def test_rowsum_phase_accumulator():
"""
Test the accuracy of the phase accumulator. This subroutine keeps track of the power that $i$ is raised to
when multiplying two PauliTerms together. PauliTerms are now composed of multi single-qubit Pauli's.
The formula is phase_accumulator(h, i) = 2 * rh + 2 * ri + \sum_{j}^{n}g(x_{ij}, z_{ij}, x_{hj}, z_{hj}
The returned value is presented mod 4.
notice that since r_h indicates +1 or -1 this corresponds to i^{0} or i^{2}. Given r_{h/i} takes on {0, 1} then
we need to multiply by 2 get the correct power of $i$ for the Pauli Term to account for multiplication.
In order to test we will generate random elements of P_{n} and then multiply them together keeping track of the
$i$ power. We will then compare this to the phase_accumulator subroutine.
We have to load in the stabilizer into an empty qvmstab object because the subroutine needs a tableau as a reference
"""
num_qubits = 2
pauli_terms = [sX(0) * sX(1), sZ(0) * sZ(1)]
stab_mat = pauli_stabilizer_to_binary_stabilizer(pauli_terms)
qvmstab = QVM_Stabilizer(num_qubits=num_qubits)
qvmstab.tableau[num_qubits:, :] = stab_mat
exp_on_i = qvmstab._rowsum_phase_accumulator(2, 3)
assert exp_on_i == 2
num_qubits = 2
pauli_terms = [sZ(0) * sI(1), sZ(0) * sZ(1)]
stab_mat = pauli_stabilizer_to_binary_stabilizer(pauli_terms)
qvmstab = QVM_Stabilizer(num_qubits=num_qubits)
qvmstab.tableau[num_qubits:, :] = stab_mat
exp_on_i = qvmstab._rowsum_phase_accumulator(2, 3)
assert exp_on_i == 0
# now try generating random valid elements from 2-qubit group
for _ in range(100):
num_qubits = 6
pauli_terms = []
for _ in range(num_qubits):
pauli_terms.append(
reduce(lambda x, y: x * y, [
pauli_subgroup[x](idx) for idx, x in enumerate(
np.random.randint(1, 4, num_qubits))
]))
stab_mat = pauli_stabilizer_to_binary_stabilizer(pauli_terms)
qvmstab = QVM_Stabilizer(num_qubits=num_qubits)
qvmstab.tableau[num_qubits:, :] = stab_mat
p_on_i = qvmstab._rowsum_phase_accumulator(num_qubits, num_qubits + 1)
coeff_test = pauli_terms[1] * pauli_terms[0]
assert np.isclose(coeff_test.coefficient, (1j)**p_on_i)
def test_rowsum_full():
"""
Test the rowsum subroutine.
This routine replaces row h with P(i) * P(h) where P is the pauli operator represented by the row
given by the index. It uses the summation to accumulate whether the phase is +1 or -1 and then
xors together the elements of the rows replacing row h
"""
# now try generating random valid elements from 2-qubit group
for _ in range(100):
num_qubits = 6
pauli_terms = []
for _ in range(num_qubits):
pauli_terms.append(
reduce(lambda x, y: x * y, [
pauli_subgroup[x](idx) for idx, x in enumerate(
np.random.randint(1, 4, num_qubits))
]))
try:
stab_mat = pauli_stabilizer_to_binary_stabilizer(pauli_terms)
except:
# we have to do this because I'm not strictly making valid n-qubit
# stabilizers
continue
qvmstab = QVM_Stabilizer(num_qubits=num_qubits)
qvmstab.tableau[num_qubits:, :] = stab_mat
p_on_i = qvmstab._rowsum_phase_accumulator(num_qubits, num_qubits + 1)
if p_on_i not in [1, 3]:
coeff_test = pauli_terms[1] * pauli_terms[0]
assert np.isclose(coeff_test.coefficient, (1j)**p_on_i)
qvmstab._rowsum(num_qubits, num_qubits + 1)
try:
pauli_op = binary_stabilizer_to_pauli_stabilizer(
qvmstab.tableau[[num_qubits], :])[0]
except:
continue
true_pauli_op = pauli_terms[1] * pauli_terms[0]
assert pauli_op == true_pauli_op