/
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 basistools
class BasisBaseTestCase(BaseTestCase):
###########################################################
## BASIS TOOLS TESTS ##################################
###########################################################
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])
mxInReducedBasis = pygsti.contract_to_std_direct_sum_mx(mxInStdBasis,[1,1])
notReallyContracted = pygsti.contract_to_std_direct_sum_mx(mxInStdBasis,4)
correctAnswer = np.array([[ 1.0, 2.0],
[ 3.0, 4.0]])
self.assertArraysAlmostEqual( mxInReducedBasis, correctAnswer )
self.assertArraysAlmostEqual( notReallyContracted, mxInStdBasis )
expandedMx = pygsti.expand_from_std_direct_sum_mx(mxInReducedBasis,[1,1])
expandedMxAgain = pygsti.expand_from_std_direct_sum_mx(expandedMx,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(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_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')
mxGM = pygsti.std_to_gm(mxStd)
mxStd2 = pygsti.gm_to_std(mxGM)
self.assertArraysAlmostEqual( mxStd, mxStd2 )
vecGM = pygsti.std_to_gm(vecStd)
vecStd2 = pygsti.gm_to_std(vecGM)
self.assertArraysAlmostEqual( vecStd, vecStd2 )
mxPP = pygsti.std_to_pp(mxStd)
mxStd2 = pygsti.pp_to_std(mxPP)
self.assertArraysAlmostEqual( mxStd, mxStd2 )
vecPP = pygsti.std_to_pp(vecStd)
vecStd2 = pygsti.pp_to_std(vecPP)
self.assertArraysAlmostEqual( vecStd, vecStd2 )
mxPP2 = pygsti.gm_to_pp(mxGM)
self.assertArraysAlmostEqual( mxPP, mxPP2 )
vecPP2 = pygsti.gm_to_pp(vecGM)
self.assertArraysAlmostEqual( vecPP, vecPP2 )
mxGM2 = pygsti.pp_to_gm(mxPP)
self.assertArraysAlmostEqual( mxGM, mxGM2 )
vecGM2 = pygsti.pp_to_gm(vecPP)
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):
pygsti.std_to_gm(non_herm_mxStd) #will result in gm mx with *imag* part
with self.assertRaises(ValueError):
pygsti.std_to_gm(non_herm_vecStd) #will result in gm vec with *imag* part
with self.assertRaises(ValueError):
pygsti.std_to_pp(non_herm_mxStd) #will result in pp mx with *imag* part
with self.assertRaises(ValueError):
pygsti.std_to_pp(non_herm_vecStd) #will result in pp vec with *imag* part
with self.assertRaises(ValueError):
pygsti.std_to_gm(rank3tensor) #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
pygsti.gm_to_std(rank3tensor) #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
pygsti.std_to_pp(rank3tensor) #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
pygsti.pp_to_std(rank3tensor) #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
pygsti.gm_to_pp(rank3tensor) #only convert rank 1 & 2 objects
with self.assertRaises(ValueError):
pygsti.pp_to_gm(rank3tensor) #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_1q(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_2q(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_basistools_misc(self):
with self.assertRaises(TypeError):
basistools._processBlockDims("FooBar") #arg should be a list,tuple,or int
basistools.pp_matrices([1])
def test_basis_longname(self):
longnames = {basistools.basis_longname(basis) for basis in {'gm', 'std', 'pp'}}
self.assertEqual(longnames, {'Gell-Mann', 'Matrix-unit', 'Pauli-prod'})
self.assertEqual(basistools.basis_longname('not a basis'), '?Unknown?')
def test_basis_element_labels(self):
basisnames = ['gm', 'std', 'pp', 'akdlfjalsdf']
# One dimensional gm
self.assertEqual([''], basistools.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 = [basistools.basis_element_labels(basisname, 2) for basisname in basisnames]
self.assertEqual(labels, expectedLabels)
# Non power of two for pp labels:
with self.assertRaises(ValueError):
label = basistools.basis_element_labels('pp', 3)
with self.assertRaises(ValueError):
label = basistools.basis_element_labels('pp', [1, 2])
# Single list arg for pp labels
self.assertEqual(basistools.basis_element_labels('pp', [2]), ['I', 'X', 'Y', 'Z'])
# Four dimensional+
expectedLabels = [['I^{(0)}', 'X^{(0)}_{0,1}', 'X^{(0)}_{0,2}', 'X^{(0)}_{0,3}', 'X^{(0)}_{1,2}', 'X^{(0)}_{1,3}', 'X^{(0)}_{2,3}', 'Y^{(0)}_{0,1}', 'Y^{(0)}_{0,2}', 'Y^{(0)}_{0,3}', 'Y^{(0)}_{1,2}', 'Y^{(0)}_{1,3}', 'Y^{(0)}_{2,3}', 'Z^{(0)}_{1}', 'Z^{(0)}_{2}', 'Z^{(0)}_{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 = [basistools.basis_element_labels(basisname, 4) 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(basistools.hamiltonian_to_lindbladian(np.zeros(shape=(2,2))),
expectedLindbladian)
def test_vec_to_stdmx(self):
vec = np.zeros(shape=(2,))
for basis in {'gm', 'pp', 'std'}:
basistools.vec_to_stdmx(vec, basis)
with self.assertRaises(ValueError):
basistools.vec_to_stdmx(vec, 'akdfj;ladskf')
def test_single_qubit_gate_matrix(self):
expected = np.array([[1.00000000e+00, 2.77555756e-16, -2.28983499e-16, 0.00000000e+00],
[ -3.53885261e-16, -8.09667193e-01, 5.22395269e-01, -2.67473774e-01],
[ -3.92523115e-17, 5.22395269e-01, 8.49200550e-01, 7.72114534e-02],
[ 1.66533454e-16, 2.67473774e-01, -7.72114534e-02, -9.60466643e-01]]
)
mx = basistools.single_qubit_gate(24.0, 83.140134, 0.0000)
self.assertArraysAlmostEqual(expected, mx)
def test_two_qubit_gate_mx(self):
gate = basistools.two_qubit_gate()
expected = np.array([
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,]])
self.assertArraysAlmostEqual(gate,expected)
if __name__ == '__main__':
unittest.main(verbosity=2)