def main():
#matrix = [[1, -1/3], [-1/3, 1]]
matrix = [[15, 9, 5, -3],
[9, 15, 3, -5],
[5, 3, 15, -9],
[-3, -5, -9, 15]]
#vector = [1, 0]
vector = [1/2,1/2,1/2,1/2]
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(matrix, vector)
# Initialize eigenvalue finding module
eigs = create_eigs(matrix, 3, 50, False)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals, evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
circuit_drawer(algo.construct_circuit(),output='mpl',filename='./hhlnew.png')
result = algo.run(QuantumInstance(Aer.get_backend('statevector_simulator')))
print("Solution:\t\t", np.round(result['solution'], 5))
result_ref = NumPyLSsolver(matrix, vector).run()
print("Classical Solution:\t", np.round(result_ref['solution'], 5))
print("Probability:\t\t %f" % result['probability_result'])
fidelity(result['solution'], result_ref['solution'])
def test_hhl_negative_eigs(self):
""" hhl negative eigs test """
self.log.debug('Testing HHL with matrix with negative eigenvalues')
# The following seed was chosen so as to ensure we get a negative eigenvalue
# and in case anything changes we assert this after the random matrix is created
aqua_globals.random_seed = 27
n = 2
matrix = rmg.random_diag(n, eigrange=[-1, 1])
vector = aqua_globals.random.random(n)
self.assertTrue(np.any(matrix < 0),
"Random matrix has no negative values")
# run NumPyLSsolver
ref_result = NumPyLSsolver(matrix, vector).run()
ref_solution = ref_result.solution
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, 4, True)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = QuantumCircuit(num_q)
init_state.initialize(vector / np.linalg.norm(vector), range(num_q))
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator'),
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
hhl_solution = hhl_result.solution
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare results
fidelity = state_fidelity(ref_normed, hhl_normed)
np.testing.assert_approx_equal(fidelity, 1, significant=3)
self.log.debug('HHL solution vector: %s', hhl_solution)
self.log.debug('algebraic solution vector: %s', ref_normed)
self.log.debug('fidelity HHL to algebraic: %s', fidelity)
self.log.debug('probability of result: %s',
hhl_result.probability_result)
def test_hhl_diagonal(self, vector, use_circuit_library):
""" hhl diagonal test """
self.log.debug(
'Testing HHL simple test in mode Lookup with statevector simulator'
)
matrix = [[1, 0], [0, 1]]
# run NumPyLSsolver
ref_result = NumPyLSsolver(matrix, vector).run()
ref_solution = ref_result['solution']
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, 3, False, use_circuit_library)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
if not use_circuit_library:
warnings.filterwarnings('ignore', category=DeprecationWarning)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator'),
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
if not use_circuit_library:
warnings.filterwarnings('always', category=DeprecationWarning)
hhl_solution = hhl_result['solution']
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare results
fidelity = state_fidelity(ref_normed, hhl_normed)
np.testing.assert_approx_equal(fidelity, 1, significant=5)
self.log.debug('HHL solution vector: %s', hhl_solution)
self.log.debug('algebraic solution vector: %s', ref_solution)
self.log.debug('fidelity HHL to algebraic: %s', fidelity)
self.log.debug('probability of result: %s',
hhl_result["probability_result"])
def test_hhl_diagonal_other_dim(self, n, num_ancillary):
""" hhl diagonal other dim test """
self.log.debug('Testing HHL with matrix dimension other than 2**n')
matrix = rmg.random_diag(n, eigrange=[0, 1])
vector = aqua_globals.random.random(n)
# run NumPyLSsolver
ref_result = NumPyLSsolver(matrix, vector).run()
ref_solution = ref_result.solution
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, num_ancillary, True)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator'),
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
hhl_solution = hhl_result.solution
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare result
fidelity = state_fidelity(ref_normed, hhl_normed)
np.testing.assert_approx_equal(fidelity, 1.0, significant=1)
self.log.debug('HHL solution vector: %s', hhl_solution)
self.log.debug('algebraic solution vector: %s', ref_solution)
self.log.debug('fidelity HHL to algebraic: %s', fidelity)
self.log.debug('probability of result: %s',
hhl_result.probability_result)
def test_hhl_diagonal_negative(self, vector):
""" hhl diagonal negative test """
self.log.debug(
'Testing HHL simple test in mode Lookup with statevector simulator'
)
matrix = [[1, 0], [0, 1]]
# run NumPyLSsolver
ref_result = NumPyLSsolver(matrix, vector).run()
ref_solution = ref_result.solution
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, 4, True)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = QuantumCircuit(num_q)
init_state.initialize(vector / np.linalg.norm(vector), range(num_q))
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator'),
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
hhl_solution = hhl_result.solution
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare results
fidelity = state_fidelity(ref_normed, hhl_normed)
np.testing.assert_approx_equal(fidelity, 1, significant=5)
self.log.debug('HHL solution vector: %s', hhl_solution)
self.log.debug('algebraic solution vector: %s', ref_normed)
self.log.debug('fidelity HHL to algebraic: %s', fidelity)
self.log.debug('probability of result: %s',
hhl_result.probability_result)
def test_hhl_negative_eigs(self):
""" hhl negative eigs test """
self.log.debug('Testing HHL with matrix with negative eigenvalues')
n = 2
matrix = rmg.random_diag(n, eigrange=[-1, 1])
vector = aqua_globals.random.random_sample(n)
# run NumPyLSsolver
ref_result = NumPyLSsolver(matrix, vector).run()
ref_solution = ref_result['solution']
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, 4, True)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator'),
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
hhl_solution = hhl_result["solution"]
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare results
fidelity = state_fidelity(ref_normed, hhl_normed)
np.testing.assert_approx_equal(fidelity, 1, significant=3)
self.log.debug('HHL solution vector: %s', hhl_solution)
self.log.debug('algebraic solution vector: %s', ref_normed)
self.log.debug('fidelity HHL to algebraic: %s', fidelity)
self.log.debug('probability of result: %s',
hhl_result["probability_result"])
def test_hhl_diagonal_qasm(self, vector):
""" hhl diagonal qasm test """
self.log.debug('Testing HHL simple test with qasm simulator')
matrix = [[1, 0], [0, 1]]
# run ExactLSsolver
ref_result = ExactLSsolver(matrix, vector).run()
ref_solution = ref_result['solution']
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, 3, False)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
scale=0.5,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('qasm_simulator'),
shots=1000,
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
hhl_solution = hhl_result['solution']
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare results
fidelity = state_fidelity(ref_normed, hhl_normed)
np.testing.assert_approx_equal(fidelity, 1, significant=1)
self.log.debug('HHL solution vector: %s', hhl_solution)
self.log.debug('algebraic solution vector: %s', ref_normed)
self.log.debug('fidelity HHL to algebraic: %s', fidelity)
self.log.debug('probability of result: %s',
hhl_result["probability_result"])
def test_hhl_non_hermitian(self):
""" hhl non hermitian test """
self.log.debug('Testing HHL with simple non-hermitian matrix')
matrix = [[1, 1], [2, 1]]
vector = [1, 0]
# run NumPyLSsolver
ref_result = NumPyLSsolver(matrix, vector).run()
ref_solution = ref_result['solution']
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, 6, True)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator'),
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
hhl_solution = hhl_result['solution']
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare result
fidelity = state_fidelity(ref_normed, hhl_normed)
self.assertGreater(fidelity, 0.8)
self.log.debug('HHL solution vector: %s', hhl_solution)
self.log.debug('algebraic solution vector: %s', ref_solution)
self.log.debug('fidelity HHL to algebraic: %s', fidelity)
self.log.debug('probability of result: %s',
hhl_result["probability_result"])
def test_hhl_random_hermitian(self):
""" hhl random hermitian test """
self.log.debug('Testing HHL with random hermitian matrix')
n = 2
matrix = rmg.random_hermitian(n, eigrange=[0, 1])
vector = aqua_globals.random.random(n)
# run NumPyLSsolver
ref_result = NumPyLSsolver(matrix, vector).run()
ref_solution = ref_result.solution
ref_normed = ref_solution / np.linalg.norm(ref_solution)
# run hhl
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = TestHHL._create_eigs(matrix, 4, False)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
with warnings.catch_warnings():
warnings.filterwarnings('ignore', category=DeprecationWarning)
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
warnings.filterwarnings('ignore', category=DeprecationWarning)
hhl_result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator'),
seed_simulator=aqua_globals.random_seed,
seed_transpiler=aqua_globals.random_seed))
warnings.filterwarnings('always', category=DeprecationWarning)
hhl_solution = hhl_result.solution
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# compare result
fidelity = state_fidelity(ref_normed, hhl_normed)
np.testing.assert_approx_equal(fidelity, 1, significant=1)
def solve(self, matrix, vector):
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = self.create_eigs(matrix, self.num_ancillae,
self.num_time_slices, self.negative_evals)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
result = algo.run(
QuantumInstance(self.backend,
optimization_level=self.optimization_level))
return result['solution']
solution_hhl_normed = hhl / np.linalg.norm(hhl)
solution_ref_normed = ref / np.linalg.norm(ref)
fidelity = state_fidelity(solution_hhl_normed, solution_ref_normed)
print("fidelity %f" % fidelity)
orig_size = len(vector)
matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(
matrix, vector)
# Initialize eigenvalue finding module
eigs = create_eigs(matrix, 3, False)
num_q, num_a = eigs.get_register_sizes()
# Initialize initial state module
init_state = Custom(num_q, state_vector=vector)
# Initialize reciprocal rotation module
reci = LookupRotation(negative_evals=eigs._negative_evals,
evo_time=eigs._evo_time)
algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,
init_state, reci, num_q, num_a, orig_size)
result = algo.run(
QuantumInstance(BasicAer.get_backend('statevector_simulator')))
print(np.round(result['solution'], 5))
# IBMQ.save_account('2014e54721e8677688e0c1dffdc92dfe0f39dbae5d75dd5b14fd087c4f93349b6ea92cbbc872d9a838e946527e10144d554b04587662f5567309b75aca0085f0')
# IBMQ.load_account()