def _bravyi_kitaev_mode(self, n): """ Bravyi-Kitaev mode. Args: n (int): number of modes Returns: numpy.ndarray: Array of mode indexes """ def parity_set(j, n): """Computes the parity set of the j-th orbital in n modes. Args: j (int) : the orbital index n (int) : the total number of modes Returns: numpy.ndarray: Array of mode indexes """ indexes = np.array([]) if n % 2 != 0: return indexes if j < n / 2: indexes = np.append(indexes, parity_set(j, n / 2)) else: indexes = np.append( indexes, np.append(parity_set(j - n / 2, n / 2) + n / 2, n / 2 - 1)) return indexes def update_set(j, n): """Computes the update set of the j-th orbital in n modes. Args: j (int) : the orbital index n (int) : the total number of modes Returns: numpy.ndarray: Array of mode indexes """ indexes = np.array([]) if n % 2 != 0: return indexes if j < n / 2: indexes = np.append(indexes, np.append(n - 1, update_set(j, n / 2))) else: indexes = np.append(indexes, update_set(j - n / 2, n / 2) + n / 2) return indexes def flip_set(j, n): """Computes the flip set of the j-th orbital in n modes. Args: j (int) : the orbital index n (int) : the total number of modes Returns: numpy.ndarray: Array of mode indexes """ indexes = np.array([]) if n % 2 != 0: return indexes if j < n / 2: indexes = np.append(indexes, flip_set(j, n / 2)) elif j >= n / 2 and j < n - 1: # pylint: disable=chained-comparison indexes = np.append(indexes, flip_set(j - n / 2, n / 2) + n / 2) else: indexes = np.append( np.append(indexes, flip_set(j - n / 2, n / 2) + n / 2), n / 2 - 1) return indexes a_list = [] # FIND BINARY SUPERSET SIZE bin_sup = 1 # pylint: disable=comparison-with-callable while n > np.power(2, bin_sup): bin_sup += 1 # DEFINE INDEX SETS FOR EVERY FERMIONIC MODE update_sets = [] update_pauli = [] parity_sets = [] parity_pauli = [] flip_sets = [] remainder_sets = [] remainder_pauli = [] for j in range(n): update_sets.append(update_set(j, np.power(2, bin_sup))) update_sets[j] = update_sets[j][update_sets[j] < n] parity_sets.append(parity_set(j, np.power(2, bin_sup))) parity_sets[j] = parity_sets[j][parity_sets[j] < n] flip_sets.append(flip_set(j, np.power(2, bin_sup))) flip_sets[j] = flip_sets[j][flip_sets[j] < n] remainder_sets.append(np.setdiff1d(parity_sets[j], flip_sets[j])) update_pauli.append( Pauli(np.zeros(n, dtype=np.bool), np.zeros(n, dtype=np.bool))) parity_pauli.append( Pauli(np.zeros(n, dtype=np.bool), np.zeros(n, dtype=np.bool))) remainder_pauli.append( Pauli(np.zeros(n, dtype=np.bool), np.zeros(n, dtype=np.bool))) for k in range(n): if np.in1d(k, update_sets[j]): update_pauli[j].update_x(True, k) if np.in1d(k, parity_sets[j]): parity_pauli[j].update_z(True, k) if np.in1d(k, remainder_sets[j]): remainder_pauli[j].update_z(True, k) x_j = Pauli(np.zeros(n, dtype=np.bool), np.zeros(n, dtype=np.bool)) x_j.update_x(True, j) y_j = Pauli(np.zeros(n, dtype=np.bool), np.zeros(n, dtype=np.bool)) y_j.update_z(True, j) y_j.update_x(True, j) a_list.append((update_pauli[j] * x_j * parity_pauli[j], update_pauli[j] * y_j * remainder_pauli[j])) return a_list
class TestPauli(QiskitTestCase): """Tests for Pauli class.""" def setUp(self): """Setup.""" z = np.asarray([1, 0, 1, 0]).astype(np.bool) x = np.asarray([1, 1, 0, 0]).astype(np.bool) self.ref_p = Pauli(z, x) self.ref_label = 'IZXY' self.ref_matrix = np.array( [[ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. - 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. - 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. - 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. - 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. - 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. - 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 1.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. - 1.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 1.j, 0. + 0.j, 0. + 0.j ], [ 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. - 1.j, 0. + 0.j, 0. + 0.j, 0. + 0.j ]]) def test_create_from_label(self): """Test creation from pauli label.""" label = 'IZXY' pauli = Pauli(label=label) self.assertEqual(pauli, self.ref_p) self.assertEqual(pauli.to_label(), self.ref_label) self.assertEqual(len(pauli), 4) def test_create_from_z_x(self): """Test creation for boolean vector.""" self.assertEqual(self.ref_p.to_label(), 'IZXY') self.assertEqual(len(self.ref_p), 4) def test_repr(self): """Test __repr__.""" p = repr(self.ref_p) self.assertEqual( p, "Pauli(z=[True, False, True, False], x=[True, True, False, False])" ) def test_random_pauli(self): """Test random pauli creation.""" length = 4 q = Pauli.random(length, seed=42) self.log.info(q) self.assertEqual(q.numberofqubits, length) self.assertEqual(len(q.z), length) self.assertEqual(len(q.x), length) self.assertEqual(len(q.to_label()), length) self.assertEqual(len(q.to_matrix()), 2**length) def test_mul(self): """Test multiplication.""" p1 = self.ref_p p2 = Pauli.from_label('ZXXI') p3 = p1 * p2 self.assertEqual(len(p3), 4) self.assertEqual(p3.to_label(), 'ZYIY') def test_imul(self): """Test in-place multiplication.""" p1 = self.ref_p p2 = Pauli.from_label('ZXXI') p3 = deepcopy(p2) p2 *= p1 self.assertTrue(p2 != p3) self.assertEqual(p2.to_label(), 'ZYIY') def test_equality_equal(self): """Test equality operator: equal Paulis.""" p1 = self.ref_p p2 = deepcopy(p1) self.assertTrue(p1 == p2) self.assertEqual(p1.to_label(), self.ref_label) self.assertEqual(p2.to_label(), self.ref_label) def test_equality_different(self): """Test equality operator: different Paulis.""" p1 = self.ref_p p2 = deepcopy(p1) p2.update_z(True, 1) self.assertFalse(p1 == p2) self.assertEqual(p1.to_label(), self.ref_label) self.assertEqual(p2.to_label(), 'IZYY') def test_inequality_equal(self): """Test inequality operator: equal Paulis.""" p1 = self.ref_p p2 = deepcopy(p1) self.assertFalse(p1 != p2) def test_inequality_different(self): """Test inequality operator: different Paulis.""" p1 = self.ref_p p2 = deepcopy(p1) p2.update_x(False, 1) self.assertTrue(p1 != p2) self.assertEqual(p2.to_label(), 'IZIY') def test_update_z(self): """Test update_z method.""" updated_z = np.asarray([0, 0, 0, 0]).astype(np.bool) self.ref_p.update_z(updated_z) np.testing.assert_equal(self.ref_p.z, np.asarray([False, False, False, False])) self.assertEqual(self.ref_p.to_label(), 'IIXX') def test_update_z_2(self): """Test update_z method, update partial z.""" updated_z = np.asarray([0, 1]).astype(np.bool) self.ref_p.update_z(updated_z, [0, 1]) np.testing.assert_equal(self.ref_p.z, np.asarray([False, True, True, False])) self.assertEqual(self.ref_p.to_label(), 'IZYX') def test_update_x(self): """Test update_x method.""" updated_x = np.asarray([0, 1, 0, 1]).astype(np.bool) self.ref_p.update_x(updated_x) np.testing.assert_equal(self.ref_p.x, np.asarray([False, True, False, True])) self.assertEqual(self.ref_p.to_label(), 'XZXZ') def test_update_x_2(self): """Test update_x method, update partial x.""" updated_x = np.asarray([0, 1]).astype(np.bool) self.ref_p.update_x(updated_x, [1, 2]) np.testing.assert_equal(self.ref_p.x, np.asarray([True, False, True, False])) self.assertEqual(self.ref_p.to_label(), 'IYIY') def test_to_matrix(self): """Test pauli to matrix.""" np.testing.assert_allclose(self.ref_p.to_matrix(), self.ref_matrix) def test_delete_qubit(self): """Test deleting single qubit.""" p1 = self.ref_p p2 = deepcopy(p1) p2.delete_qubits(0) self.assertTrue(p1 != p2) self.assertEqual(len(p2), 3) self.assertEqual(p2.to_label(), 'IZX') def test_delete_qubits(self): """Test deleting multiple qubits.""" p1 = self.ref_p p2 = deepcopy(p1) p2.delete_qubits([0, 2]) self.assertTrue(p1 != p2) self.assertEqual(len(p2), 2) self.assertEqual(p2.to_label(), 'IX') def test_append_pauli_labels(self): """Test appending paulis via labels.""" p1 = self.ref_p p2 = deepcopy(p1) p2.append_paulis(pauli_labels=['Z', 'Y', 'I']) self.assertTrue(p1 != p2) self.assertEqual(len(p2), 7) self.assertEqual(p2.to_label(), 'IYZ' + self.ref_label) def test_append_paulis(self): """Test appending paulis via pauli object.""" p1 = self.ref_p p2 = deepcopy(p1) p2.append_paulis(paulis=p1) self.assertTrue(p1 != p2) self.assertEqual(len(p2), 8) self.assertEqual(p2.to_label(), self.ref_label + self.ref_label) def test_insert_pauli_labels_1(self): """Test inserting paulis via labels.""" p2 = deepcopy(self.ref_p) p2.insert_paulis(indices=[1, 2], pauli_labels=['Y', 'I']) self.assertTrue(self.ref_p != p2) self.assertEqual(len(p2), 6) self.assertEqual(p2.to_label(), 'IZIXYY') def test_insert_pauli_labels_2(self): """Test inserting paulis via labels.""" p2 = deepcopy(self.ref_p) p2.insert_paulis(indices=[3, 2], pauli_labels=['Y', 'I']) self.assertTrue(self.ref_p != p2) self.assertEqual(len(p2), 6) self.assertEqual(p2.to_label(), 'IYZIXY') def test_insert_paulis(self): """Test inserting paulis via pauli object.""" p1 = deepcopy(self.ref_p) new_p = Pauli.from_label('XY') p1.insert_paulis(indices=[0], paulis=new_p) self.assertTrue(p1 != self.ref_p) self.assertEqual(len(p1), 6) self.assertEqual(p1.to_label(), self.ref_label + 'XY') def test_kron(self): """Test kron production.""" p1 = deepcopy(self.ref_p) p2 = self.ref_p p2.kron(p1) self.assertTrue(p1 != p2) self.assertEqual(len(p2), 8) self.assertEqual(p2.to_label(), self.ref_label + self.ref_label) def test_pauli_single(self): """Test pauli single.""" num_qubits = 5 pz = Pauli.pauli_single(num_qubits, 2, 'Z') self.assertTrue(pz.to_label(), 'IIIZI') py = Pauli.pauli_single(num_qubits, 4, 'Y') self.assertTrue(py.to_label(), 'IYIII') px = Pauli.pauli_single(num_qubits, 3, 'X') self.assertTrue(px.to_label(), 'IIXII') def test_pauli_group(self): """Test pauli group.""" self.log.info("Group in tensor order:") expected = [ 'III', 'XII', 'YII', 'ZII', 'IXI', 'XXI', 'YXI', 'ZXI', 'IYI', 'XYI', 'YYI', 'ZYI', 'IZI', 'XZI', 'YZI', 'ZZI', 'IIX', 'XIX', 'YIX', 'ZIX', 'IXX', 'XXX', 'YXX', 'ZXX', 'IYX', 'XYX', 'YYX', 'ZYX', 'IZX', 'XZX', 'YZX', 'ZZX', 'IIY', 'XIY', 'YIY', 'ZIY', 'IXY', 'XXY', 'YXY', 'ZXY', 'IYY', 'XYY', 'YYY', 'ZYY', 'IZY', 'XZY', 'YZY', 'ZZY', 'IIZ', 'XIZ', 'YIZ', 'ZIZ', 'IXZ', 'XXZ', 'YXZ', 'ZXZ', 'IYZ', 'XYZ', 'YYZ', 'ZYZ', 'IZZ', 'XZZ', 'YZZ', 'ZZZ' ] grp = pauli_group(3, case='tensor') for j in grp: self.log.info('==== j (tensor order) ====') self.log.info(j.to_label()) self.assertEqual(expected.pop(0)[::-1], j.to_label()) self.log.info("Group in weight order:") expected = [ 'III', 'XII', 'YII', 'ZII', 'IXI', 'IYI', 'IZI', 'IIX', 'IIY', 'IIZ', 'XXI', 'YXI', 'ZXI', 'XYI', 'YYI', 'ZYI', 'XZI', 'YZI', 'ZZI', 'XIX', 'YIX', 'ZIX', 'IXX', 'IYX', 'IZX', 'XIY', 'YIY', 'ZIY', 'IXY', 'IYY', 'IZY', 'XIZ', 'YIZ', 'ZIZ', 'IXZ', 'IYZ', 'IZZ', 'XXX', 'YXX', 'ZXX', 'XYX', 'YYX', 'ZYX', 'XZX', 'YZX', 'ZZX', 'XXY', 'YXY', 'ZXY', 'XYY', 'YYY', 'ZYY', 'XZY', 'YZY', 'ZZY', 'XXZ', 'YXZ', 'ZXZ', 'XYZ', 'YYZ', 'ZYZ', 'XZZ', 'YZZ', 'ZZZ' ] grp = pauli_group(3, case='weight') for j in grp: self.log.info('==== j (weight order) ====') self.log.info(j.to_label()) self.assertEqual(expected.pop(0)[::-1], j.to_label()) def test_sgn_prod(self): """Test sgn prod.""" p1 = Pauli(np.array([False]), np.array([True])) p2 = Pauli(np.array([True]), np.array([True])) self.log.info("sign product:") p3, sgn = Pauli.sgn_prod(p1, p2) self.log.info("p1: %s", p1.to_label()) self.log.info("p2: %s", p2.to_label()) self.log.info("p3: %s", p3.to_label()) self.log.info("sgn_prod(p1, p2): %s", str(sgn)) self.assertEqual(p1.to_label(), 'X') self.assertEqual(p2.to_label(), 'Y') self.assertEqual(p3.to_label(), 'Z') self.assertEqual(sgn, 1j) self.log.info("sign product reverse:") p3, sgn = Pauli.sgn_prod(p2, p1) # pylint: disable=arguments-out-of-order self.log.info("p2: %s", p2.to_label()) self.log.info("p1: %s", p1.to_label()) self.log.info("p3: %s", p3.to_label()) self.log.info("sgn_prod(p2, p1): %s", str(sgn)) self.assertEqual(p1.to_label(), 'X') self.assertEqual(p2.to_label(), 'Y') self.assertEqual(p3.to_label(), 'Z') self.assertEqual(sgn, -1j)