def test_composite_basis(self):
comp = Basis([('std', 2,), ('std', 1)])
a = Basis([('std', 2), ('std', 2)])
b = Basis('std', [2,2])
self.assertEqual(len(a), len(b))
self.assertArraysAlmostEqual(np.array(a._matrices), np.array(b._matrices))
def test_errgen_construction(self):
from pygsti.models.gaugegroup import UnitaryGaugeGroupElement
mx_basis = Basis.cast('pp', 4)
basis = Basis.cast('pp', 4)
X = basis['X']
Y = basis['Y']
Z = basis['Z']
# Build known combination to project back to
errgen = (0.1 * lt.create_elementary_errorgen('H', Z) -
0.01 * lt.create_elementary_errorgen('H', X) +
0.2 * lt.create_elementary_errorgen('S', X) +
0.25 * lt.create_elementary_errorgen('S', Y) +
0.05 * lt.create_elementary_errorgen('C', X, Y) -
0.01 * lt.create_elementary_errorgen('A', X, Y))
errgen = bt.change_basis(errgen, 'std', mx_basis)
eg = op.LindbladErrorgen.from_error_generator(errgen,
"CPTP",
'pp',
truncate=False,
mx_basis="pp",
evotype='default')
self.assertTrue(np.allclose(eg.to_dense(), errgen))
errgen_copy = eg.copy()
T = UnitaryGaugeGroupElement(np.identity(4, 'd'))
errgen_copy.transform_inplace(T)
self.assertTrue(np.allclose(errgen_copy.to_dense(), eg.to_dense()))
def test_expand_contract(self):
# matrix that operates on 2x2 density matrices, but only on the 0-th and 3-rd
# elements which correspond to the diagonals of the 2x2 density matrix.
mxInStdBasis = np.array([[1,0,0,2],
[0,0,0,0],
[0,0,0,0],
[3,0,0,4]],'d')
# Reduce to a matrix operating on a density matrix space with 2 1x1 blocks (hence [1,1])
begin = Basis('std', [1,1])
end = Basis('std', 2)
mxInReducedBasis = bt.resize_std_mx(mxInStdBasis, 'contract', end, begin)
#mxInReducedBasis = bt.change_basis(mxInStdBasis, begin, end)
notReallyContracted = bt.change_basis(mxInStdBasis, 'std', 'std', 4)
correctAnswer = np.array([[ 1.0, 2.0],
[ 3.0, 4.0]])
#self.assertArraysAlmostEqual( mxInReducedBasis, correctAnswer )
self.assertArraysAlmostEqual( notReallyContracted, mxInStdBasis )
expandedMx = bt.resize_std_mx(mxInReducedBasis, 'expand', begin, end)
#expandedMx = bt.change_basis(mxInReducedBasis, end, begin)
expandedMxAgain = bt.change_basis(expandedMx, 'std', 'std', 4)
self.assertArraysAlmostEqual( expandedMx, mxInStdBasis )
self.assertArraysAlmostEqual( expandedMxAgain, mxInStdBasis )
def setUp(self):
#Set Model objects to "strict" mode for testing
ExplicitOpModel._strict = True
# density matrix == 3x3 block diagonal matrix: a 2x2 block followed by a 1x1 block
self.stateSpaceDims = [(4, ), (1, )]
self.stateSpaceUDims = [(2, ), (1, )]
self.std = Basis.cast('std', 9)
self.gm = Basis.cast('gm', 9)
self.stdSmall = Basis.cast('std', [4, 1])
self.gmSmall = Basis.cast('gm', [4, 1])
#labels which give a tensor product interp. for the states within each density matrix block
self.stateSpaceLabels = [('Qhappy', ), ('Lsad', )]
# Adjust for deprecation of _create_operation
self.sslbls = statespace.ExplicitStateSpace(self.stateSpaceLabels,
self.stateSpaceUDims)
#Build a test gate -- old # X(pi,Qhappy)*LX(pi,0,2)
self.testGate = create_operation("LX(pi,0,2)", self.sslbls,
self.stdSmall)
self.testGateGM_mx = bt.change_basis(self.testGate, self.stdSmall,
self.gmSmall)
self.expTestGate_mx = bt.flexible_change_basis(self.testGate,
self.stdSmall, self.std)
self.expTestGateGM_mx = bt.change_basis(self.expTestGate_mx, self.std,
self.gm)
def test_auto_expand(self):
comp = Basis(matrices=[('std', 2,), ('std', 1)])
std = Basis('std', 3)
mxStd = np.identity(5)
test = bt.resize_std_mx(mxStd, 'expand', comp, std)
test2 = bt.resize_std_mx(test, 'contract', std, comp)
self.assertArraysAlmostEqual(test2, mxStd)
def test_change_between_composites(self):
a = Basis('std', [2, 1])
b = Basis('gm', [2, 1])
mxStd = np.identity(5)
test = bt.change_basis(mxStd, a, b)
self.assertEqual(test.shape, mxStd.shape)
test2 = bt.change_basis(test, b, a)
self.assertArraysAlmostEqual(test2, mxStd)
def test_flexible_change_basis(self):
comp = Basis(matrices=[('gm', 2,), ('gm', 1)])
std = Basis('std', 3)
mx = np.identity(5)
test = bt.flexible_change_basis(mx, comp, std)
self.assertEqual(test.shape[0], sum(comp.dim.blockDims) ** 2)
test2 = bt.flexible_change_basis(test, std, comp)
self.assertArraysAlmostEqual(test2, mx)
def setUp(self):
self.gm = Basis.cast('gm', 4)
self.pp = Basis.cast('pp', 4)
self.std = Basis.cast('std', 4)
self.mxGM = np.array(
[[1, 0, 0, 0], [0, 0, 1, 0], [0, -1, 0, 0], [0, 0, 0, 1]],
'complex')
self.mxStd = bt.change_basis(self.mxGM, self.gm, self.std)
self.mxPP = bt.change_basis(self.mxGM, self.gm, self.pp)
def test_basis_object(self):
#test a few aspects of a Basis object that other tests miss...
b = Basis("pp",2)
beq = b.expanded_equivalent()
longnm = bt.basis_longname(b)
lbls = bt.basis_element_labels(b)
raw_mxs = bt.basis_matrices("pp",2)
with self.assertRaises(NotImplementedError):
bt.basis_matrices("foobar",2) #invalid basis name
print("Dim = ", repr(b.dim) ) # calls Dim.__repr__
def __init__(self, errormap, povm=None, mx_basis=None):
"""
Creates a new LindbladPOVM object.
Parameters
----------
errormap : MapOperator
The error generator action and parameterization, encapsulated in
a gate object. Usually a :class:`LindbladOp`
or :class:`ComposedOp` object. (This argument is *not* copied,
to allow ComposedPOVMEffects to share error generator
parameters with other gates and spam vectors.)
povm : POVM, optional
A sub-POVM which supplies the set of "reference" effect vectors
that `errormap` acts on to produce the final effect vectors of
this LindbladPOVM. This POVM must be *static*
(have zero parameters) and its evolution type must match that of
`errormap`. If None, then a :class:`ComputationalBasisPOVM` is
used on the number of qubits appropriate to `errormap`'s dimension.
mx_basis : {'std', 'gm', 'pp', 'qt'} or Basis object
The basis for this spam vector. Allowed values are Matrix-unit (std),
Gell-Mann (gm), Pauli-product (pp), and Qutrit (qt) (or a custom
basis object). If None, then this is extracted (if possible) from
`errormap`.
"""
self.error_map = errormap
state_space = self.error_map.state_space
if mx_basis is None:
if isinstance(errormap, _op.ExpErrorgenOp) and isinstance(
errormap.errorgen, _op.LindbladErrorgen):
mx_basis = errormap.errorgen.matrix_basis
else:
raise ValueError(
"Cannot extract a matrix-basis from `errormap` (type %s)" %
str(type(errormap)))
self.matrix_basis = _Basis.cast(mx_basis, state_space)
evotype = self.error_map._evotype
if povm is None:
assert(state_space.num_qubits >= 0), \
("A default computational-basis POVM can only be used with an"
" integral number of qubits!")
povm = _ComputationalBasisPOVM(state_space.num_qubits, evotype)
else:
assert(povm.evotype == evotype), \
("Evolution type of `povm` (%s) must match that of "
"`errormap` (%s)!") % (povm.evotype, evotype)
assert(povm.num_params == 0), \
"Given `povm` must be static (have 0 parameters)!"
self.base_povm = povm
items = [] # init as empty (lazy creation of members)
_POVM.__init__(self, state_space, evotype, items)
self.init_gpindices(
) # initialize gpindices and subm_rpindices from sub-members
def test_build_gatesets(self):
SQ2 = 1 / np.sqrt(2)
for defParamType in ("full", "full TP", "static"):
gateset_simple = pygsti.models.ExplicitOpModel(['Q0'], 'pp',
defParamType)
gateset_simple['rho0'] = [SQ2, 0, 0, SQ2]
gateset_simple[
'Mdefault'] = pygsti.modelmembers.povms.UnconstrainedPOVM(
[('0', [SQ2, 0, 0, -SQ2])], evotype='default')
gateset_simple['Gi'] = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]]
with self.assertRaises(TypeError):
gateset_simple['rho0'] = 3.0
with self.assertRaises(ValueError):
gateset_simple['rho0'] = [3.0]
with self.assertRaises(ValueError):
gateset_simple['Gx'] = [1, 2, 3, 4]
with self.assertRaises(ValueError):
gateset_simple['Gx'] = [[1, 2, 3, 4], [5, 6, 7]]
gateset_badDefParam = pygsti.models.ExplicitOpModel(['Q0'], "pp",
"full")
gateset_badDefParam.preps.default_param = "foobar"
gateset_badDefParam.operations.default_param = "foobar"
with self.assertRaises(ValueError):
gateset_badDefParam['rho0'] = [1, 0, 0, 0]
with self.assertRaises(ValueError):
gateset_badDefParam['Gi'] = np.identity(4, 'd')
stateSpace = [(4, )] # density matrix is a 2x2 matrix
spaceLabels = [
('Q0', )
] # interpret the 2x2 density matrix as a single qubit named 'Q0'
with self.assertRaises(AssertionError):
modelconstruction.create_identity_vec(
Basis.cast("foobar", stateSpace))
gateset_povm_first = pygsti.models.ExplicitOpModel(
['Q0']) #set effect vector first
gateset_povm_first['Mdefault'] = pygsti.modelmembers.povms.TPPOVM(
[('0', modelconstruction.create_spam_vector("0", stateSpace,
"gm")),
('1', modelconstruction.create_spam_vector("1", stateSpace, "gm"))
],
evotype='default')
with self.assertRaises(ValueError):
gateset_povm_first['rhoBad'] = np.array([1, 2, 3],
'd') #wrong dimension
with self.assertRaises(ValueError):
gateset_povm_first[
'Mdefault'] = pygsti.modelmembers.povms.UnconstrainedPOVM(
[('0', np.array([1, 2, 3], 'd'))],
evotype='default',
state_space=pygsti.baseobjs.StateSpace.cast([
('L0', ), ('L1', ), ('L2', )
])) #wrong dimension
def test_elementary_errorgen_bases(self):
bases = [Basis.cast('gm', 4), Basis.cast('pp', 4), Basis.cast('PP', 4)]
for basis in bases:
print(basis)
primals = []
duals = []
lbls = []
for lbl, bel in zip(basis.labels[1:], basis.elements[1:]):
lbls.append("H_%s" % lbl)
primals.append(lt.create_elementary_errorgen('H', bel))
duals.append(lt.create_elementary_errorgen_dual('H', bel))
for lbl, bel in zip(basis.labels[1:], basis.elements[1:]):
lbls.append("S_%s" % lbl)
primals.append(lt.create_elementary_errorgen('S', bel))
duals.append(lt.create_elementary_errorgen_dual('S', bel))
for i, (lbl,
bel) in enumerate(zip(basis.labels[1:],
basis.elements[1:])):
for lbl2, bel2 in zip(basis.labels[1 + i + 1:],
basis.elements[1 + i + 1:]):
lbls.append("C_%s_%s" % (lbl, lbl2))
primals.append(
lt.create_elementary_errorgen('C', bel, bel2))
duals.append(
lt.create_elementary_errorgen_dual('C', bel, bel2))
for i, (lbl,
bel) in enumerate(zip(basis.labels[1:],
basis.elements[1:])):
for lbl2, bel2 in zip(basis.labels[1 + i + 1:],
basis.elements[1 + i + 1:]):
lbls.append("A_%s_%s" % (lbl, lbl2))
primals.append(
lt.create_elementary_errorgen('A', bel, bel2))
duals.append(
lt.create_elementary_errorgen_dual('A', bel, bel2))
dot_mx = np.empty((len(duals), len(primals)), complex)
for i, dual in enumerate(duals):
for j, primal in enumerate(primals):
dot_mx[i, j] = np.vdot(dual.flatten(), primal.flatten())
self.assertTrue(np.allclose(dot_mx, np.identity(len(lbls), 'd')))
def build_gate():
mx = np.identity(4, 'd')
ppBasis = Basis.cast("pp", 4)
return op.LindbladErrorgen.from_operation_matrix(mx,
"GLND",
ppBasis,
truncate=False,
mx_basis="pp",
evotype='default')
def test_instance(self):
state_space = statespace.default_space_for_dim(4)
sop = op.StochasticNoiseOp(state_space)
sop.from_vector(np.array([0.1, 0.0, 0.0]))
self.assertArraysAlmostEqual(sop.to_vector(), np.array([0.1, 0., 0.]))
expected_mx = np.identity(4)
expected_mx[2, 2] = expected_mx[3, 3] = 0.98 # = 2*(0.1^2)
self.assertArraysAlmostEqual(sop.to_dense(), expected_mx)
rho = create_spam_vector("0", "Q0", Basis.cast("pp", [4]))
self.assertAlmostEqual(
float(np.dot(rho.T, np.dot(sop.to_dense(), rho))),
0.99) # b/c X dephasing w/rate is 0.1^2 = 0.01
def __init__(self, state_space, labels, basis1q=None):
# TODO: docstring - labels must be of form (sslbls, elementary_errorgen_lbl)
self._labels = tuple(labels) if not isinstance(labels,
tuple) else labels
self._label_indices = _collections.OrderedDict([
(lbl, i) for i, lbl in enumerate(self._labels)
])
self.basis_1q = basis1q if (basis1q is not None) else _Basis.cast(
'pp', 4)
self.state_space = state_space
assert (self.state_space.is_entirely_qubits
), "FOGI only works for models containing just qubits (so far)"
sslbls = self.state_space.tensor_product_block_labels(
0) # all the model's state space labels
self.sslbls = sslbls # the "support" of this space - the qubit labels
self._cached_elements = None
def __init__(self, vec, basis="pp", evotype="default", state_space=None):
vector = _State._to_vector(vec)
if basis is not None:
if not isinstance(basis, _Basis):
basis = _Basis.cast(basis, len(
vector)) # don't perform this cast if we're given a basis
firstEl = basis.elsize**-0.25 # not dim, as the dimension of the vector space may be less
if not _np.isclose(vector[0], firstEl):
raise ValueError(
"Cannot create TPState: first element must equal %g!" %
firstEl)
# if basis is None, don't check first element (hackfor de-serialization, so we don't need to store basis)
_DenseState.__init__(self, vector, evotype, state_space)
assert (isinstance(self.columnvec, _ProtectedArray))
self._paramlbls = _np.array(
["VecElement %d" % i for i in range(1, self.dim)], dtype=object)
def test_depol_noise_op(self):
state_space = statespace.default_space_for_dim(4)
dop = op.DepolarizeOp(state_space)
dop.from_vector(np.array([0.1]))
self.assertArraysAlmostEqual(dop.to_vector(), np.array([0.1]))
expected_mx = np.identity(4)
expected_mx[1,
1] = expected_mx[2,
2] = expected_mx[3,
3] = 0.96 # = 4*(0.1^2)
self.assertArraysAlmostEqual(dop.to_dense(), expected_mx)
rho = create_spam_vector("0", "Q0", Basis.cast("pp", [4]))
# b/c both X and Y dephasing rates => 0.01 reduction
self.assertAlmostEqual(
float(np.dot(rho.T, np.dot(dop.to_dense(), rho))), 0.98)
def test_jamiolkowski_ops(self):
gm = Basis('gm', 2)
pp = Basis('pp', 2)
std = Basis('std', 2)
mxGM = np.array(
[[1, 0, 0, 0], [0, 0, 1, 0], [0, -1, 0, 0], [0, 0, 0, 1]],
'complex')
mxStd = bt.change_basis(mxGM, gm, std)
mxPP = bt.change_basis(mxGM, gm, pp)
choiStd = pygsti.jamiolkowski_iso(mxStd, std, std)
choiStd2 = pygsti.jamiolkowski_iso(mxGM, gm, std)
choiStd3 = pygsti.jamiolkowski_iso(mxPP, pp, std)
fastChoiStd = pygsti.fast_jamiolkowski_iso_std(mxStd, std)
fastChoiStd2 = pygsti.fast_jamiolkowski_iso_std(mxGM, gm)
fastChoiStd3 = pygsti.fast_jamiolkowski_iso_std(mxPP, pp)
choiGM = pygsti.jamiolkowski_iso(mxStd, std, gm)
choiGM2 = pygsti.jamiolkowski_iso(mxGM, gm, gm)
choiGM3 = pygsti.jamiolkowski_iso(mxPP, pp, gm)
choiPP = pygsti.jamiolkowski_iso(mxStd, std, pp)
choiPP2 = pygsti.jamiolkowski_iso(mxGM, gm, pp)
choiPP3 = pygsti.jamiolkowski_iso(mxPP, pp, pp)
self.assertArraysAlmostEqual(choiStd, choiStd2)
self.assertArraysAlmostEqual(choiStd, choiStd3)
self.assertArraysAlmostEqual(choiStd, fastChoiStd)
self.assertArraysAlmostEqual(choiStd, fastChoiStd2)
self.assertArraysAlmostEqual(choiStd, fastChoiStd3)
self.assertArraysAlmostEqual(choiGM, choiGM2)
self.assertArraysAlmostEqual(choiGM, choiGM3)
self.assertArraysAlmostEqual(choiPP, choiPP2)
self.assertArraysAlmostEqual(choiPP, choiPP3)
gateStd = pygsti.jamiolkowski_iso_inv(choiStd, std, std)
gateStd2 = pygsti.jamiolkowski_iso_inv(choiGM, gm, std)
gateStd3 = pygsti.jamiolkowski_iso_inv(choiPP, pp, std)
gateGM = pygsti.jamiolkowski_iso_inv(choiStd, std, gm)
gateGM2 = pygsti.jamiolkowski_iso_inv(choiGM, gm, gm)
gateGM3 = pygsti.jamiolkowski_iso_inv(choiPP, pp, gm)
gatePP = pygsti.jamiolkowski_iso_inv(choiStd, std, pp)
gatePP2 = pygsti.jamiolkowski_iso_inv(choiGM, gm, pp)
gatePP3 = pygsti.jamiolkowski_iso_inv(choiPP, pp, pp)
fastGateStd = pygsti.fast_jamiolkowski_iso_std_inv(choiStd, std)
fastGateGM = pygsti.fast_jamiolkowski_iso_std_inv(choiStd, gm)
fastGatePP = pygsti.fast_jamiolkowski_iso_std_inv(choiStd, pp)
self.assertArraysAlmostEqual(gateStd, mxStd)
self.assertArraysAlmostEqual(gateStd2, mxStd)
self.assertArraysAlmostEqual(gateStd3, mxStd)
self.assertArraysAlmostEqual(fastGateStd, mxStd)
self.assertArraysAlmostEqual(gateGM, mxGM)
self.assertArraysAlmostEqual(gateGM2, mxGM)
self.assertArraysAlmostEqual(gateGM3, mxGM)
self.assertArraysAlmostEqual(fastGateGM, mxGM)
self.assertArraysAlmostEqual(gatePP, mxPP)
self.assertArraysAlmostEqual(gatePP2, mxPP)
self.assertArraysAlmostEqual(gatePP3, mxPP)
self.assertArraysAlmostEqual(fastGatePP, mxPP)
'''
with self.assertRaises(NotImplementedError):
pygsti.jamiolkowski_iso(mxStd, "foobar", gm) #invalid gate basis
with self.assertRaises(NotImplementedError):
pygsti.jamiolkowski_iso(mxStd, std, "foobar") #invalid choi basis
with self.assertRaises(NotImplementedError):
pygsti.jamiolkowski_iso_inv(choiStd, "foobar", gm) #invalid choi basis
with self.assertRaises(NotImplementedError):
pygsti.jamiolkowski_iso_inv(choiStd, std, "foobar") #invalid gate basis
'''
sumOfNeg = pygsti.sum_of_negative_choi_evals(std1Q.gs_target)
sumOfNegWt = pygsti.sum_of_negative_choi_evals(std1Q.gs_target, {
'Gx': 1.0,
'Gy': 0.5
})
sumsOfNeg = pygsti.sums_of_negative_choi_evals(std1Q.gs_target)
magsOfNeg = pygsti.mags_of_negative_choi_evals(std1Q.gs_target)
self.assertAlmostEqual(sumOfNeg, 0.0)
self.assertArraysAlmostEqual(sumsOfNeg,
np.zeros(3,
'd')) # 3 gates in std.gs_target
self.assertArraysAlmostEqual(magsOfNeg, np.zeros(
12, 'd')) # 3 gates * 4 evals each = 12
def test_gm_basis(self):
cmb = Basis('gm', sum(self.stateSpaceDims))
self.checkBasis(cmb)
def test_std_basis(self):
cmb = Basis('std', sum(self.stateSpaceDims))
self.checkBasis(cmb)
def test_raises_on_invalid_conversion_type(self):
basis = Basis.cast("pp", 4)
with self.assertRaises(ValueError):
states.convert(self.vec, "foobar", basis)
def test_gm_basis(self):
#mx_dim = sum([ int(np.sqrt(d)) for d in self.stateSpaceDims])
cmb = Basis.cast('gm', self.stateSpaceDims)
self.checkBasis(cmb)
def test_convert(self):
basis = Basis.cast("pp", 4)
conv = states.convert(self.vec, "static", basis)
def _from_memoized_dict(cls, mm_dict, serial_memo):
errormap = serial_memo[mm_dict['submembers'][0]]
base_povm = serial_memo[mm_dict['submembers'][1]] if len(
mm_dict['submembers']) > 1 else None
mx_basis = _Basis.from_nice_serialization(mm_dict['matrix_basis'])
return cls(errormap, base_povm, mx_basis)
def test_sparse_basis(self):
sparsePP = Basis("pp",2,sparse=True)
sparsePP2 = Basis("pp",2,sparse=True)
sparseBlockPP = Basis("pp",[2,2],sparse=True)
sparsePP_2Q = Basis("pp",4,sparse=True)
sparseGM_2Q = Basis("gm",2,sparse=True) #different sparsity structure than PP 2Q
denseGM = Basis("gm",2,sparse=False)
mxs = sparsePP.get_composite_matrices()
block_mxs = sparseBlockPP.get_composite_matrices()
expeq = sparsePP.expanded_equivalent()
block_expeq = sparseBlockPP.expanded_equivalent()
raw_mxs = bt.basis_matrices("pp",2,sparse=True)
#test equality of bases with other bases and matrices
self.assertEqual(sparsePP, sparsePP2)
self.assertEqual(sparsePP, raw_mxs)
self.assertNotEqual(sparsePP, sparsePP_2Q)
self.assertNotEqual(sparsePP_2Q, sparseGM_2Q)
#sparse transform matrix
trans = sparsePP.transform_matrix(sparsePP2)
self.assertArraysAlmostEqual(trans, np.identity(4,'d'))
trans2 = sparsePP.transform_matrix(denseGM)
#test equality for large bases, which is too expensive so it always returns false
large_sparsePP = Basis("pp",16,sparse=True)
large_sparsePP2 = Basis("pp",16,sparse=True)
self.assertNotEqual(large_sparsePP, large_sparsePP2)
def test_general(self):
Basis('pp', 2)
Basis('std', [2, 1])
Basis([('std', 2), ('gm', 2)])
std = Basis('std', 2)
std4 = Basis('std', 4)
std2x2 = Basis([('std', 2), ('std', 2)])
gm = Basis('gm', 2)
ungm = Basis('gm_unnormalized', 2)
empty = Basis([]) #special "empty" basis
self.assertEqual(empty.name, "*Empty*")
from_basis,to_basis = pygsti.tools.build_basis_pair(np.identity(4,'d'),"std","gm")
from_basis,to_basis = pygsti.tools.build_basis_pair(np.identity(4,'d'),std,"gm")
from_basis,to_basis = pygsti.tools.build_basis_pair(np.identity(4,'d'),"std",gm)
gm_mxs = gm.get_composite_matrices()
unnorm = Basis(matrices=[ gm_mxs[0], 2*gm_mxs[1] ])
std[0]
std.get_sub_basis_matrices(0)
print(gm.get_composite_matrices())
self.assertTrue(gm.is_normalized())
self.assertFalse(ungm.is_normalized())
self.assertFalse(unnorm.is_normalized())
transMx = bt.transform_matrix(std, gm)
composite = Basis([std, gm])
comp = Basis(matrices=[std, gm], name='comp', longname='CustomComposite')
comp.labels = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H']
comp = Basis(matrices=[std, gm], name='comp', longname='CustomComposite', labels=[
'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'
])
std2x2Matrices = np.array([
[[1, 0],
[0, 0]],
[[0, 1],
[0, 0]],
[[0, 0],
[1, 0]],
[[0, 0],
[0, 1]]
],'complex')
empty = Basis(matrices=[])
alt_standard = Basis(matrices=std2x2Matrices)
print("MXS = \n",alt_standard._matrices)
alt_standard = Basis(matrices=std2x2Matrices,
name='std',
longname='Standard'
)
self.assertEqual(alt_standard, std2x2Matrices)
mx = np.array([
[1, 0, 0, 1],
[0, 1, 2, 0],
[0, 2, 1, 0],
[1, 0, 0, 1]
])
bt.change_basis(mx, 'std', 'gm') # shortname lookup
bt.change_basis(mx, std, gm) # object
bt.change_basis(mx, std, 'gm') # combination
bt.flexible_change_basis(mx, std, gm) #same dimension
I2x2 = np.identity(8,'d')
I4 = bt.flexible_change_basis(I2x2, std2x2, std4)
self.assertArraysAlmostEqual(bt.flexible_change_basis(I4, std4, std2x2), I2x2)
with self.assertRaises(ValueError):
bt.change_basis(mx, std, std4) # basis size mismatch
mxInStdBasis = np.array([[1,0,0,2],
[0,0,0,0],
[0,0,0,0],
[3,0,0,4]],'d')
begin = Basis('std', [1,1])
end = Basis('std', 2)
mxInReducedBasis = bt.resize_std_mx(mxInStdBasis, 'contract', end, begin)
original = bt.resize_std_mx(mxInReducedBasis, 'expand', begin, end)
def test_qt(self):
qt = Basis('qt', 3)
qt = Basis('qt', [3])
def create_qutrit_model(error_scale, x_angle=_np.pi / 2, y_angle=_np.pi / 2,
ms_global=_np.pi / 2, ms_local=0,
similarity=False, seed=None, basis='qt', evotype='default'):
"""
Constructs a standard qutrit :class:`Model`.
This model contains the identity, XX, YY, and Molmer-Sorenson gates.
Parameters
----------
error_scale : float
Magnitude of random rotations to apply to the returned model. If
zero, then perfect "ideal" gates are constructed.
x_angle : float, optional
The rotation angle of each X in the XX gate.
y_angle : float, optional
The rotation angle of each Y in the YY gate.
ms_global : float, optional
The global Molmer-Sorenson angle (theta)
ms_local : float, optional
The local Molmer-Sorenson angle (theta)
similarity : bool, optional
If true, then apply the random rotations (whose strengths are given
by `error_scale`) as similarity transformations rather than just as
post-multiplications to the ideal operation matrices.
seed : int, optional
The seed used to generate random rotations.
basis : str, optional
The string abbreviation of the basis of the returned vector. Allowed
values are Matrix-unit (std), Gell-Mann (gm) and Qutrit (qt). A `Basis`
object may also be used.
evotype : Evotype or str, optional
The evolution type. The special value `"default"` is equivalent
to specifying the value of `pygsti.evotypes.Evotype.default_evotype`.
Returns
-------
Model
"""
arrType = _np.array # Are we casting gates as matrices or arrays?
rho0 = arrType(([[1, 0, 0],
[0, 0, 0],
[0, 0, 0]]))
identity3 = arrType(_np.identity(3))
E0 = arrType(_np.diag([1, 0, 0]))
E1 = arrType(_np.diag([0, 1, 0]))
E2 = arrType(_np.diag([0, 0, 1]))
#Define gates as unitary ops on Hilbert space
gateImx = arrType(identity3)
gateXmx = arrType(_xx_qutrit(x_angle))
gateYmx = arrType(_yy_qutrit(y_angle))
gateMmx = arrType(_ms_qutrit(ms_global, ms_local))
#Now introduce unitary noise.
scale = error_scale
rndm = _np.random.RandomState(seed)
Xrand = _random_rot(scale, rndm)
Yrand = _random_rot(scale, rndm)
Mrand = _random_rot(scale, rndm)
Irand = _random_rot(scale, rndm)
if similarity: # Change basis for each gate; this preserves rotation angles, and should map identity to identity
gateXmx = _np.dot(_np.dot(_np.conj(Xrand).T, gateXmx), Xrand)
gateYmx = _np.dot(_np.dot(_np.conj(Yrand).T, gateYmx), Yrand)
gateMmx = _np.dot(_np.dot(_np.conj(Mrand).T, gateMmx), Mrand)
gateImx = _np.dot(_np.dot(_np.conj(Irand).T, gateImx), Irand)
else:
gateXmx = _np.dot(gateXmx, Xrand)
gateYmx = _np.dot(gateYmx, Yrand)
gateMmx = _np.dot(gateMmx, Mrand)
gateImx = _np.dot(gateImx, Irand)
#Change gate representation to superoperator in Gell-Mann basis
gateISOfinal = unitary_to_superop(gateImx, basis)
gateXSOfinal = unitary_to_superop(gateXmx, basis)
gateYSOfinal = unitary_to_superop(gateYmx, basis)
gateMSOfinal = unitary_to_superop(gateMmx, basis)
rho0final = change_basis(_np.reshape(rho0, (9, 1)), "std", basis)
E0final = change_basis(_np.reshape(E0, (9, 1)), "std", basis)
E1final = change_basis(_np.reshape(E1, (9, 1)), "std", basis)
E2final = change_basis(_np.reshape(E2, (9, 1)), "std", basis)
state_space = _statespace.ExplicitStateSpace(['QT'], [3])
qutritMDL = _ExplicitOpModel(state_space, _Basis.cast(basis, 9), evotype=evotype)
qutritMDL.preps['rho0'] = rho0final
qutritMDL.povms['Mdefault'] = _UnconstrainedPOVM([('0bright', E0final),
('1bright', E1final),
('2bright', E2final)], evotype=evotype)
qutritMDL.operations['Gi'] = _FullArbitraryOp(arrType(gateISOfinal), evotype, state_space)
qutritMDL.operations['Gx'] = _FullArbitraryOp(arrType(gateXSOfinal), evotype, state_space)
qutritMDL.operations['Gy'] = _FullArbitraryOp(arrType(gateYSOfinal), evotype, state_space)
qutritMDL.operations['Gm'] = _FullArbitraryOp(arrType(gateMSOfinal), evotype, state_space)
qutritMDL.default_gauge_group = _FullGaugeGroup(state_space, evotype)
return qutritMDL