def test_conditional_value_at_risk(self, simulator):
""" conditional value at risk test """
# define backend to be used
backend = BasicAer.get_backend(simulator)
# set problem parameters
n_z = 2
z_max = 2
# z_values = np.linspace(-z_max, z_max, 2 ** n_z)
p_zeros = [0.15, 0.25]
rhos = [0.1, 0.05]
lgd = [1, 2]
k_l = len(p_zeros)
# alpha = 0.05
# set var value
var = 2
var_prob = 0.961940
# determine number of qubits required to represent total loss
# n_s = WeightedSumOperator.get_required_sum_qubits(lgd)
# create circuit factory (add Z qubits with weight/loss 0)
agg = WeightedSumOperator(n_z + k_l, [0] * n_z + lgd)
# define linear objective
breakpoints = [0, var]
slopes = [0, 1]
offsets = [0, 0] # subtract VaR and add it later to the estimate
f_min = 0
f_max = 3 - var
c_approx = 0.25
# construct circuit factory for uncertainty model (Gaussian Conditional Independence model)
gci = GCI(n_z, z_max, p_zeros, rhos)
cvar_objective = PwlObjective(
agg.num_sum_qubits,
0,
2**agg.num_sum_qubits -
1, # max value that can be reached by the qubit register
breakpoints,
slopes,
offsets,
f_min,
f_max,
c_approx)
multivariate_cvar = MultivariateProblem(gci, agg, cvar_objective)
num_qubits = multivariate_cvar.num_target_qubits
num_ancillas = multivariate_cvar.required_ancillas()
q = QuantumRegister(num_qubits, name='q')
q_a = QuantumRegister(num_ancillas, name='q_a')
qc = QuantumCircuit(q, q_a)
multivariate_cvar.build(qc, q, q_a)
job = execute(qc, backend=backend)
# evaluate resulting statevector
value = 0
for i, a_i in enumerate(job.result().get_statevector()):
b = ('{0:0%sb}' %
multivariate_cvar.num_target_qubits).\
format(i)[-multivariate_cvar.num_target_qubits:]
a_m = np.round(np.real(a_i), decimals=4)
if np.abs(a_m) > 1e-6 and b[0] == '1':
value += a_m**2
# normalize and add VaR to estimate
value = multivariate_cvar.value_to_estimation(value)
normalized_value = value / (1.0 - var_prob) + var
# compare to precomputed solution
self.assertEqual(0.0, np.round(normalized_value - 3.3796, decimals=4))
# In[3]: # set the model parameters n_z = 2 z_max = 2 z_values = np.linspace(-z_max, z_max, 2**n_z) p_zeros = [0.15, 0.25] rhos = [0.1, 0.05] lgd = [1, 2] K = len(p_zeros) alpha = 0.05 # In[4]: # construct circuit factory for uncertainty model (Gaussian Conditional Independence model) u = GCI(n_z, z_max, p_zeros, rhos) # In[5]: # determine the number of qubits required to represent the uncertainty model num_qubits = u.num_target_qubits # initialize quantum register and circuit q = QuantumRegister(num_qubits, name='q') qc = QuantumCircuit(q) # construct circuit u.build(qc, q) # In[6]: