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testBasisTools.py
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testBasisTools.py
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from ..testutils import BaseTestCase, compare_files, temp_files
import unittest
import numpy as np
import scipy
import pygsti
import pygsti.tools.basistools as bt
import pygsti.tools.lindbladtools as lindbladtools
from pygsti.baseobjs import Basis, ExplicitBasis, DirectSumBasis
from functools import partial
class BasisBaseTestCase(BaseTestCase):
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.cast('std', [1,1])
end = Basis.cast('std', 4)
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 test_GellMann(self):
id2x2 = np.array([[1,0],[0,1]])
sigmax = np.array([[0,1],[1,0]])
sigmay = np.array([[0,-1.0j],[1.0j,0]])
sigmaz = np.array([[1,0],[0,-1]])
# Gell-Mann 2x2 matrices should just be the sigma matrices
GM2_mxs = pygsti.gm_matrices_unnormalized(2)
self.assertTrue(len(GM2_mxs) == 4)
self.assertArraysAlmostEqual( GM2_mxs[0], id2x2 )
self.assertArraysAlmostEqual( GM2_mxs[1], sigmax )
self.assertArraysAlmostEqual( GM2_mxs[2], sigmay )
self.assertArraysAlmostEqual( GM2_mxs[3], sigmaz )
with self.assertRaises(TypeError):
pygsti.gm_matrices_unnormalized("FooBar") #arg must be tuple,list,or int
'''
# GM [1,1] matrices are the basis matrices for each block, concatenated together
GM11_mxs = pygsti.gm_matrices_unnormalized([1,1])
self.assertTrue(len(GM11_mxs) == 2)
self.assertArraysAlmostEqual( GM11_mxs[0], np.array([[1,0],[0,0]],'d') )
self.assertArraysAlmostEqual( GM11_mxs[1], np.array([[0,0],[0,1]],'d') )
'''
# Normalized Gell-Mann 2x2 matrices should just be the sigma matrices / sqrt(2)
NGM2_mxs = pygsti.gm_matrices(2)
self.assertTrue(len(NGM2_mxs) == 4)
self.assertArraysAlmostEqual( NGM2_mxs[0], id2x2/np.sqrt(2) )
self.assertArraysAlmostEqual( NGM2_mxs[1], sigmax/np.sqrt(2) )
self.assertArraysAlmostEqual( NGM2_mxs[2], sigmay/np.sqrt(2) )
self.assertArraysAlmostEqual( NGM2_mxs[3], sigmaz/np.sqrt(2) )
#TODO: test 4x4 matrices?
def test_orthogonality(self):
#Gell Mann
dim = 5
mxs = pygsti.gm_matrices(dim)
N = len(mxs); self.assertTrue(N == dim**2)
gm_trMx = np.zeros((N,N), 'complex')
for i in range(N):
for j in range(N):
gm_trMx[i,j] = np.trace(np.dot(np.conjugate(np.transpose(mxs[i])),mxs[j]))
#Note: conjugate transpose not needed since mxs are Hermitian
self.assertArraysAlmostEqual( gm_trMx, np.identity(N,'complex') )
#Std Basis
dim = 5
mxs = pygsti.std_matrices(dim)
N = len(mxs); self.assertTrue(N == dim**2)
std_trMx = np.zeros((N,N), 'complex')
for i in range(N):
for j in range(N):
std_trMx[i,j] = np.trace(np.dot(np.conjugate(np.transpose(mxs[i])),mxs[j]))
self.assertArraysAlmostEqual( std_trMx, np.identity(N,'complex') )
#Pauli-product basis
dim = 4
mxs = pygsti.pp_matrices(dim)
N = len(mxs); self.assertTrue(N == dim**2)
with self.assertRaises(TypeError):
pygsti.pp_matrices("Foobar") #dim must be an int
with self.assertRaises(ValueError):
pygsti.pp_matrices(3) #dim must be a power of 4
specialCase = pygsti.pp_matrices(1) #single 1x1 identity mx
self.assertEqual( specialCase, [ np.identity(1,'complex') ] )
pp_trMx = np.zeros((N,N), 'complex')
for i in range(N):
for j in range(N):
pp_trMx[i,j] = np.trace(np.dot(np.conjugate(np.transpose(mxs[i])),mxs[j]))
#Note: conjugate transpose not needed since mxs are Hermitian
self.assertArraysAlmostEqual( pp_trMx, np.identity(N,'complex') )
def test_transforms(self):
mxStd = np.array([[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]], 'complex')
vecStd = np.array([1,0,0,0], 'complex')
change = bt.change_basis
mxGM = change(mxStd, 'std', 'gm')
mxStd2 = change(mxGM, 'gm', 'std')
self.assertArraysAlmostEqual( mxStd, mxStd2)
vecGM = change(vecStd, 'std', 'gm')
vecStd2 = change(vecGM, 'gm', 'std')
self.assertArraysAlmostEqual( vecStd, vecStd2 )
mxPP = change(mxStd, 'std', 'pp')
mxStd2 = change(mxPP, 'pp', 'std')
self.assertArraysAlmostEqual( mxStd, mxStd2 )
vecPP = change(vecStd, 'std', 'pp')
vecStd2 = change(vecPP, 'pp', 'std')
self.assertArraysAlmostEqual( vecStd, vecStd2 )
mxPP2 = change(mxGM, 'gm', 'pp')
self.assertArraysAlmostEqual( mxPP, mxPP2 )
vecPP2 = change(vecGM, 'gm', 'pp')
self.assertArraysAlmostEqual( vecPP, vecPP2 )
mxGM2 = change(mxPP, 'pp', 'gm')
self.assertArraysAlmostEqual( mxGM, mxGM2 )
vecGM2 = change(vecPP, 'pp', 'gm')
self.assertArraysAlmostEqual( vecGM, vecGM2 )
non_herm_mxStd = np.array([[1,0,2,3j],
[0,1,0,2],
[0,0,1,0],
[0,0,0,1]], 'complex')
non_herm_vecStd = np.array([1,0,2,3j], 'complex') # ~ non-herm 2x2 density mx
rank3tensor = np.ones((4,4,4),'d')
with self.assertRaises(ValueError):
change(non_herm_mxStd, 'std', 'gm') #will result in gm mx with *imag* part
with self.assertRaises(ValueError):
change(non_herm_vecStd, 'std', 'gm') #will result in gm vec with *imag* part
with self.assertRaises(ValueError):
change(non_herm_mxStd, 'std', 'pp') #will result in pp mx with *imag* part
with self.assertRaises(ValueError):
change(non_herm_vecStd, 'std', 'pp') #will result in pp vec with *imag* part
with self.assertRaises(ValueError):
change(rank3tensor, 'std', 'gm') #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'gm', 'std') #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'std', 'pp') #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'pp', 'std') #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'gm', 'pp') #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
change(rank3tensor, 'pp', 'gm') #only convert rank 1 & 2 objects
densityMx = np.array( [[1,0],[0,-1]], 'complex' )
gmVec = pygsti.stdmx_to_gmvec(densityMx)
ppVec = pygsti.stdmx_to_ppvec(densityMx)
stdVec = pygsti.stdmx_to_stdvec(densityMx)
self.assertArraysAlmostEqual( gmVec, np.array( [[0],[0],[0],[np.sqrt(2)]], 'd') )
self.assertArraysAlmostEqual( ppVec, np.array( [[0],[0],[0],[np.sqrt(2)]], 'd') )
self.assertArraysAlmostEqual( stdVec, np.array( [[1],[0],[0],[-1]], 'complex') )
mxFromGM = pygsti.gmvec_to_stdmx(gmVec)
mxFromPP = pygsti.ppvec_to_stdmx(ppVec)
mxFromStd = pygsti.stdvec_to_stdmx(stdVec)
self.assertArraysAlmostEqual( mxFromGM, densityMx)
self.assertArraysAlmostEqual( mxFromPP, densityMx)
self.assertArraysAlmostEqual( mxFromStd, densityMx)
def test_few_qubit_fns(self):
state_vec = np.array([1,0],'complex')
dmVec = pygsti.state_to_pauli_density_vec(state_vec)
self.assertArraysAlmostEqual(dmVec, np.array([[0.70710678],[0],[0],[0.70710678]], 'complex'))
theta = np.pi
ex = 1j * theta*pygsti.sigmax/2
U = scipy.linalg.expm(ex)
# U is 2x2 unitary matrix operating on single qubit in [0,1] basis (X(pi) rotation)
op = pygsti.unitary_to_pauligate(U)
op_ans = np.array([[ 1., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., -1., 0.],
[ 0., 0., 0., -1.]], 'd')
self.assertArraysAlmostEqual(op, op_ans)
U_2Q = np.identity(4, 'complex'); U_2Q[2:,2:] = U
# U_2Q is 4x4 unitary matrix operating on isolated two-qubit space (CX(pi) rotation)
op_2Q = pygsti.unitary_to_pauligate(U_2Q)
stdMx = np.array( [[1,0],[0,0]], 'complex' ) #density matrix
pauliVec = pygsti.stdmx_to_ppvec(stdMx)
self.assertArraysAlmostEqual(pauliVec, np.array([[0.70710678],[0],[0],[0.70710678]], 'complex'))
stdMx2 = pygsti.ppvec_to_stdmx(pauliVec)
self.assertArraysAlmostEqual( stdMx, stdMx2 )
def test_basis_misc(self):
#with self.assertRaises(TypeError):
# Dim("FooBar") #arg should be a list,tuple,or int
bt.pp_matrices(1) # was [1] but this shouldn't be allowed
def test_basis_longname(self):
longnames = {bt.basis_longname(b) for b in {'gm', 'std', 'pp', 'qt'}}
self.assertEqual(longnames, {'Gell-Mann basis', 'Matrix-unit basis', 'Pauli-Product basis', 'Qutrit basis'})
with self.assertRaises(KeyError):
bt.basis_longname('not a basis')
def test_basis_element_labels(self):
basisnames = ['gm', 'std', 'pp']
# One dimensional gm
self.assertEqual([''], bt.basis_element_labels('gm', 1))
# Two dimensional
expectedLabels = [
['I', 'X', 'Y', 'Z'],
['(0,0)', '(0,1)', '(1,0)', '(1,1)'],
['I', 'X', 'Y', 'Z']]
labels = [bt.basis_element_labels(basisname, 4) for basisname in basisnames]
self.assertEqual(labels, expectedLabels)
with self.assertRaises(AssertionError):
bt.basis_element_labels('asdklfasdf', 4)
# Non power of two for pp labels:
with self.assertRaises(ValueError):
label = bt.basis_element_labels('pp', 9)
# Single list arg for pp labels
self.assertEqual(bt.basis_element_labels('pp',4), ['I', 'X', 'Y', 'Z'])
# Four dimensional+
expectedLabels = [['I', 'X_{0,1}', 'X_{0,2}', 'X_{0,3}', 'X_{1,2}', 'X_{1,3}', 'X_{2,3}', 'Y_{0,1}', 'Y_{0,2}', 'Y_{0,3}', 'Y_{1,2}', 'Y_{1,3}', 'Y_{2,3}', 'Z_{1}', 'Z_{2}', 'Z_{3}'], ['(0,0)', '(0,1)', '(0,2)', '(0,3)', '(1,0)', '(1,1)', '(1,2)', '(1,3)', '(2,0)', '(2,1)', '(2,2)', '(2,3)', '(3,0)', '(3,1)', '(3,2)', '(3,3)'], ['II', 'IX', 'IY', 'IZ', 'XI', 'XX', 'XY', 'XZ', 'YI', 'YX', 'YY', 'YZ', 'ZI', 'ZX', 'ZY', 'ZZ']]
labels = [bt.basis_element_labels(basisname, 16) for basisname in basisnames]
self.assertEqual(expectedLabels, labels)
def test_hamiltonian_to_lindbladian(self):
expectedLindbladian = np.array([[ 0, 0, 0, 0],
[ 0, 0, 0, 0,],
[ 0, 0, 0, 0,],
[ 0, 0, 0, 0]]
)
self.assertArraysAlmostEqual(lindbladtools.hamiltonian_to_lindbladian(np.zeros(shape=(2,2))),
expectedLindbladian)
def test_vec_to_stdmx(self):
vec = np.zeros(shape=(4,))
for b in {'gm', 'pp', 'std'}:
bt.vec_to_stdmx(vec, b)
with self.assertRaises(AssertionError):
bt.vec_to_stdmx(vec, 'akdfj;ladskf')
def test_composite_basis(self):
comp = Basis.cast([('std', 4,), ('std', 1)])
a = Basis.cast([('std', 4), ('std', 4)])
b = Basis.cast('std', [4,4])
self.assertEqual(len(a), len(b))
self.assertArraysAlmostEqual(np.array(a.elements), np.array(b.elements))
def test_auto_expand(self):
comp = Basis.cast([('std', 4,), ('std', 1)])
std = Basis.cast('std', 9)
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_flexible_change_basis(self):
comp = Basis.cast([('gm', 4,), ('gm', 1)])
std = Basis.cast('std', 9)
mx = np.identity(5)
test = bt.flexible_change_basis(mx, comp, std)
self.assertEqual(test.shape[0], comp.elsize)
test2 = bt.flexible_change_basis(test, std, comp)
self.assertArraysAlmostEqual(test2, mx)
def test_change_between_composites(self):
a = Basis.cast('std', [4, 1])
b = Basis.cast('gm', [4, 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_qt(self):
qt = Basis.cast('qt', 9)
qt = Basis.cast('qt', [9])
def test_general(self):
Basis.cast('pp', 4)
Basis.cast('std', [4, 1])
with self.assertRaises(AssertionError):
Basis.cast([('std', 16), ('gm', 4)]) # inconsistent .real values of components!
std = Basis.cast('std', 4)
std4 = Basis.cast('std', 16)
std2x2 = Basis.cast([('std', 4), ('std', 4)])
gm = Basis.cast('gm', 4)
ungm = Basis.cast('gm_unnormalized', 4)
empty = Basis.cast([]) #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.elements
unnorm = ExplicitBasis([ gm_mxs[0], 2*gm_mxs[1] ])
std[0]
#std.get_sub_basis_matrices(0)
#print(gm.elements)
self.assertTrue(gm.is_normalized())
self.assertFalse(ungm.is_normalized())
self.assertFalse(unnorm.is_normalized())
#transMx = bt.transform_matrix(std, gm) #REMOVED
composite = DirectSumBasis([gm, gm])
comp = DirectSumBasis([gm, gm], name='comp', longname='CustomComposite')
#comp.labels = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'] #read-only
comp = DirectSumBasis([gm, gm], name='comp', longname='CustomComposite')
comp._labels=['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'] # TODO: make a set_labels?
std2x2Matrices = np.array([
[[1, 0],
[0, 0]],
[[0, 1],
[0, 0]],
[[0, 0],
[1, 0]],
[[0, 0],
[0, 1]]
],'complex')
empty = ExplicitBasis([])
alt_standard = ExplicitBasis(std2x2Matrices)
print("MXS = \n",alt_standard.elements)
alt_standard = ExplicitBasis(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(AssertionError):
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.cast('std', [1,1])
end = Basis.cast('std', 4)
mxInReducedBasis = bt.resize_std_mx(mxInStdBasis, 'contract', end, begin)
original = bt.resize_std_mx(mxInReducedBasis, 'expand', begin, end)
def test_basis_object(self):
#test a few aspects of a Basis object that other tests miss...
b = Basis.cast("pp",4)
beq = b.simple_equivalent()
longnm = bt.basis_longname(b)
lbls = bt.basis_element_labels(b,None)
raw_mxs = bt.basis_matrices("pp",4)
with self.assertRaises(AssertionError):
bt.basis_matrices("foobar",4) #invalid basis name
print("Dim = ", repr(b.dim) ) # calls Dim.__repr__
def test_basis_constructors(self):
#special constructions not covered elsewhere
ppMax1 = bt.pp_matrices(2,maxWeight=1) #using maxWeight
qutrit1 = bt.qt_matrices(1) #special case when dim==1
#Cover invalid Dim construction (DIM REMOVED)
#with self.assertRaises(TypeError):
# pygsti.baseobjs.Dim(1.2)
def test_sparse_basis(self):
sparsePP = Basis.cast("pp",4,sparse=True)
sparsePP2 = Basis.cast("pp",4,sparse=True)
sparseBlockPP = Basis.cast("pp",[4,4],sparse=True)
sparsePP_2Q = Basis.cast("pp",16,sparse=True)
sparseGM_2Q = Basis.cast("gm",4,sparse=True) #different sparsity structure than PP 2Q
denseGM = Basis.cast("gm",4,sparse=False)
mxs = sparsePP.elements
block_mxs = sparseBlockPP.elements
expeq = sparsePP.simple_equivalent()
block_expeq = sparseBlockPP.simple_equivalent()
raw_mxs = bt.basis_matrices("pp",4,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
large_sparsePP = Basis.cast("pp",256,sparse=True)
large_sparsePP2 = Basis.cast("pp",256,sparse=True)
self.assertEqual(large_sparsePP, large_sparsePP2)
#OLD: was too expensive so it always returns false; now compares names & dim...
if __name__ == '__main__':
unittest.main(verbosity=2)