def test_good_state(self, backend_str, expect):
"""Test with a good state function."""
def is_good_state(bitstr):
return bitstr[1] == "1"
# construct the estimation problem where the second qubit is ignored
a_op = QuantumCircuit(2)
a_op.ry(2 * np.arcsin(np.sqrt(0.2)), 0)
# oracle only affects first qubit
oracle = QuantumCircuit(2)
oracle.z(0)
# reflect only on first qubit
q_op = GroverOperator(oracle, a_op, reflection_qubits=[0])
# but we measure both qubits (hence both are objective qubits)
problem = EstimationProblem(
a_op, objective_qubits=[0, 1], grover_operator=q_op, is_good_state=is_good_state
)
# construct algo
backend = QuantumInstance(
BasicAer.get_backend(backend_str), seed_simulator=2, seed_transpiler=2
)
# cannot use rescaling with a custom grover operator
fae = FasterAmplitudeEstimation(0.01, 5, rescale=False, quantum_instance=backend)
# run the algo
result = fae.estimate(problem)
# assert the result is correct
self.assertAlmostEqual(result.estimation, expect, places=5)
def test_run_without_rescaling(self):
"""Run Faster AE without rescaling if the amplitude is in [0, 1/4]."""
# construct estimation problem
prob = 0.11
a_op = QuantumCircuit(1)
a_op.ry(2 * np.arcsin(np.sqrt(prob)), 0)
problem = EstimationProblem(a_op, objective_qubits=[0])
# construct algo without rescaling
backend = BasicAer.get_backend('statevector_simulator')
fae = FasterAmplitudeEstimation(0.1,
1,
rescale=False,
quantum_instance=backend)
# run the algo
result = fae.estimate(problem)
# assert the result is correct
self.assertAlmostEqual(result.estimation, prob)
# assert no rescaling was used
theta = np.mean(result.theta_intervals[-1])
value_without_scaling = np.sin(theta)**2
self.assertAlmostEqual(result.estimation, value_without_scaling)
def test_rescaling_with_custom_grover_raises(self):
"""Test that the rescaling option fails if a custom Grover operator is used."""
prob = 0.8
a_op = BernoulliStateIn(prob)
q_op = BernoulliGrover(prob)
problem = EstimationProblem(a_op, objective_qubits=[0], grover_operator=q_op)
# construct algo without rescaling
backend = BasicAer.get_backend("statevector_simulator")
fae = FasterAmplitudeEstimation(0.1, 1, quantum_instance=backend)
# run the algo
with self.assertWarns(Warning):
_ = fae.estimate(problem)
class TestBernoulli(QiskitAlgorithmsTestCase):
"""Tests based on the Bernoulli A operator.
This class tests
* the estimation result
* the constructed circuits
"""
def setUp(self):
super().setUp()
self._statevector = QuantumInstance(
backend=BasicAer.get_backend("statevector_simulator"),
seed_simulator=2,
seed_transpiler=2,
)
self._unitary = QuantumInstance(
backend=BasicAer.get_backend("unitary_simulator"),
shots=1,
seed_simulator=42,
seed_transpiler=91,
)
def qasm(shots=100):
return QuantumInstance(
backend=BasicAer.get_backend("qasm_simulator"),
shots=shots,
seed_simulator=2,
seed_transpiler=2,
)
self._qasm = qasm
@idata(
[
[0.2, AmplitudeEstimation(2), {"estimation": 0.5, "mle": 0.2}],
[0.49, AmplitudeEstimation(3), {"estimation": 0.5, "mle": 0.49}],
[0.2, MaximumLikelihoodAmplitudeEstimation([0, 1, 2]), {"estimation": 0.2}],
[0.49, MaximumLikelihoodAmplitudeEstimation(3), {"estimation": 0.49}],
[0.2, IterativeAmplitudeEstimation(0.1, 0.1), {"estimation": 0.2}],
[0.49, IterativeAmplitudeEstimation(0.001, 0.01), {"estimation": 0.49}],
[0.2, FasterAmplitudeEstimation(0.1, 3, rescale=False), {"estimation": 0.2}],
[0.12, FasterAmplitudeEstimation(0.1, 2, rescale=False), {"estimation": 0.12}],
]
)
@unpack
def test_statevector(self, prob, qae, expect):
"""statevector test"""
qae.quantum_instance = self._statevector
problem = EstimationProblem(BernoulliStateIn(prob), 0, BernoulliGrover(prob))
result = qae.estimate(problem)
self.assertGreaterEqual(self._statevector.time_taken, 0.0)
self._statevector.reset_execution_results()
for key, value in expect.items():
self.assertAlmostEqual(
value, getattr(result, key), places=3, msg=f"estimate `{key}` failed"
)
@idata(
[
[0.2, 100, AmplitudeEstimation(4), {"estimation": 0.14644, "mle": 0.193888}],
[0.0, 1000, AmplitudeEstimation(2), {"estimation": 0.0, "mle": 0.0}],
[
0.2,
100,
MaximumLikelihoodAmplitudeEstimation([0, 1, 2, 4, 8]),
{"estimation": 0.199606},
],
[0.8, 10, IterativeAmplitudeEstimation(0.1, 0.05), {"estimation": 0.811711}],
[0.2, 1000, FasterAmplitudeEstimation(0.1, 3, rescale=False), {"estimation": 0.198640}],
[
0.12,
100,
FasterAmplitudeEstimation(0.01, 3, rescale=False),
{"estimation": 0.119037},
],
]
)
@unpack
def test_qasm(self, prob, shots, qae, expect):
"""qasm test"""
qae.quantum_instance = self._qasm(shots)
problem = EstimationProblem(BernoulliStateIn(prob), [0], BernoulliGrover(prob))
result = qae.estimate(problem)
for key, value in expect.items():
self.assertAlmostEqual(
value, getattr(result, key), places=3, msg=f"estimate `{key}` failed"
)
@data(True, False)
def test_qae_circuit(self, efficient_circuit):
"""Test circuits resulting from canonical amplitude estimation.
Build the circuit manually and from the algorithm and compare the resulting unitaries.
"""
prob = 0.5
problem = EstimationProblem(BernoulliStateIn(prob), objective_qubits=[0])
for m in [2, 5]:
qae = AmplitudeEstimation(m)
angle = 2 * np.arcsin(np.sqrt(prob))
# manually set up the inefficient AE circuit
qr_eval = QuantumRegister(m, "a")
qr_objective = QuantumRegister(1, "q")
circuit = QuantumCircuit(qr_eval, qr_objective)
# initial Hadamard gates
for i in range(m):
circuit.h(qr_eval[i])
# A operator
circuit.ry(angle, qr_objective)
if efficient_circuit:
qae.grover_operator = BernoulliGrover(prob)
for power in range(m):
circuit.cry(2 * 2 ** power * angle, qr_eval[power], qr_objective[0])
else:
oracle = QuantumCircuit(1)
oracle.z(0)
state_preparation = QuantumCircuit(1)
state_preparation.ry(angle, 0)
grover_op = GroverOperator(oracle, state_preparation)
grover_op.global_phase = np.pi
for power in range(m):
circuit.compose(
grover_op.power(2 ** power).control(),
qubits=[qr_eval[power], qr_objective[0]],
inplace=True,
)
# fourier transform
iqft = QFT(m, do_swaps=False).inverse().reverse_bits()
circuit.append(iqft.to_instruction(), qr_eval)
actual_circuit = qae.construct_circuit(problem, measurement=False)
self.assertEqual(Operator(circuit), Operator(actual_circuit))
@data(True, False)
def test_iqae_circuits(self, efficient_circuit):
"""Test circuits resulting from iterative amplitude estimation.
Build the circuit manually and from the algorithm and compare the resulting unitaries.
"""
prob = 0.5
problem = EstimationProblem(BernoulliStateIn(prob), objective_qubits=[0])
for k in [2, 5]:
qae = IterativeAmplitudeEstimation(0.01, 0.05)
angle = 2 * np.arcsin(np.sqrt(prob))
# manually set up the inefficient AE circuit
q_objective = QuantumRegister(1, "q")
circuit = QuantumCircuit(q_objective)
# A operator
circuit.ry(angle, q_objective)
if efficient_circuit:
qae.grover_operator = BernoulliGrover(prob)
circuit.ry(2 * k * angle, q_objective[0])
else:
oracle = QuantumCircuit(1)
oracle.z(0)
state_preparation = QuantumCircuit(1)
state_preparation.ry(angle, 0)
grover_op = GroverOperator(oracle, state_preparation)
grover_op.global_phase = np.pi
for _ in range(k):
circuit.compose(grover_op, inplace=True)
actual_circuit = qae.construct_circuit(problem, k, measurement=False)
self.assertEqual(Operator(circuit), Operator(actual_circuit))
@data(True, False)
def test_mlae_circuits(self, efficient_circuit):
"""Test the circuits constructed for MLAE"""
prob = 0.5
problem = EstimationProblem(BernoulliStateIn(prob), objective_qubits=[0])
for k in [2, 5]:
qae = MaximumLikelihoodAmplitudeEstimation(k)
angle = 2 * np.arcsin(np.sqrt(prob))
# compute all the circuits used for MLAE
circuits = []
# 0th power
q_objective = QuantumRegister(1, "q")
circuit = QuantumCircuit(q_objective)
circuit.ry(angle, q_objective)
circuits += [circuit]
# powers of 2
for power in range(k):
q_objective = QuantumRegister(1, "q")
circuit = QuantumCircuit(q_objective)
# A operator
circuit.ry(angle, q_objective)
# Q^(2^j) operator
if efficient_circuit:
qae.grover_operator = BernoulliGrover(prob)
circuit.ry(2 * 2 ** power * angle, q_objective[0])
else:
oracle = QuantumCircuit(1)
oracle.z(0)
state_preparation = QuantumCircuit(1)
state_preparation.ry(angle, 0)
grover_op = GroverOperator(oracle, state_preparation)
grover_op.global_phase = np.pi
for _ in range(2 ** power):
circuit.compose(grover_op, inplace=True)
circuits += [circuit]
actual_circuits = qae.construct_circuits(problem, measurement=False)
for actual, expected in zip(actual_circuits, circuits):
self.assertEqual(Operator(actual), Operator(expected))
class TestSineIntegral(QiskitAlgorithmsTestCase):
"""Tests based on the A operator to integrate sin^2(x).
This class tests
* the estimation result
* the confidence intervals
"""
def setUp(self):
super().setUp()
self._statevector = QuantumInstance(
backend=BasicAer.get_backend("statevector_simulator"),
seed_simulator=123,
seed_transpiler=41,
)
def qasm(shots=100):
return QuantumInstance(
backend=BasicAer.get_backend("qasm_simulator"),
shots=shots,
seed_simulator=7192,
seed_transpiler=90000,
)
self._qasm = qasm
@idata(
[
[2, AmplitudeEstimation(2), {"estimation": 0.5, "mle": 0.270290}],
[4, MaximumLikelihoodAmplitudeEstimation(4), {"estimation": 0.272675}],
[3, IterativeAmplitudeEstimation(0.1, 0.1), {"estimation": 0.272082}],
[3, FasterAmplitudeEstimation(0.01, 1), {"estimation": 0.272082}],
]
)
@unpack
def test_statevector(self, n, qae, expect):
"""Statevector end-to-end test"""
# construct factories for A and Q
# qae.state_preparation = SineIntegral(n)
qae.quantum_instance = self._statevector
estimation_problem = EstimationProblem(SineIntegral(n), objective_qubits=[n])
# result = qae.run(self._statevector)
result = qae.estimate(estimation_problem)
self.assertGreaterEqual(self._statevector.time_taken, 0.0)
self._statevector.reset_execution_results()
for key, value in expect.items():
self.assertAlmostEqual(
value, getattr(result, key), places=3, msg=f"estimate `{key}` failed"
)
@idata(
[
[4, 10, AmplitudeEstimation(2), {"estimation": 0.5, "mle": 0.333333}],
[3, 10, MaximumLikelihoodAmplitudeEstimation(2), {"estimation": 0.256878}],
[3, 1000, IterativeAmplitudeEstimation(0.01, 0.01), {"estimation": 0.271790}],
[3, 1000, FasterAmplitudeEstimation(0.1, 4), {"estimation": 0.274168}],
]
)
@unpack
def test_qasm(self, n, shots, qae, expect):
"""QASM simulator end-to-end test."""
# construct factories for A and Q
qae.quantum_instance = self._qasm(shots)
estimation_problem = EstimationProblem(SineIntegral(n), objective_qubits=[n])
result = qae.estimate(estimation_problem)
for key, value in expect.items():
self.assertAlmostEqual(
value, getattr(result, key), places=3, msg=f"estimate `{key}` failed"
)
@idata(
[
[
AmplitudeEstimation(3),
"mle",
{
"likelihood_ratio": (0.2494734, 0.3003771),
"fisher": (0.2486176, 0.2999286),
"observed_fisher": (0.2484562, 0.3000900),
},
],
[
MaximumLikelihoodAmplitudeEstimation(3),
"estimation",
{
"likelihood_ratio": (0.2598794, 0.2798536),
"fisher": (0.2584889, 0.2797018),
"observed_fisher": (0.2659279, 0.2722627),
},
],
]
)
@unpack
def test_confidence_intervals(self, qae, key, expect):
"""End-to-end test for all confidence intervals."""
n = 3
qae.quantum_instance = self._statevector
estimation_problem = EstimationProblem(SineIntegral(n), objective_qubits=[n])
# statevector simulator
result = qae.estimate(estimation_problem)
self.assertGreater(self._statevector.time_taken, 0.0)
self._statevector.reset_execution_results()
methods = ["lr", "fi", "oi"] # short for likelihood_ratio, fisher, observed_fisher
alphas = [0.1, 0.00001, 0.9] # alpha shouldn't matter in statevector
for alpha, method in zip(alphas, methods):
confint = qae.compute_confidence_interval(result, alpha, method)
# confidence interval based on statevector should be empty, as we are sure of the result
self.assertAlmostEqual(confint[1] - confint[0], 0.0)
self.assertAlmostEqual(confint[0], getattr(result, key))
# qasm simulator
shots = 100
alpha = 0.01
qae.quantum_instance = self._qasm(shots)
result = qae.estimate(estimation_problem)
for method, expected_confint in expect.items():
confint = qae.compute_confidence_interval(result, alpha, method)
np.testing.assert_array_almost_equal(confint, expected_confint)
self.assertTrue(confint[0] <= getattr(result, key) <= confint[1])
def test_iqae_confidence_intervals(self):
"""End-to-end test for the IQAE confidence interval."""
n = 3
qae = IterativeAmplitudeEstimation(0.1, 0.01, quantum_instance=self._statevector)
expected_confint = (0.1984050, 0.3511015)
estimation_problem = EstimationProblem(SineIntegral(n), objective_qubits=[n])
# statevector simulator
result = qae.estimate(estimation_problem)
self.assertGreaterEqual(self._statevector.time_taken, 0.0)
self._statevector.reset_execution_results()
confint = result.confidence_interval
# confidence interval based on statevector should be empty, as we are sure of the result
self.assertAlmostEqual(confint[1] - confint[0], 0.0)
self.assertAlmostEqual(confint[0], result.estimation)
# qasm simulator
shots = 100
qae.quantum_instance = self._qasm(shots)
result = qae.estimate(estimation_problem)
confint = result.confidence_interval
np.testing.assert_array_almost_equal(confint, expected_confint)
self.assertTrue(confint[0] <= result.estimation <= confint[1])
