def test_state_gradient4(self, method):
"""Test the state gradient 4
Tr(|psi><psi|ZX) = -cos(a)
daTr(|psi><psi|ZX) = sin(a)
"""
ham = X ^ Z
a = Parameter('a')
params = a
q = QuantumRegister(2)
qc = QuantumCircuit(q)
qc.x(q[0])
qc.h(q[1])
qc.crz(a, q[0], q[1])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
state_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{a: np.pi / 4}, {a: 0}, {a: np.pi / 2}]
correct_values = [1 / np.sqrt(2), 0, 1]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(
state_grad.assign_parameters(value_dict).eval(),
correct_values[i],
decimal=1)
def test_grad_combo_fn_chain_rule(self, method):
"""
Test the chain rule for a custom gradient combo function
"""
np.random.seed(2)
def combo_fn(x):
amplitudes = x[0].primitive.data
pdf = np.multiply(amplitudes, np.conj(amplitudes))
return np.sum(np.log(pdf)) / (-len(amplitudes))
def grad_combo_fn(x):
amplitudes = x[0].primitive.data
pdf = np.multiply(amplitudes, np.conj(amplitudes))
grad = []
for prob in pdf:
grad += [-1 / prob]
return grad
qc = RealAmplitudes(2, reps=1)
grad_op = ListOp([StateFn(qc)],
combo_fn=combo_fn,
grad_combo_fn=grad_combo_fn)
grad = Gradient(grad_method=method).convert(grad_op,
qc.ordered_parameters)
value_dict = dict(
zip(qc.ordered_parameters,
np.random.rand(len(qc.ordered_parameters))))
correct_values = [[(-0.16666259133549044 + 0j)],
[(-7.244949702732864 + 0j)],
[(-2.979791752749964 + 0j)],
[(-5.310186078432614 + 0j)]]
np.testing.assert_array_almost_equal(
grad.assign_parameters(value_dict).eval(), correct_values)
def test_state_gradient3(self, method):
"""Test the state gradient 3
Tr(|psi><psi|Z) = sin(a)sin(c(a)) = sin(a)sin(cos(a)+1)
Tr(|psi><psi|X) = cos(a)
d<H>/da = - 0.5 sin(a) - 1 cos(a)sin(cos(a)+1) + 1 sin^2(a)cos(cos(a)+1)
"""
ham = 0.5 * X - 1 * Z
a = Parameter('a')
# b = Parameter('b')
params = a
c = np.cos(a) + 1
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(a, q[0])
qc.rx(c, q[0])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
state_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{a: np.pi / 4}, {a: 0}, {a: np.pi / 2}]
correct_values = [-1.1220, -0.9093, 0.0403]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(
state_grad.assign_parameters(value_dict).eval(),
correct_values[i],
decimal=1)
def test_operator_coefficient_gradient(self, method):
"""Test the operator coefficient gradient
Tr( | psi > < psi | Z) = sin(a)sin(b)
Tr( | psi > < psi | X) = cos(a)
"""
a = Parameter('a')
b = Parameter('b')
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(a, q[0])
qc.rx(b, q[0])
coeff_0 = Parameter('c_0')
coeff_1 = Parameter('c_1')
ham = coeff_0 * X + coeff_1 * Z
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.0)
gradient_coeffs = [coeff_0, coeff_1]
coeff_grad = Gradient(grad_method=method).convert(op, gradient_coeffs)
values_dict = [{coeff_0: 0.5, coeff_1: -1, a: np.pi / 4, b: np.pi},
{coeff_0: 0.5, coeff_1: -1, a: np.pi / 4, b: np.pi / 4}]
correct_values = [[1 / np.sqrt(2), 0], [1 / np.sqrt(2), 1 / 2]]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(coeff_grad.assign_parameters(value_dict).eval(),
correct_values[i],
decimal=1)
def test_prob_grad(self, method):
"""Test the probability gradient
dp0/da = cos(a)sin(b) / 2
dp1/da = - cos(a)sin(b) / 2
dp0/db = sin(a)cos(b) / 2
dp1/db = - sin(a)cos(b) / 2
"""
a = Parameter('a')
b = Parameter('b')
params = [a, b]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(params[0], q[0])
qc.rx(params[1], q[0])
op = CircuitStateFn(primitive=qc, coeff=1.)
prob_grad = Gradient(grad_method=method).convert(operator=op, params=params)
values_dict = [{a: np.pi / 4, b: 0}, {params[0]: np.pi / 4, params[1]: np.pi / 4},
{params[0]: np.pi / 2, params[1]: np.pi}]
correct_values = [[[0, 0], [1 / (2 * np.sqrt(2)), - 1 / (2 * np.sqrt(2))]],
[[1 / 4, - 1 / 4], [1 / 4, - 1 / 4]],
[[0, 0], [- 1 / 2, 1 / 2]]]
for i, value_dict in enumerate(values_dict):
for j, prob_grad_result in enumerate(prob_grad.assign_parameters(value_dict).eval()):
np.testing.assert_array_almost_equal(prob_grad_result,
correct_values[i][j], decimal=1)
def test_state_gradient5(self, method):
"""Test the state gradient
Tr(|psi><psi|Z) = sin(a0)sin(a1)
Tr(|psi><psi|X) = cos(a0)
d<H>/da0 = - 0.5 sin(a0) - 1 cos(a0)sin(a1)
d<H>/da1 = - 1 sin(a0)cos(a1)
"""
ham = 0.5 * X - 1 * Z
a = ParameterVector('a', 2)
params = a
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(params[0], q[0])
qc.rx(params[1], q[0])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
state_grad = Gradient(grad_method=method).convert(operator=op, params=params)
values_dict = [{a: [np.pi / 4, np.pi]}, {a: [np.pi / 4, np.pi / 4]},
{a: [np.pi / 2, np.pi / 4]}]
correct_values = [[-0.5 / np.sqrt(2), 1 / np.sqrt(2)], [-0.5 / np.sqrt(2) - 0.5, -1 / 2.],
[-0.5, -1 / np.sqrt(2)]]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(state_grad.assign_parameters(value_dict).eval(),
correct_values[i], decimal=1)
def test_gradient_p(self, method):
"""Test the state gradient for p
|psi> = 1/sqrt(2)[[1, exp(ia)]]
Tr(|psi><psi|Z) = 0
Tr(|psi><psi|X) = cos(a)
d<H>/da = - 0.5 sin(a)
"""
ham = 0.5 * X - 1 * Z
a = Parameter('a')
params = a
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.p(a, q[0])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
state_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{a: np.pi / 4}, {a: 0}, {a: np.pi / 2}]
correct_values = [-0.5 / np.sqrt(2), 0, -0.5]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(
state_grad.assign_parameters(value_dict).eval(),
correct_values[i],
decimal=1)
def test_circuit_sampler2(self, method):
"""Test the probability gradient with the circuit sampler
dp0/da = cos(a)sin(b) / 2
dp1/da = - cos(a)sin(b) / 2
dp0/db = sin(a)cos(b) / 2
dp1/db = - sin(a)cos(b) / 2
"""
a = Parameter('a')
b = Parameter('b')
params = [a, b]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(params[0], q[0])
qc.rx(params[1], q[0])
op = CircuitStateFn(primitive=qc, coeff=1.)
shots = 8000
if method == 'fin_diff':
np.random.seed(8)
prob_grad = Gradient(grad_method=method,
epsilon=shots**(-1 / 6.)).convert(
operator=op, params=params)
else:
prob_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{
a: [np.pi / 4],
b: [0]
}, {
params[0]: [np.pi / 4],
params[1]: [np.pi / 4]
}, {
params[0]: [np.pi / 2],
params[1]: [np.pi]
}]
correct_values = [[[0, 0],
[1 / (2 * np.sqrt(2)), -1 / (2 * np.sqrt(2))]],
[[1 / 4, -1 / 4], [1 / 4, -1 / 4]],
[[0, 0], [-1 / 2, 1 / 2]]]
backend = BasicAer.get_backend('qasm_simulator')
q_instance = QuantumInstance(backend=backend, shots=shots)
for i, value_dict in enumerate(values_dict):
sampler = CircuitSampler(backend=q_instance).convert(
prob_grad, params=value_dict)
result = sampler.eval()
np.testing.assert_array_almost_equal(result[0],
correct_values[i],
decimal=1)
def test_circuit_sampler(self, method):
"""Test the gradient with circuit sampler
Tr(|psi><psi|Z) = sin(a)sin(b)
Tr(|psi><psi|X) = cos(a)
d<H>/da = - 0.5 sin(a) - 1 cos(a)sin(b)
d<H>/db = - 1 sin(a)cos(b)
"""
ham = 0.5 * X - 1 * Z
a = Parameter('a')
b = Parameter('b')
params = [a, b]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(params[0], q[0])
qc.rx(params[1], q[0])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
shots = 8000
if method == 'fin_diff':
np.random.seed(8)
state_grad = Gradient(grad_method=method,
epsilon=shots**(-1 / 6.)).convert(
operator=op, params=params)
else:
state_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{
a: np.pi / 4,
b: np.pi
}, {
params[0]: np.pi / 4,
params[1]: np.pi / 4
}, {
params[0]: np.pi / 2,
params[1]: np.pi / 4
}]
correct_values = [[-0.5 / np.sqrt(2), 1 / np.sqrt(2)],
[-0.5 / np.sqrt(2) - 0.5, -1 / 2.],
[-0.5, -1 / np.sqrt(2)]]
backend = BasicAer.get_backend('qasm_simulator')
q_instance = QuantumInstance(backend=backend, shots=shots)
for i, value_dict in enumerate(values_dict):
sampler = CircuitSampler(backend=q_instance).convert(
state_grad, params={k: [v]
for k, v in value_dict.items()})
np.testing.assert_array_almost_equal(sampler.eval()[0],
correct_values[i],
decimal=1)
def test_jax_chain_rule(self, method: str, autograd: bool):
"""Test the chain rule functionality using Jax
d<H>/d<X> = 2<X>
d<H>/d<Z> = - sin(<Z>)
<Z> = Tr(|psi><psi|Z) = sin(a)sin(b)
<X> = Tr(|psi><psi|X) = cos(a)
d<H>/da = d<H>/d<X> d<X>/da + d<H>/d<Z> d<Z>/da = - 2 cos(a)sin(a)
- sin(sin(a)sin(b)) * cos(a)sin(b)
d<H>/db = d<H>/d<X> d<X>/db + d<H>/d<Z> d<Z>/db = - sin(sin(a)sin(b)) * sin(a)cos(b)
"""
a = Parameter('a')
b = Parameter('b')
params = [a, b]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(params[0], q[0])
qc.rx(params[1], q[0])
def combo_fn(x):
return jnp.power(x[0], 2) + jnp.cos(x[1])
def grad_combo_fn(x):
return np.array([2 * x[0], -np.sin(x[1])])
op = ListOp([
~StateFn(X) @ CircuitStateFn(primitive=qc, coeff=1.),
~StateFn(Z) @ CircuitStateFn(primitive=qc, coeff=1.)
],
combo_fn=combo_fn,
grad_combo_fn=None if autograd else grad_combo_fn)
state_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{
a: np.pi / 4,
b: np.pi
}, {
params[0]: np.pi / 4,
params[1]: np.pi / 4
}, {
params[0]: np.pi / 2,
params[1]: np.pi / 4
}]
correct_values = [[-1., 0.], [-1.2397, -0.2397], [0, -0.45936]]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(
state_grad.assign_parameters(value_dict).eval(),
correct_values[i],
decimal=1)
def test_vqe(self):
"""Test VQE with gradients"""
method = 'lin_comb'
backend = 'qasm_simulator'
q_instance = QuantumInstance(BasicAer.get_backend(backend), seed_simulator=79,
seed_transpiler=2)
# Define the Hamiltonian
h2_hamiltonian = -1.05 * (I ^ I) + 0.39 * (I ^ Z) - 0.39 * (Z ^ I) \
- 0.01 * (Z ^ Z) + 0.18 * (X ^ X)
h2_energy = -1.85727503
# Define the Ansatz
wavefunction = QuantumCircuit(2)
params = ParameterVector('theta', length=8)
itr = iter(params)
wavefunction.ry(next(itr), 0)
wavefunction.ry(next(itr), 1)
wavefunction.rz(next(itr), 0)
wavefunction.rz(next(itr), 1)
wavefunction.cx(0, 1)
wavefunction.ry(next(itr), 0)
wavefunction.ry(next(itr), 1)
wavefunction.rz(next(itr), 0)
wavefunction.rz(next(itr), 1)
# Conjugate Gradient algorithm
optimizer = CG(maxiter=10)
grad = Gradient(grad_method=method)
# Gradient callable
vqe = VQE(h2_hamiltonian, wavefunction, optimizer=optimizer, gradient=grad)
result = vqe.run(q_instance)
np.testing.assert_almost_equal(result['optimal_value'], h2_energy, decimal=0)
def test_gradient_ryy(self, method):
# pylint: disable=wrong-spelling-in-comment
"""Test the state gradient for YY rotation
"""
ham = Y ^ Y
a = Parameter('a')
q = QuantumRegister(2)
qc = QuantumCircuit(q)
qc.ryy(a, q[0], q[1])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
state_grad = Gradient(grad_method=method).convert(operator=op, params=a)
values_dict = [{a: np.pi / 8}, {a: np.pi}]
correct_values = [[0], [0]]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(state_grad.assign_parameters(value_dict).eval(),
correct_values[i], decimal=1)
def test_qgan_training_analytic_gradients(self):
"""Test QGAN training with analytic gradients"""
self.qgan.set_generator(self.generator_circuit)
numeric_results = self.qgan.run(self.qi_qasm)
self.qgan.set_generator(self.generator_circuit,
generator_gradient=Gradient('param_shift'))
analytic_results = self.qgan.run(self.qi_qasm)
self.assertAlmostEqual(numeric_results['rel_entr'],
analytic_results['rel_entr'], delta=0.1)
def test_gradient_rzx(self, method):
"""Test the state gradient for ZX rotation
"""
ham = Z ^ Z
a = Parameter('a')
q = QuantumRegister(2)
qc = QuantumCircuit(q)
qc.h(q)
qc.rzx(a, q[0], q[1])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
params = [a]
state_grad = Gradient(grad_method=method).convert(operator=op, params=params)
values_dict = [{a: np.pi / 8}, {a: np.pi / 2}]
correct_values = [[0.], [0.]]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(state_grad.assign_parameters(value_dict).eval(),
correct_values[i], decimal=1)
def test_gradient_wrapper(self, backend):
"""Test the gradient wrapper for probability gradients
dp0/da = cos(a)sin(b) / 2
dp1/da = - cos(a)sin(b) / 2
dp0/db = sin(a)cos(b) / 2
dp1/db = - sin(a)cos(b) / 2
"""
method = 'param_shift'
a = Parameter('a')
b = Parameter('b')
params = [a, b]
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.rz(params[0], q[0])
qc.rx(params[1], q[0])
op = CircuitStateFn(primitive=qc, coeff=1.)
shots = 8000
backend = BasicAer.get_backend(backend)
q_instance = QuantumInstance(backend=backend, shots=shots)
if method == 'fin_diff':
np.random.seed(8)
prob_grad = Gradient(grad_method=method,
epsilon=shots**(-1 / 6.)).gradient_wrapper(
operator=op,
bind_params=params,
backend=q_instance)
else:
prob_grad = Gradient(grad_method=method).gradient_wrapper(
operator=op, bind_params=params, backend=q_instance)
values = [[np.pi / 4, 0], [np.pi / 4, np.pi / 4], [np.pi / 2, np.pi]]
correct_values = [[[0, 0],
[1 / (2 * np.sqrt(2)), -1 / (2 * np.sqrt(2))]],
[[1 / 4, -1 / 4], [1 / 4, -1 / 4]],
[[0, 0], [-1 / 2, 1 / 2]]]
for i, value in enumerate(values):
result = prob_grad(value)
np.testing.assert_array_almost_equal(result,
correct_values[i],
decimal=1)
def test_grad(self):
"""Test taking the gradient of parameter expressions."""
x, y = Parameter('x'), Parameter('y')
with self.subTest('linear'):
expr = 2 * x + y
grad = Gradient.parameter_expression_grad(expr, x)
self.assertEqual(grad, 2)
grad = Gradient.parameter_expression_grad(expr, y)
self.assertEqual(grad, 1)
with self.subTest('polynomial'):
expr = x * x * x - x * y + y * y
grad = Gradient.parameter_expression_grad(expr, x)
self.assertEqual(grad, 3 * x * x - y)
grad = Gradient.parameter_expression_grad(expr, y)
self.assertEqual(grad, -1 * x + 2 * y)
def test_gradient_u(self, method):
"""Test the state gradient for U
Tr(|psi><psi|Z) = - 0.5 sin(a)cos(c)
Tr(|psi><psi|X) = cos^2(a/2) cos(b+c) - sin^2(a/2) cos(b-c)
"""
ham = 0.5 * X - 1 * Z
a = Parameter('a')
b = Parameter('b')
c = Parameter('c')
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.u(a, b, c, q[0])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
params = [a, b, c]
state_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{
a: np.pi / 4,
b: 0,
c: 0
}, {
a: np.pi / 4,
b: np.pi / 4,
c: np.pi / 4
}]
correct_values = [[0.3536, 0, 0], [0.3232, -0.42678, -0.92678]]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(
state_grad.assign_parameters(value_dict).eval(),
correct_values[i],
decimal=1)
# Tr(|psi><psi|Z) = - 0.5 sin(a)cos(c)
# Tr(|psi><psi|X) = cos^2(a/2) cos(b+c) - sin^2(a/2) cos(b-c)
# dTr(|psi><psi|H)/da = 0.5(cos(2a)) + 0.5()
q = QuantumRegister(1)
qc = QuantumCircuit(q)
qc.h(q)
qc.u(a, a, a, q[0])
op = ~StateFn(ham) @ CircuitStateFn(primitive=qc, coeff=1.)
params = [a]
state_grad = Gradient(grad_method=method).convert(operator=op,
params=params)
values_dict = [{a: np.pi / 4}, {a: np.pi / 2}]
correct_values = [[-1.03033], [-1]]
for i, value_dict in enumerate(values_dict):
np.testing.assert_array_almost_equal(
state_grad.assign_parameters(value_dict).eval(),
correct_values[i],
decimal=1)
def test_converted_to_float_if_bound(self):
"""Test the gradient is a float when no free symbols are left."""
x = Parameter('x')
expr = 2 * x + 1
grad = Gradient.parameter_expression_grad(expr, x)
self.assertIsInstance(grad, float)
