def test_signal(self):
"""Test Signal."""
# Signal with constant amplitude
signal = Signal(0.25, carrier_freq=0.3)
self.assertEqual(signal.envelope_value(), 0.25)
self.assertEqual(signal.envelope_value(1.23), 0.25)
self.assertEqual(signal.value(), 0.25)
self.assertEqual(signal.value(1.0), 0.25 * np.exp(0.3 * 2.0j * np.pi))
signal = Signal(0.25, carrier_freq=0.3, phase=0.5)
self.assertEqual(signal.value(1.0),
0.25 * np.exp(0.3 * 2.0j * np.pi + 0.5j))
# Signal with parabolic amplitude
signal = Signal(lambda t: 2.0 * t**2, carrier_freq=0.1)
self.assertEqual(signal.envelope_value(), 0.0)
self.assertEqual(signal.envelope_value(3.0), 18.0)
self.assertEqual(signal.value(), 0.0)
self.assertEqual(signal.value(2.0),
8.0 * np.exp(0.1 * 2.0j * np.pi * 2.0))
signal = Signal(lambda t: 2.0 * t**2, carrier_freq=0.1, phase=-0.1)
self.assertEqual(signal.value(2.0),
8.0 * np.exp(0.1 * 2.0j * np.pi * 2.0 - 0.1j))
def test_addition(self):
"""Tests the multiplication of signals."""
# Test Constant
const1 = Constant(0.3)
const2 = Constant(0.5)
self.assertTrue(isinstance(const1 + const2, Signal))
self.assertEqual((const1 + const2).value(), 0.8)
# Test Signal
signal1 = Signal(3.0, carrier_freq=0.1)
signal2 = Signal(lambda t: 2.0 * t ** 2, carrier_freq=0.1)
self.assertTrue(isinstance(const1 + signal1, Signal))
self.assertTrue(isinstance(signal1 + const1, Signal))
self.assertTrue(isinstance(signal1 + signal2, Signal))
self.assertEqual((signal1 + signal2).carrier_freq, 0.0)
self.assertEqual((signal1 + const1).carrier_freq, 0.0)
self.assertEqual((signal1 + signal2).envelope_value(), 3.0)
expected = 21.0 * np.cos(0.1 * 2.0 * np.pi * 3.0)
self.assertAlmostEqual((signal1 + signal2).envelope_value(3.0), expected, places=8)
self.assertEqual((signal1 + signal2).value(), 3.0)
self.assertEqual((signal1 + signal2).value(2.0), 11.0 * np.cos(0.1 * 2.0 * np.pi * 2.0))
# Test piecewise constant
dt = 1.0
samples = Array([0.0, 0.0, 1.0, 2.0, 1.0, 0.0, 0.0])
carrier_freq = 0.5
pwc1 = PiecewiseConstant(dt=dt, samples=samples, carrier_freq=carrier_freq)
dt = 1.0
samples = Array([0.0, 0.0, 1.0, 2.0, 1.0, 0.0, 0.0])
carrier_freq = 0.1
pwc2 = PiecewiseConstant(dt=dt, samples=samples, carrier_freq=carrier_freq)
# Test types
self.assertTrue(isinstance(const1 + pwc1, Signal))
self.assertTrue(isinstance(signal1 + pwc1, Signal))
self.assertTrue(isinstance(pwc1 + pwc2, Signal))
self.assertTrue(isinstance(pwc1 + const1, Signal))
self.assertTrue(isinstance(pwc1 + signal1, Signal))
# Test values
self.assertEqual((pwc1 + pwc2).carrier_freq, 0.0)
self.assertEqual((pwc1 + pwc2).envelope_value(), 0.0)
expected = 1.0 * np.cos(0.5 * 2.0 * np.pi * 4.0) + 1.0 * np.cos(0.1 * 2.0 * np.pi * 4.0)
self.assertAlmostEqual((pwc1 + pwc2).envelope_value(4.0), expected, places=8)
self.assertEqual((pwc1 + pwc2).value(), 0.0)
expected = 1.0 * np.cos(0.5 * 2.0 * np.pi * 4.0) + 1.0 * np.cos(0.1 * 2.0 * np.pi * 4.0)
self.assertAlmostEqual((pwc1 + pwc2).value(4.0), expected, places=8)
# Test phase
pwc2 = PiecewiseConstant(dt=dt, samples=samples, carrier_freq=carrier_freq, phase=0.5)
expected = 1.0 * np.cos(0.5 * 2.0 * np.pi * 4.0) + 1.0 * np.cos(
0.1 * 2.0 * np.pi * 4.0 + 0.5
)
self.assertAlmostEqual((pwc1 + pwc2).envelope_value(4.0), expected, places=8)
def test_multiplication(self):
"""Tests the multiplication of signals."""
# Test Constant
const1 = Constant(0.3)
const2 = Constant(0.5)
self.assertTrue(isinstance(const1 * const2, Signal))
self.assertEqual((const1 * const2).value(), 0.15)
self.assertEqual((const1 * const2).value(10.0), 0.15)
# Test Signal
signal1 = Signal(3.0, carrier_freq=0.1)
signal2 = Signal(lambda t: 2.0 * t ** 2, carrier_freq=0.1)
self.assertTrue(isinstance(const1 * signal1, Signal))
self.assertTrue(isinstance(signal1 * const1, Signal))
self.assertTrue(isinstance(signal1 * signal2, Signal))
self.assertEqual((signal1 * signal2).carrier_freq, 0.2)
self.assertEqual((signal1 * const1).carrier_freq, 0.1)
self.assertEqual((signal1 * signal2).envelope_value(), 0.0)
self.assertEqual((signal1 * signal2).envelope_value(3.0), 3.0 * 18.0)
self.assertEqual((signal1 * signal2).value(), 0.0)
self.assertEqual((signal1 * signal2).value(2.0), 24.0 * np.cos(0.2 * 2.0 * np.pi * 2.0))
# Test piecewise constant
dt = 1.0
samples = Array([0.0, 0.0, 1.0, 2.0, 1.0, 0.0, 0.0])
carrier_freq = 0.5
pwc1 = PiecewiseConstant(dt=dt, samples=samples, carrier_freq=carrier_freq)
dt = 2.0
samples = Array([0.0, 0.0, 1.0, 2.0, 1.0, 0.0, 0.0])
carrier_freq = 0.1
pwc2 = PiecewiseConstant(dt=dt, samples=samples, carrier_freq=carrier_freq)
# Test types
self.assertTrue(isinstance(const1 * pwc1, Signal))
self.assertTrue(isinstance(signal1 * pwc1, Signal))
self.assertTrue(isinstance(pwc1 * pwc2, Signal))
self.assertTrue(isinstance(pwc1 * const1, Signal))
self.assertTrue(isinstance(pwc1 * signal1, Signal))
# Test values
self.assertEqual((pwc1 * pwc2).carrier_freq, 0.6)
self.assertEqual((pwc1 * pwc2).envelope_value(), 0.0)
self.assertEqual((pwc1 * pwc2).envelope_value(4.0), 1.0)
self.assertEqual((pwc1 * pwc2).value(), 0.0)
self.assertEqual((pwc1 * pwc2).value(4.0), 1.0 * np.cos(0.6 * 2.0 * np.pi * 4.0))
# Test phase
pwc2 = PiecewiseConstant(dt=dt, samples=samples, carrier_freq=carrier_freq, phase=0.5)
self.assertEqual((pwc1 * pwc2).value(4.0), 1.0 * np.cos(0.6 * 2.0 * np.pi * 4.0 + 0.5))
def test_cutoff_freq(self):
"""Test evaluation with a cutoff frequency."""
# enter frame of drift
self.basic_hamiltonian.frame = self.basic_hamiltonian.drift
# set cutoff freq to 2 * drive freq (standard RWA)
self.basic_hamiltonian.cutoff_freq = 2 * self.w
# result should just be the X term halved
eval_rwa = self.basic_hamiltonian.evaluate(2.0)
expected = 2 * np.pi * (self.r / 2) * self.X.data / 2
self.assertAllClose(eval_rwa, expected)
def drive_func(t):
return t ** 2 + t ** 3 * 1j
self.basic_hamiltonian.signals = [Constant(self.w), Signal(drive_func, self.w)]
# result should now contain both X and Y terms halved
t = 2.1231 * np.pi
dRe = np.real(drive_func(t))
dIm = np.imag(drive_func(t))
eval_rwa = self.basic_hamiltonian.evaluate(t)
expected = (
2 * np.pi * (self.r / 2) * dRe * self.X.data / 2
+ 2 * np.pi * (self.r / 2) * dIm * self.Y.data / 2
)
self.assertAllClose(eval_rwa, expected)
def setUp(self):
self.t_span = [0.0, 1.0]
self.y0 = Array(np.eye(2, dtype=complex))
self.X = Array([[0.0, 1.0], [1.0, 0.0]], dtype=complex)
self.Y = Array([[0.0, -1j], [1j, 0.0]], dtype=complex)
self.Z = Array([[1.0, 0.0], [0.0, -1.0]], dtype=complex)
# simple generator and rhs
# pylint: disable=unused-argument
def generator(t):
return -1j * 2 * np.pi * self.X / 2
def rhs(t, y):
return generator(t) @ y
self.basic_generator = generator
self.basic_rhs = rhs
# define simple model
self.w = 2.0
self.r = 0.1
signals = [Constant(self.w), Signal(lambda t: 1.0, self.w)]
operators = [
-1j * 2 * np.pi * self.Z / 2, -1j * 2 * np.pi * self.r * self.X / 2
]
self.basic_model = GeneratorModel(operators=operators, signals=signals)
def setUp(self):
self.X = Array(Operator.from_label("X").data)
self.Y = Array(Operator.from_label("Y").data)
self.Z = Array(Operator.from_label("Z").data)
# define a basic hamiltonian
w = 2.0
r = 0.5
operators = [2 * np.pi * self.Z / 2, 2 * np.pi * r * self.X / 2]
signals = [Constant(w), Signal(1.0, w)]
self.w = w
self.r = r
self.basic_hamiltonian = HamiltonianModel(operators=operators, signals=signals)
def setUp(self):
self.X = Array(Operator.from_label("X").data)
self.Y = Array(Operator.from_label("Y").data)
self.Z = Array(Operator.from_label("Z").data)
# define a basic model
w = 2.0
r = 0.5
operators = [
-1j * 2 * np.pi * self.Z / 2, -1j * 2 * np.pi * r * self.X / 2
]
signals = [Constant(w), Signal(1.0, w)]
self.w = 2
self.r = r
self.basic_model = GeneratorModel(operators=operators, signals=signals)
def setUp(self):
self.X = Array([[0.0, 1.0], [1.0, 0.0]], dtype=complex)
self.Y = Array([[0.0, -1j], [1j, 0.0]], dtype=complex)
self.Z = Array([[1.0, 0.0], [0.0, -1.0]], dtype=complex)
# define a basic model
w = 2.0
r = 0.5
operators = [-1j * 2 * np.pi * self.Z / 2, -1j * 2 * np.pi * r * self.X / 2]
signals = [Constant(w), Signal(1.0, w)]
self.w = 2
self.r = r
self.basic_model = GeneratorModel(operators=operators, signals=signals)
self.y0 = Array([1.0, 0.0], dtype=complex)
def param_sim(amp, drive_freq):
signals = [
Constant(1.0),
Signal(lambda t: amp, carrier_freq=drive_freq)
]
ham_copy = ham.copy()
ham_copy.signals = signals
results = solve_lmde(
ham_copy,
t_span=[0.0, 1 / self.r],
y0=Array([0.0, 1.0], dtype=complex),
method="jax_odeint",
atol=1e-10,
rtol=1e-10,
)
return results.y[-1]
def setUp(self):
self.X = Array(Operator.from_label("X").data)
self.Y = Array(Operator.from_label("Y").data)
self.Z = Array(Operator.from_label("Z").data)
# define a basic hamiltonian
w = 2.0
r = 0.5
ham_operators = [2 * np.pi * self.Z / 2, 2 * np.pi * r * self.X / 2]
ham_signals = [Constant(w), Signal(1.0, w)]
self.w = w
self.r = r
noise_operators = Array([[[0.0, 0.0], [1.0, 0.0]]])
self.basic_lindblad = LindbladModel(
hamiltonian_operators=ham_operators,
hamiltonian_signals=ham_signals,
noise_operators=noise_operators,
)