def test_sprepost(self):
U1 = rand_unitary(3)
U2 = rand_unitary(3)
S1 = spre(U1) * spost(U2)
S2 = sprepost(U1, U2)
assert_(S1 == S2)
def test_sprepost(self):
U1 = rand_unitary(3)
U2 = rand_unitary(3)
S1 = spre(U1) * spost(U2)
S2 = sprepost(U1, U2)
assert_(S1 == S2)
def unitary_channel(dimension,desired_fidelity,error):
noise_operator = qt.to_super(qt.rand_unitary(dimension))
count=0
while np.abs(qt.average_gate_fidelity(noise_operator)-desired_fidelity)>error and count<400:
noise_operator = qt.to_super(qt.rand_unitary(dimension))
count=count+1
if count>=400:
print("Could not achieve desired fidelity within margin of error")
return noise_operator
def testRandUnitarySeed(self):
"random Unitary with seed"
seed = 12345
U0 = rand_unitary(5, seed=seed)
U1 = rand_unitary(5, seed=None)
U2 = rand_unitary(5, seed=seed)
assert_(U0 != U1)
assert_(U0 == U2)
def testRandUnitarySeed(self):
"random Unitary with seed"
seed = 12345
U0 = rand_unitary(5, seed=seed)
U1 = rand_unitary(5, seed=None)
U2 = rand_unitary(5, seed=seed)
assert_(U0 != U1)
assert_(U0 == U2)
def test_reshuffle(self):
U1 = rand_unitary(2)
U2 = rand_unitary(3)
U3 = rand_unitary(4)
U = tensor(U1, U2, U3)
S = to_super(U)
S_col = reshuffle(S)
assert_equal(S_col.dims[0], [[2, 2], [3, 3], [4, 4]])
assert_(reshuffle(S_col) == S)
def test_reshuffle(self):
U1 = rand_unitary(2)
U2 = rand_unitary(3)
U3 = rand_unitary(4)
U = tensor(U1, U2, U3)
S = to_super(U)
S_col = reshuffle(S)
assert_equal(S_col.dims[0], [[2, 2], [3, 3], [4, 4]])
assert_(reshuffle(S_col) == S)
def initialise(no_inputs, ancilla, bond_dimension,identity=0):
"""generates the right number of random unitaries of the right size"""
total=no_inputs+ancilla
operator_list=[]
temp_operator_list=[]
for i in range(no_inputs):
if identity==1:
operator_list.append(np.identity(bond_dimension).astype(complex))
elif identity==2:
tt=qutip.rand_unitary(bond_dimension).full()
operator_list.append(np.dot(tt,tt*1J))
else:
operator_list.append(qutip.rand_unitary(bond_dimension).full().astype(complex))
return operator_list
def test_invariant_under_unitary_transformation(self, dimension):
rho1 = rand_dm(dimension, 0.25)
rho2 = rand_dm(dimension, 0.25)
U = rand_unitary(dimension, 0.25)
D = tracedist(rho1, rho2)
DU = tracedist(U * rho1 * U.dag(), U * rho2 * U.dag())
assert D == pytest.approx(DU, rel=1e-5)
def test_permutation_without_expansion(self, permutation):
base = qutip.tensor([qutip.rand_unitary(2) for _ in permutation])
test = gates.expand_operator(base,
N=len(permutation),
targets=permutation)
expected = base.permute(_apply_permutation(permutation))
np.testing.assert_allclose(test.full(), expected.full(), atol=1e-15)
def new_game(self):
self.unitary = qt.rand_unitary(2**self.n_players)
self.player_colors = [[random.uniform(0,1), random.uniform(0,1), random.uniform(0,1)] for i in range(self.n_players)]
self.current_state = qt.basis(self.unitary.shape[0], 0)
self.desired_state = self.unitary*self.current_state
self.winning = False
self.goal_stars = q_SurfaceXYZ(self.desired_state)
def test_DenseValsOnly():
"""
Dense eigvals only Hermitian
"""
H = rand_herm(10)
spvals = H.eigenenergies(sparse=False)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(np.isreal(spvals[k]), True)
spvals = H.eigenenergies(sparse=False, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = H.eigenenergies(sparse=False, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
U = rand_unitary(10)
spvals = U.eigenenergies(sparse=False)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(np.iscomplex(spvals[k]), True)
spvals = U.eigenenergies(sparse=False, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = U.eigenenergies(sparse=False, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
def test_DenseValsOnly():
"""
Dense eigvals only Hermitian
"""
H = rand_herm(10)
spvals = H.eigenenergies(sparse=False)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(np.isreal(spvals[k]), True)
spvals = H.eigenenergies(sparse=False, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = H.eigenenergies(sparse=False, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
U = rand_unitary(10)
spvals = U.eigenenergies(sparse=False)
assert_equal(len(spvals), 10)
# check that sorting is lowest eigval first
assert_equal(spvals[0] <= spvals[-1], True)
# check that spvals equal expect vals
for k in range(10):
# check that ouput is real for Hermitian operator
assert_equal(np.iscomplex(spvals[k]), True)
spvals = U.eigenenergies(sparse=False, sort='high')
# check that sorting is lowest eigval first
assert_equal(spvals[0] >= spvals[-1], True)
spvals = U.eigenenergies(sparse=False, sort='high', eigvals=4)
assert_equal(len(spvals), 4)
def test_invariant_under_unitary_transformation(self, dimension):
rho1 = rand_dm(dimension, 0.25)
rho2 = rand_dm(dimension, 0.25)
U = rand_unitary(dimension, 0.25)
F = fidelity(rho1, rho2)
FU = fidelity(U * rho1 * U.dag(), U * rho2 * U.dag())
assert F == pytest.approx(FU, rel=1e-5)
def _make_random_three_qubit_gate():
"""Create a random three-qubit gate."""
operation = qutip.rand_unitary(8, dims=[[2]*3]*2)
def gate(N=None, controls=None, target=None):
if N is None:
return operation
return gates.gate_expand_3toN(operation, N, controls, target)
return gate
def rand_rotate_hol(self):
'''Description: rotates evolved states and operators by
random unitaries (one for each item in a list)'''
randunitary = qt.rand_unitary(2, density=0.75)
self.rand_rotate_op_list = [randunitary * i for i in self.op_list]
self.rand_rotate_state_list = [
randunitary * i for i in self.state_list
]
self.rand_rotate_Uj_list = [randunitary * i for i in self.Uj_list_hol]
return self.rand_rotate_op_list, self.rand_rotate_state_list, self.rand_rotate_Uj_list
def test_general_qubit_expansion(self, n_targets):
# Test all permutations with the given number of targets.
n_qubits = 5
operation = qutip.rand_unitary(2**n_targets, dims=[[2]*n_targets]*2)
for targets in itertools.permutations(range(n_qubits), n_targets):
expected = _tensor_with_entanglement([qutip.qeye(2)] * n_qubits,
operation, targets)
test = gates.expand_operator(operation, n_qubits, targets)
np.testing.assert_allclose(test.full(), expected.full(),
atol=1e-15)
def test_SparseValsVecs():
"""
Sparse eigs non-Hermitian
"""
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=True)
assert_equal(np.real(spvals[0]) <= np.real(spvals[-1]), True)
for k in range(10):
# check that eigenvectors are right and in right order
assert_equal(abs(expect(U, spvecs[k]) - spvals[k]) < 5e-14, True)
assert_equal(np.iscomplex(spvals[k]), True)
# check sorting
spvals, spvecs = U.eigenstates(sparse=True, sort='high')
assert_equal(np.real(spvals[0]) >= np.real(spvals[-1]), True)
# check for N-1 eigenvals
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=True, eigvals=9)
assert_equal(len(spvals), 9)
def test_SparseValsVecs():
"""
Sparse eigs non-Hermitian
"""
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=True)
assert_equal(np.real(spvals[0]) <= np.real(spvals[-1]), True)
for k in range(10):
# check that eigenvectors are right and in right order
assert_equal(abs(expect(U, spvecs[k]) - spvals[k]) < 5e-14, True)
assert_equal(np.iscomplex(spvals[k]), True)
# check sorting
spvals, spvecs = U.eigenstates(sparse=True, sort='high')
assert_equal(np.real(spvals[0]) >= np.real(spvals[-1]), True)
# check for N-1 eigenvals
U = rand_unitary(10)
spvals, spvecs = U.eigenstates(sparse=True, eigvals=9)
assert_equal(len(spvals), 9)
def test_non_qubit_systems(self, dimensions):
n_qubits = len(dimensions)
for targets in itertools.permutations(range(n_qubits), 2):
operators = [qutip.rand_unitary(dimension) if n in targets
else qutip.qeye(dimension)
for n, dimension in enumerate(dimensions)]
expected = qutip.tensor(*operators)
base_test = qutip.tensor(*[operators[x] for x in targets])
test = gates.expand_operator(base_test, N=n_qubits,
targets=targets, dims=dimensions)
assert test.dims == expected.dims
np.testing.assert_allclose(test.full(), expected.full())
def testOperatorUnitaryTransform(self):
"""
Superoperator: Unitary transformation with operators and superoperators
"""
N = 3
rho = rand_dm(N)
U = rand_unitary(N)
rho1 = U * rho * U.dag()
rho2_vec = spre(U) * spost(U.dag()) * operator_to_vector(rho)
rho2 = vector_to_operator(rho2_vec)
assert_((rho1 - rho2).norm() < 1e-8)
def testOperatorSpostAppl(self):
"""
Superoperator: apply operator and superoperator from right (spost)
"""
N = 3
rho = rand_dm(N)
U = rand_unitary(N)
rho1 = rho * U
rho2_vec = spost(U) * operator_to_vector(rho)
rho2 = vector_to_operator(rho2_vec)
assert_((rho1 - rho2).norm() < 1e-8)
def testOperatorSpreAppl(self):
"""
Superoperator: apply operator and superoperator from left (spre)
"""
N = 3
rho = rand_dm(N)
U = rand_unitary(N)
rho1 = U * rho
rho2_vec = spre(U) * operator_to_vector(rho)
rho2 = vector_to_operator(rho2_vec)
assert_((rho1 - rho2).norm() < 1e-8)
def __init__(self, players):
self.n_players = players
self.unitary = qt.rand_unitary(2**self.n_players)
#self.unitary = (-2*math.pi*1j*0.001*qt.rand_herm(2**self.n_players)).expm()
self.current_players = []
self.player_colors = [[random.uniform(0,1), random.uniform(0,1), random.uniform(0,1)] for i in range(self.n_players)]
self.current_state = qt.basis(self.unitary.shape[0], 0)
self.desired_state = self.unitary*self.current_state
#self.current_state = self.desired_state
#self.current_history = []
self.winning = False
self.goal_stars = q_SurfaceXYZ(self.desired_state)
self.ai_on = False
def test_simdiag(num_mat):
N = 10
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags(np.random.rand(N), 0) * U.dag()
for _ in range(num_mat)
]
all_evals, evecs = qutip.simdiag(commuting_matrices)
for matrix, evals in zip(commuting_matrices, all_evals):
for eval, evec in zip(evals, evecs):
assert matrix * evec == evec * eval
def test_simdiag_degen_large():
N = 20
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags(np.random.randint(0, 3, N), 0) * U.dag()
for _ in range(5)
]
all_evals, evecs = qutip.simdiag(commuting_matrices, tol=1e-12)
for matrix, evals in zip(commuting_matrices, all_evals):
for eval, evec in zip(evals, evecs):
np.testing.assert_allclose((matrix * evec).full(),
(evec * eval).full())
def testOperatorUnitaryTransform(self):
"""
Superoperator: Unitary transformation with operators and superoperators
"""
N = 3
rho = rand_dm(N)
U = rand_unitary(N)
rho1 = U * rho * U.dag()
rho2_vec = spre(U) * spost(U.dag()) * operator_to_vector(rho)
rho2 = vector_to_operator(rho2_vec)
assert_((rho1 - rho2).norm() < 1e-8)
def testOperatorSpostAppl(self):
"""
Superoperator: apply operator and superoperator from right (spost)
"""
N = 3
rho = rand_dm(N)
U = rand_unitary(N)
rho1 = rho * U
rho2_vec = spost(U) * operator_to_vector(rho)
rho2 = vector_to_operator(rho2_vec)
assert_((rho1 - rho2).norm() < 1e-8)
def testOperatorSpreAppl(self):
"""
Superoperator: apply operator and superoperator from left (spre)
"""
N = 3
rho = rand_dm(N)
U = rand_unitary(N)
rho1 = U * rho
rho2_vec = spre(U) * operator_to_vector(rho)
rho2 = vector_to_operator(rho2_vec)
assert_((rho1 - rho2).norm() < 1e-8)
def test_simdiag_degen():
N = 10
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags([0, 0, 0, 1, 1, 1, 2, 2, 3, 4], 0) * U.dag(),
U * qutip.qdiags([0, 0, 0, 1, 2, 2, 2, 2, 2, 2], 0) * U.dag(),
U * qutip.qdiags([0, 0, 2, 1, 1, 2, 2, 3, 3, 4], 0) * U.dag(),
]
all_evals, evecs = qutip.simdiag(commuting_matrices)
for matrix, evals in zip(commuting_matrices, all_evals):
for eval, evec in zip(evals, evecs):
np.testing.assert_allclose((matrix * evec).full(),
(evec * eval).full())
def test_simdiag_no_evals(num_mat):
N = 10
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags(np.random.rand(N), 0) * U.dag()
for _ in range(num_mat)
]
evecs = qutip.simdiag(commuting_matrices, evals=False)
for matrix in commuting_matrices:
for evec in evecs:
Mvec = matrix * evec
eval = Mvec.norm() / evec.norm()
assert matrix * evec == evec * eval
def test_DenseValsVecs():
"""
Dense eigs non-Hermitian
"""
W = rand_herm(10,0.5) + 1j*rand_herm(10,0.5)
spvals, spvecs = W.eigenstates(sparse=False)
assert_equal(np.real(spvals[0]) <= np.real(spvals[-1]), True)
for k in range(10):
# check that eigenvectors are right and in right order
assert_equal(abs(expect(W, spvecs[k]) - spvals[k]) < 1e-14, True)
assert_(np.iscomplex(spvals[k]))
# check sorting
spvals, spvecs = W.eigenstates(sparse=False, sort='high')
assert_equal(np.real(spvals[0]) >= np.real(spvals[-1]), True)
# check for N-1 eigenvals
W = rand_unitary(10)
spvals, spvecs = W.eigenstates(sparse=False, eigvals=9)
assert_equal(len(spvals), 9)
def test_DenseValsVecs():
"""
Dense eigs non-Hermitian
"""
W = rand_herm(10,0.5) + 1j*rand_herm(10,0.5)
spvals, spvecs = W.eigenstates(sparse=False)
assert_equal(np.real(spvals[0]) <= np.real(spvals[-1]), True)
for k in range(10):
# check that eigenvectors are right and in right order
assert_equal(abs(expect(W, spvecs[k]) - spvals[k]) < 1e-14, True)
assert_(np.iscomplex(spvals[k]))
# check sorting
spvals, spvecs = W.eigenstates(sparse=False, sort='high')
assert_equal(np.real(spvals[0]) >= np.real(spvals[-1]), True)
# check for N-1 eigenvals
W = rand_unitary(10)
spvals, spvecs = W.eigenstates(sparse=False, eigvals=9)
assert_equal(len(spvals), 9)
else:
for pr in combinations(list(range(N)), n):
s = reduce(lambda x, y: x * y, [m[p] for p in pr])
terms.append(op[c] * s)
terms[-1].dims = m[0].dims
c += 1
return sum(terms)
#########################################################################################
n_ = int(n / 2)
f_ = fermion_operators(n_)
m_ = reduce(lambda x, y: x + y, majorana_operators(f_))
O = qt.rand_unitary(2**n_)
O.dims = [[2] * n_, [2] * n_]
OL = from_majorana_basis(to_majorana_basis(O, m_), mL)
OR = from_majorana_basis(to_majorana_basis(O, m_), [1j * r for r in mR])
def size(O, i=None):
global f, mL, m_, I, N
majorana_state = (from_majorana_basis(to_majorana_basis(O, m_), mL) *
I).unit()
if type(i) != type(None):
return qt.expect(f[i].dag() * f[i], majorana_state)
else:
return qt.expect(N, majorana_state)
# Fidelity closer to 1 means the two states are similar to each other
H = snot(1, 0)
sigmax = sigmax()
sigmay = sigmay()
sigmaz = sigmaz()
SQRTNOT = sqrtnot(N=1, target=0)
T = Qobj([[1, 0], [0, cmath.rect(1, np.pi / 4)]])
S = Qobj([[1, 0], [0, 1j]])
target = 0
num_qubits = 1
# Tests for private functions
@pytest.mark.parametrize(
"gate", [H, sigmax, sigmay, sigmaz, SQRTNOT, S, T,
rand_unitary(2)])
@pytest.mark.parametrize("method",
[_ZYZ_rotation, _ZXZ_rotation, _ZYZ_pauli_X])
def test_single_qubit_to_rotations(gate, method):
"""Initial matrix and product of final decompositions are same within some
phase."""
gate_list = method(gate)
circuit = QubitCircuit(num_qubits)
circuit.add_gates(gate_list)
decomposed_gates_final_matrix = circuit.compute_unitary()
fidelity_of_input_output = average_gate_fidelity(
gate, decomposed_gates_final_matrix)
assert np.isclose(fidelity_of_input_output, 1.0)
@pytest.mark.parametrize(
def testRandUnitary(self):
"random Unitary"
U = [rand_unitary(5) for k in range(5)]
for u in U:
assert_(u * u.dag() == qeye(5))
# # TO DO LIST: # # ## - check the existing quantum architectures that we are using # # ## - read on "proper" evolution with unitarity constraints # # ## - code the circuit # # ## - try a completely adaptive implementation # # ## - consider a purely quantum optimisation # In[34]: A=qutip.rand_unitary(4).full() A # In[35]: q,r=np.linalg.qr(A) # In[36]: np.imag(r)[abs(np.imag(r))<0.000001]=0 np.real(r)[abs(np.real(r))<0.000001]=0 r
def testRandUnitary(self):
"random Unitary"
U = [rand_unitary(5) for k in range(5)]
for u in U:
assert_(u * u.dag() == qeye(5))
