 6. Controlled X gate with |0⟩ target
// Input: Two unentangled qubits (stored in an array of length 2).
// The first qubit will be in state |ψ⟩ = α |0⟩ + β |1⟩, the second - in state |0⟩
// (this can be written as two-qubit state (α|0⟩ + β|1⟩) ⊕ |0⟩).
// Goal: Change the two-qubit state to α |00⟩ + β |11⟩ using only single-qubit gates and joint measurements.
// Do not use two-qubit gates.
// You do not need to allocate extra qubits."""
for _ in range(20):
for rnd in [0.1, 0.9]:
a, b = self.random_unit_vector(2)
q = Qubits.create(2, [(0, a), (2, b)])
qq = q.clone()
Gates.CNOT(qq, 0, 1)
self.controlled_x(q, rnd)
self.assert_qubits(q, qq)
def test_05_different_basis(self):
"""// Task 5. Parity measurement in different basis
// Input: Two qubits (stored in an array) which are guaranteed to be
// either in superposition α|00⟩ + β|01⟩ + β|10⟩ + α|11⟩
// or in superposition α|00⟩ - β|01⟩ + β|10⟩ - α|11⟩.
// Output: 0 if qubits were in the first superposition,
// 1 if they were in the second superposition.
// The state of the qubits at the end of the operation should be the same as the starting state."""
for _ in range(10):
for mul in [1, -1]:
a, b = self.random_unit_vector(2)
a = a / sqrt(2.0)
b = b / sqrt(2.0)
q = Qubits.create(2, [(0, a), (1, mul * b), (2, b),
(3, mul * a)])
qq = q.clone()
d = self.different_basis(q)
self.assert_qubits(q, qq)
expected = 0 if mul == 1 else 1
assert d == expected
def test_106_basis_state_measurement(self):
for ix in range(4):
q = Qubits.create(2, [(ix, 1)])
assert self.basis_state_measurement(q) == ix