def _test_generator_out_of_frame(self,
t,
frame_op,
y,
y_in_frame_basis=False,
return_in_frame_basis=False):
"""Helper function for testing generator_into_frame."""
evals, U = np.linalg.eigh(1j * frame_op)
evals = -1j * Array(evals)
Uadj = U.conj().transpose()
frame = Frame(frame_op)
value = frame.generator_out_of_frame(t, y, y_in_frame_basis,
return_in_frame_basis)
expected = y
if not y_in_frame_basis:
expected = Uadj @ expected @ U
expected = np.diag(np.exp(t * evals)) @ expected @ np.diag(
np.exp(-t * evals))
expected = expected + np.diag(evals)
if not return_in_frame_basis:
expected = U @ expected @ Uadj
self.assertAllClose(value, expected, rtol=1e-10, atol=1e-10)
def test_instantiation_errors(self):
"""Check different modes of error raising for frame setting."""
with self.assertRaises(QiskitError):
Frame(Array([1.0, 1j]))
with self.assertRaises(QiskitError):
Frame(Array([[1.0, 0.0], [0.0, 1j]]))
with self.assertRaises(QiskitError):
Frame(self.Z + 1j * self.X)
def test_instantiation_errors(self):
"""Check different modes of error raising for frame setting.
Needs to be overwrititen for jax due to different behaviour.
"""
# pylint: disable=import-outside-toplevel
import jax.numpy as jnp
frame = Frame(Array([1.0, 1j]))
self.assertTrue(jnp.isnan(frame.frame_diag[0]))
frame = Frame(Array([[1.0, 0.0], [0.0, 1j]]))
self.assertTrue(jnp.isnan(frame.frame_diag[0]))
frame = Frame(self.Z + 1j * self.X)
self.assertTrue(jnp.isnan(frame.frame_diag[0]))
def test_operators_into_frame_basis_with_cutoff_no_cutoff(self):
"""Test function for construction of operators with cutoff,
without a cutoff.
"""
# no cutoff with already diagonal frame
frame_op = -1j * np.pi * Array([1.0, -1.0])
operators = Array([self.X.data, self.Y.data, self.Z.data])
carrier_freqs = Array([1.0, 2.0, 3.0])
frame = Frame(frame_op)
ops_w_cutoff, ops_w_conj_cutoff = frame.operators_into_frame_basis_with_cutoff(
operators, carrier_freqs=carrier_freqs)
self.assertAllClose(ops_w_cutoff, operators)
self.assertAllClose(ops_w_conj_cutoff, operators)
# same test but with frame given as a 2d array
# in this case diagonalization will occur, causing eigenvalues to
# be sorted in ascending order. This will flip Y and Z
frame_op = -1j * np.pi * Array([[1.0, 0], [0, -1.0]])
carrier_freqs = Array([1.0, 2.0, 3.0])
frame = Frame(frame_op)
ops_w_cutoff, ops_w_conj_cutoff = frame.operators_into_frame_basis_with_cutoff(
operators, carrier_freqs=carrier_freqs)
expected_ops = Array([self.X.data, -self.Y.data, -self.Z.data])
self.assertAllClose(ops_w_cutoff, expected_ops)
self.assertAllClose(ops_w_conj_cutoff, expected_ops)
def test_state_out_of_frame_basis(self):
"""Test state_out_of_frame_basis."""
rng = np.random.default_rng(10933)
rand_op = rng.uniform(low=-10, high=10, size=(
6, 6)) + 1j * rng.uniform(low=-10, high=10, size=(6, 6))
frame_op = Array(rand_op - rand_op.conj().transpose())
frame = Frame(frame_op)
_, U = np.linalg.eigh(1j * frame_op)
y0 = Array(
rng.uniform(low=-10, high=10, size=(6, 6)) +
1j * rng.uniform(low=-10, high=10, size=(6, 6)))
val = frame.state_into_frame_basis(y0)
expected = U.conj().transpose() @ y0
self.assertAllClose(val, expected)
val = frame.state_out_of_frame_basis(y0)
expected = U @ y0
self.assertAllClose(val, expected)
def test_operators_into_frame_basis_with_cutoff(self):
"""Test function for construction of operators with cutoff."""
# cutoff test
frame_op = -1j * np.pi * Array([1.0, -1.0])
operators = Array([self.X.data, self.Y.data, self.Z.data])
carrier_freqs = Array([1.0, 2.0, 3.0])
cutoff_freq = 3.0
frame = Frame(frame_op)
cutoff_mat = Array([[[1, 1], [1, 1]], [[1, 0], [1, 1]], [[0, 0],
[1, 0]]])
ops_w_cutoff, ops_w_conj_cutoff = frame.operators_into_frame_basis_with_cutoff(
operators, cutoff_freq=cutoff_freq, carrier_freqs=carrier_freqs)
ops_w_cutoff_expect = cutoff_mat * operators
ops_w_conj_cutoff_expect = cutoff_mat.transpose([0, 2, 1]) * operators
self.assertAllClose(ops_w_cutoff, ops_w_cutoff_expect)
self.assertAllClose(ops_w_conj_cutoff, ops_w_conj_cutoff_expect)
# same test with lower cutoff
cutoff_freq = 2.0
cutoff_mat = Array([[[1, 0], [1, 1]], [[0, 0], [1, 0]], [[0, 0],
[0, 0]]])
ops_w_cutoff, ops_w_conj_cutoff = frame.operators_into_frame_basis_with_cutoff(
operators, cutoff_freq=cutoff_freq, carrier_freqs=carrier_freqs)
ops_w_cutoff_expect = cutoff_mat * operators
ops_w_conj_cutoff_expect = cutoff_mat.transpose([0, 2, 1]) * operators
self.assertAllClose(ops_w_cutoff, ops_w_cutoff_expect)
self.assertAllClose(ops_w_conj_cutoff, ops_w_conj_cutoff_expect)
def _test_state_out_of_frame(self,
t,
frame_op,
y,
y_in_frame_basis=False,
return_in_frame_basis=False):
evals, U = np.linalg.eigh(1j * frame_op)
evals = -1j * Array(evals)
frame = Frame(frame_op)
value = frame.state_out_of_frame(t, y, y_in_frame_basis,
return_in_frame_basis)
expected = y
if not y_in_frame_basis:
expected = U.conj().transpose() @ expected
expected = np.diag(np.exp(t * evals)) @ expected
if not return_in_frame_basis:
expected = U @ expected
self.assertAllClose(value, expected, rtol=1e-10, atol=1e-10)
def test_state_transformations_no_frame(self):
"""Test frame transformations with no frame."""
frame = Frame(Array(np.zeros(2)))
t = 0.123
y = Array([1.0, 1j])
out = frame.state_into_frame(t, y)
self.assertAllClose(out, y)
out = frame.state_out_of_frame(t, y)
self.assertAllClose(out, y)
t = 100.12498
y = Array(np.eye(2))
out = frame.state_into_frame(t, y)
self.assertAllClose(out, y)
out = frame.state_out_of_frame(t, y)
self.assertAllClose(out, y)