def get_error_hamming_distributions_from_results(results: Sequence[Sequence[Sequence[int]]]) \
-> Sequence[Sequence[float]]:
"""
Get the distribution of the hamming weight of the error vector (number of bits flipped
between output and expected answer) for each possible pair of two n_bit summands using
results output by get_n_bit_adder_results
:param results: a list of results output from a call to get_n_bit_adder_results
:return: the relative frequency of observing each hamming weight, 0 to n_bits+1, for the error
that occurred when adding each pair of two n_bit summands
"""
num_shots = len(results[0])
n_bits = len(results[0][0]) - 1
hamming_wt_distrs = []
# loop over all binary strings of length n_bits
for result, bits in zip(results, all_bitstrings(2 * n_bits)):
# Input nums are written from (MSB .... LSB) = (a_n, ..., a_1, a_0)
num_a = bit_array_to_int(bits[:n_bits])
num_b = bit_array_to_int(bits[n_bits:])
# add the numbers
ans = num_a + num_b
ans_bits = int_to_bit_array(ans, n_bits + 1)
# record the fraction of shots that resulted in an error of the given weight
hamming_wt_distr = [0. for _ in range(len(ans_bits) + 1)]
for shot in result:
# multiply relative hamming distance by the length of the output for the weight
wt = len(ans_bits) * hamming(ans_bits, shot)
hamming_wt_distr[int(wt)] += 1. / num_shots
hamming_wt_distrs.append(hamming_wt_distr)
return hamming_wt_distrs
def get_success_probabilities_from_results(results: Sequence[Sequence[Sequence[int]]]) \
-> Sequence[float]:
"""
Get the probability of a successful addition for each possible pair of two n_bit summands
from the results output by get_n_bit_adder_results
:param results: a list of results output from a call to get_n_bit_adder_results
:return: the success probability for the summation of each possible pair of n_bit summands
"""
num_shots = len(results[0])
n_bits = len(results[0][0]) - 1
probabilities = []
# loop over all binary strings of length n_bits
for result, bits in zip(results, all_bitstrings(2 * n_bits)):
# Input nums are written from (MSB .... LSB) = (a_n, ..., a_1, a_0)
num_a = bit_array_to_int(bits[:n_bits])
num_b = bit_array_to_int(bits[n_bits:])
# add the numbers
ans = num_a + num_b
ans_bits = int_to_bit_array(ans, n_bits + 1)
# a success occurs if a shot matches the expected ans bit for bit
probability = 0
for shot in result:
if np.array_equal(ans_bits, shot):
probability += 1. / num_shots
probabilities.append(probability)
return probabilities