def test_hhl_non_hermitian(self):
self.log.debug('Testing HHL with simple non-hermitian matrix')
nonherm_params = self.params
nonherm_params['eigs']['num_ancillae'] = 6
nonherm_params['eigs']['num_time_slices'] = 80
nonherm_params['eigs']['negative_evals'] = True
nonherm_params['reciprocal']['negative_evals'] = True
matrix = [[1, 1], [2, 1]]
vector = [1, 0]
algo_input = LinearSystemInput()
algo_input.matrix = matrix
algo_input.vector = vector
# run ExactLSsolver
ref_result = run_algorithm(self.els_params, algo_input)
ref_solution = ref_result['solution']
ref_normed = ref_solution/np.linalg.norm(ref_solution)
# run hhl
hhl_result = run_algorithm(nonherm_params, algo_input)
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: {}'.format(hhl_solution))
self.log.debug('algebraic solution vector: {}'.format(ref_solution))
self.log.debug('fidelity HHL to algebraic: {}'.format(fidelity))
self.log.debug('probability of result: {}'.format(hhl_result["probability_result"]))
def test_hhl_random_hermitian(self):
self.log.debug('Testing HHL with random hermitian matrix')
hermitian_params = self.params
hermitian_params['eigs']['num_ancillae'] = 4
n = 2
np.random.seed(0)
matrix = rmg.random_hermitian(n, eigrange=[0, 1])
vector = random(n)
algo_input = LinearSystemInput()
algo_input.matrix = matrix
algo_input.vector = vector
# run ExactLSsolver
ref_result = run_algorithm(self.els_params, algo_input)
ref_solution = ref_result['solution']
ref_normed = ref_solution/np.linalg.norm(ref_solution)
# run hhl
hhl_result = run_algorithm(hermitian_params, algo_input)
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=2)
self.log.debug('HHL solution vector: {}'.format(hhl_solution))
self.log.debug('algebraic solution vector: {}'.format(ref_normed))
self.log.debug('fidelity HHL to algebraic: {}'.format(fidelity))
self.log.debug('probability of result: {}'.format(hhl_result["probability_result"]))
def test_hhl_negative_eigs(self):
self.log.debug('Testing HHL with matrix with negative eigenvalues')
neg_params = self.params
neg_params['eigs']['num_ancillae'] = 4
neg_params['eigs']['negative_evals'] = True
neg_params['reciprocal']['negative_evals'] = True
n = 2
np.random.seed(0)
matrix = rmg.random_diag(n, eigrange=[-1, 1])
vector = random(n)
algo_input = LinearSystemInput()
algo_input.matrix = matrix
algo_input.vector = vector
# run ExactLSsolver
ref_result = run_algorithm(self.els_params, algo_input)
ref_solution = ref_result['solution']
ref_normed = ref_solution/np.linalg.norm(ref_solution)
# run hhl
hhl_result = run_algorithm(neg_params, algo_input)
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: {}'.format(hhl_solution))
self.log.debug('algebraic solution vector: {}'.format(ref_normed))
self.log.debug('fidelity HHL to algebraic: {}'.format(fidelity))
self.log.debug('probability of result: {}'.format(hhl_result["probability_result"]))
def test_hhl_diagonal_other_dim(self, n, num_ancillary):
self.log.debug('Testing HHL with matrix dimension other than 2**n')
dim_params = self.params
dim_params['eigs']['num_ancillae'] = num_ancillary
dim_params['eigs']['negative_evals'] = True
dim_params['reciprocal']['negative_evals'] = True
np.random.seed(0)
matrix = rmg.random_diag(n, eigrange=[0, 1])
vector = random(n)
algo_input = LinearSystemInput()
algo_input.matrix = matrix
algo_input.vector = vector
# run ExactLSsolver
ref_result = run_algorithm(self.els_params, algo_input)
ref_solution = ref_result['solution']
ref_normed = ref_solution/np.linalg.norm(ref_solution)
# run hhl
hhl_result = run_algorithm(dim_params, algo_input)
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)
self.log.debug('HHL solution vector: {}'.format(hhl_solution))
self.log.debug('algebraic solution vector: {}'.format(ref_solution))
self.log.debug('fidelity HHL to algebraic: {}'.format(fidelity))
self.log.debug('probability of result: {}'.format(hhl_result["probability_result"]))
def test_hhl_random_hermitian_sv(self):
self.log.debug('Testing HHL with random hermitian matrix')
hermitian_params = self.params
hermitian_params['eigs']['num_ancillae'] = 4
n = 2
matrix = rmg.random_hermitian(n, eigrange=[0, 1])
vector = random(2)
algo_input = LinearSystemInput()
algo_input.matrix = matrix
algo_input.vector = vector
# run hhl
result = run_algorithm(hermitian_params, algo_input)
hhl_solution = result["solution_hhl"]
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# linear algebra solution
linalg_solution = np.linalg.solve(matrix, vector)
linalg_normed = linalg_solution / np.linalg.norm(linalg_solution)
# compare result
fidelity = abs(linalg_normed.dot(hhl_normed.conj()))**2
np.testing.assert_approx_equal(fidelity, 1, significant=2)
self.log.debug('HHL solution vector: {}'.format(hhl_solution))
self.log.debug('algebraic solution vector: {}'.format(linalg_solution))
self.log.debug('fidelity HHL to algebraic: {}'.format(fidelity))
self.log.debug('probability of result: {}'.format(
result["probability_result"]))
def test_hhl_negative_eigs_sv(self):
self.log.debug('Testing HHL with matrix with negative eigenvalues')
neg_params = self.params
neg_params['eigs']['num_ancillae'] = 4
neg_params['eigs']['negative_evals'] = True
neg_params['reciprocal']['negative_evals'] = True
n = 2
matrix = rmg.random_diag(n, eigrange=[-1, 1])
vector = random(2)
algo_input = LinearSystemInput()
algo_input.matrix = matrix
algo_input.vector = vector
# run hhl
result = run_algorithm(neg_params, algo_input)
hhl_solution = result["solution_hhl"]
hhl_normed = hhl_solution / np.linalg.norm(hhl_solution)
# linear algebra solution
linalg_solution = np.linalg.solve(matrix, vector)
linalg_normed = linalg_solution / np.linalg.norm(linalg_solution)
# compare result
fidelity = abs(linalg_normed.dot(hhl_normed.conj()))**2
np.testing.assert_approx_equal(fidelity, 1, significant=3)
self.log.debug('HHL solution vector: {}'.format(hhl_solution))
self.log.debug('algebraic solution vector: {}'.format(linalg_solution))
self.log.debug('fidelity HHL to algebraic: {}'.format(fidelity))
self.log.debug('probability of result: {}'.format(
result["probability_result"]))