# This code is part of Qiskit.
#
# (C) Copyright IBM 2021.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""Quasidistribution class"""
from math import sqrt
import re
from .probability import ProbDistribution
# NOTE: A dict subclass should not overload any dunder methods like __getitem__
# this can cause unexpected behavior and issues as the cPython dict
# implementation has many standard methods in C for performance and the dunder
# methods are not always used as expected. For example, update() doesn't call
# __setitem__ so overloading __setitem__ would not always provide the expected
# result
[docs]class QuasiDistribution(dict):
"""A dict-like class for representing quasi-probabilities."""
_bitstring_regex = re.compile(r"^[01]+$")
def __init__(self, data, shots=None, stddev_upper_bound=None):
"""Builds a quasiprobability distribution object.
Parameters:
data (dict): Input quasiprobability data. Where the keys
represent a measured classical value and the value is a
float for the quasiprobability of that result.
The keys can be one of several formats:
* A hexadecimal string of the form ``"0x4a"``
* A bit string e.g. ``'0b1011'`` or ``"01011"``
* An integer
shots (int): Number of shots the distribution was derived from.
stddev_upper_bound (float): An upper bound for the standard deviation
Raises:
TypeError: If the input keys are not a string or int
ValueError: If the string format of the keys is incorrect
"""
self.shots = shots
self._stddev_upper_bound = stddev_upper_bound
self._num_bits = 0
if data:
first_key = next(iter(data.keys()))
if isinstance(first_key, int):
# `self._num_bits` is not always the exact number of qubits measured,
# but the number of bits to represent the largest key.
self._num_bits = len(bin(max(data.keys()))) - 2
elif isinstance(first_key, str):
if first_key.startswith("0x") or first_key.startswith("0b"):
data = {int(key, 0): value for key, value in data.items()}
# `self._num_bits` is not always the exact number of qubits measured,
# but the number of bits to represent the largest key.
self._num_bits = len(bin(max(data.keys()))) - 2
elif self._bitstring_regex.search(first_key):
# `self._num_bits` is the exact number of qubits measured.
self._num_bits = max(len(key) for key in data)
data = {int(key, 2): value for key, value in data.items()}
else:
raise ValueError(
"The input keys are not a valid string format, must either "
"be a hex string prefixed by '0x' or a binary string "
"optionally prefixed with 0b"
)
else:
raise TypeError("Input data's keys are of invalid type, must be str or int")
super().__init__(data)
[docs] def nearest_probability_distribution(self, return_distance=False):
"""Takes a quasiprobability distribution and maps
it to the closest probability distribution as defined by
the L2-norm.
Parameters:
return_distance (bool): Return the L2 distance between distributions.
Returns:
ProbDistribution: Nearest probability distribution.
float: Euclidean (L2) distance of distributions.
Notes:
Method from Smolin et al., Phys. Rev. Lett. 108, 070502 (2012).
"""
sorted_probs = dict(sorted(self.items(), key=lambda item: item[1]))
num_elems = len(sorted_probs)
new_probs = {}
beta = 0
diff = 0
for key, val in sorted_probs.items():
temp = val + beta / num_elems
if temp < 0:
beta += val
num_elems -= 1
diff += val * val
else:
diff += (beta / num_elems) * (beta / num_elems)
new_probs[key] = sorted_probs[key] + beta / num_elems
if return_distance:
return ProbDistribution(new_probs, self.shots), sqrt(diff)
return ProbDistribution(new_probs, self.shots)
[docs] def binary_probabilities(self, num_bits=None):
"""Build a quasi-probabilities dictionary with binary string keys
Parameters:
num_bits (int): number of bits in the binary bitstrings (leading
zeros will be padded). If None, a default value will be used.
If keys are given as integers or strings with binary or hex prefix,
the default value will be derived from the largest key present.
If keys are given as bitstrings without prefix,
the default value will be derived from the largest key length.
Returns:
dict: A dictionary where the keys are binary strings in the format
``"0110"``
"""
n = self._num_bits if num_bits is None else num_bits
return {format(key, "b").zfill(n): value for key, value in self.items()}
[docs] def hex_probabilities(self):
"""Build a quasi-probabilities dictionary with hexadecimal string keys
Returns:
dict: A dictionary where the keys are hexadecimal strings in the
format ``"0x1a"``
"""
return {hex(key): value for key, value in self.items()}
@property
def stddev_upper_bound(self):
"""Return an upper bound on standard deviation of expval estimator."""
return self._stddev_upper_bound