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(ValueError):
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) )
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(ValueError):
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) )
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(ValueError):
pygsti.pp_matrices("Foobar") #dim must be an int
with self.assertRaises(ValueError):
pygsti.pp_matrices(3) #dim must be a power of 2
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_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(ValueError):
pygsti.pp_matrices("Foobar") #dim must be an int
with self.assertRaises(ValueError):
pygsti.pp_matrices(3) #dim must be a power of 2
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') )
