truth_table_oracle.py

# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 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.

"""
The Truth Table-based Quantum Oracle.
"""

from typing import Union, List
import logging
import operator
import math
from functools import reduce

import numpy as np
from dlx import DLX
from sympy import symbols
from sympy.logic.boolalg import Xor, And
from qiskit import QuantumRegister, QuantumCircuit

from qiskit.aqua import AquaError
from qiskit.aqua.circuits import ESOP
from qiskit.aqua.components.oracles import Oracle
from qiskit.aqua.utils.arithmetic import is_power_of_2
from qiskit.aqua.utils.validation import validate_in_set
from .ast_utils import get_ast

logger = logging.getLogger(__name__)

# pylint: disable=invalid-name


class TruthTableOracle(Oracle):
    """
    The Truth Table-based Quantum Oracle.

    Besides logical expressions, (see :class:`LogicalExpressionOracle`) another common way of
    specifying boolean functions is using truth tables, which is basically an exhaustive mapping
    from input binary bit-strings of length :math:`n` to corresponding output bit-strings of
    length :math:`m`. For example, the following is a simple truth table that corresponds to
    the `XOR` of two variables:

    =====  =====  =============
       Inputs        Output
    ------------  -------------
      A      B       A xor B
    =====  =====  =============
      0      0       0
      0      1       1
      1      0       1
      1      1       0
    =====  =====  =============

    In this case :math:`n=2`, and :math:`m=1`. Often, for brevity, the input bit-strings are
    omitted because they can be easily derived for any given :math:`n`. So to completely specify a
    truth table, we only need a Length-2 :sup:`n` bit-string for each of the :math:`m` outputs.
    In the above example, a single bit-string `'0110'` would suffice. Besides `'0'` and `'1'`,
    one can also use `'x'` in the output string to indicate `'do-not-care'` entries.
    For example, `'101x'` specifies a truth table (again :math:`n=2` and :math:`m=1`)
    for which the output upon input `'11'` doesn't matter. The truth table oracle takes either a
    single string or a list of equal-length strings for truth table specifications.

    Regarding circuit optimization and mct usages, the truth table oracle is similar to the
    :class:`LogicalExpressionOracle`. One difference is that, unlike the logical expression oracle
    which builds circuits out of CNF or DNF, the truth table oracle uses Exclusive Sum of Products
    (ESOP), which is similar to DNF, with the only difference being the outermost operation
    being `XOR` as opposed to a disjunction. Because of this difference, an implicant-based method
    is used here for circuit optimization: First, the `Quine-McCluskey algorithm
    <https://en.wikipedia.org/wiki/Quine-McCluskey_algorithm>`__  is used to find all prime
    implicants of the input truth table; then an `Exact Cover
    <https://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X>`__ is found among all prime implicants
    and truth table onset row entries. The exact cover is then used to build the
    corresponding oracle circuit.
    """

    def __init__(self,
                 bitmaps: Union[str, List[str]],
                 optimization: bool = False,
                 mct_mode: str = 'basic'):
        """
        Args:
            bitmaps: A single binary string or a list of binary strings
                representing the desired single- and multi-value truth table.
            optimization: Boolean flag for attempting circuit optimization.
                When set, the Quine-McCluskey algorithm is used to compute the prime
                implicants of the truth table,
                and then its exact cover is computed to try to reduce the circuit.
            mct_mode: The mode to use when constructing multiple-control Toffoli.
        Raises:
            AquaError: Invalid input
        """
        if isinstance(bitmaps, str):
            bitmaps = [bitmaps]

        validate_in_set('mct_mode', mct_mode,
                        {'basic', 'basic-dirty-ancilla',
                         'advanced', 'noancilla'})
        super().__init__()

        self._mct_mode = mct_mode.strip().lower()
        self._optimization = optimization

        self._bitmaps = bitmaps

        # check that the input bitmaps length is a power of 2
        if not is_power_of_2(len(bitmaps[0])):
            raise AquaError('Length of any bitmap must be a power of 2.')
        for bitmap in bitmaps[1:]:
            if not len(bitmap) == len(bitmaps[0]):
                raise AquaError('Length of all bitmaps must be the same.')
        self._nbits = int(math.log(len(bitmaps[0]), 2))
        self._num_outputs = len(bitmaps)

        self._lit_to_var = None
        self._var_to_lit = None

        esop_exprs = []
        for bitmap in bitmaps:
            esop_expr = self._get_esop_ast(bitmap)
            esop_exprs.append(esop_expr)

        self._esops = [
            ESOP(esop_expr, num_vars=self._nbits) for esop_expr in esop_exprs
        ] if esop_exprs else None

        self.construct_circuit()

    def _get_esop_ast(self, bitmap):
        v = symbols('v:{}'.format(self._nbits))
        if self._lit_to_var is None:
            self._lit_to_var = [None] + sorted(v, key=str)
        if self._var_to_lit is None:
            self._var_to_lit = dict(zip(self._lit_to_var[1:], range(1, self._nbits + 1)))

        def binstr_to_vars(binstr):
            return [(~v[x[1] - 1] if x[0] == '0' else v[x[1] - 1])
                    for x in zip(binstr, reversed(range(1, self._nbits + 1)))][::-1]

        if not self._optimization:
            expression = Xor(*[
                And(*binstr_to_vars(term)) for term in
                [np.binary_repr(idx, self._nbits) for idx, v in enumerate(bitmap) if v == '1']
            ])
        else:
            ones = [i for i, v in enumerate(bitmap) if v == '1']
            if not ones:
                return 'const', 0
            dcs = [i for i, v in enumerate(bitmap) if v == '*' or v == '-' or v.lower() == 'x']
            pis = get_prime_implicants(ones=ones, dcs=dcs)
            cover = get_exact_covers(ones, pis)[-1]
            clauses = []
            for c in cover:
                if len(c) == 1:
                    term = np.binary_repr(c[0], self._nbits)
                    clause = And(*[
                        v for i, v in enumerate(binstr_to_vars(term))
                    ])
                elif len(c) > 1:
                    c_or = reduce(operator.or_, c)
                    c_and = reduce(operator.and_, c)
                    _ = np.binary_repr(c_and ^ c_or, self._nbits)[::-1]
                    clause = And(*[
                        v for i, v in enumerate(binstr_to_vars(np.binary_repr(c_and, self._nbits)))
                        if _[i] == '0'])
                else:
                    raise AquaError('Unexpected cover term size {}.'.format(len(c)))
                if clause:
                    clauses.append(clause)
            expression = Xor(*clauses)

        ast = get_ast(self._var_to_lit, expression)
        if ast is not None:
            return ast
        else:
            return 'const', 0

    @property
    def variable_register(self):
        """ returns variable register """
        return self._variable_register

    @property
    def ancillary_register(self):
        """ returns ancillary register """
        return self._ancillary_register

    @property
    def output_register(self):
        """ returns output register """
        return self._output_register

    def construct_circuit(self):
        """ construct circuit """
        if self._circuit is not None:
            return self._circuit
        self._output_register = QuantumRegister(self._num_outputs, name='o')
        self._variable_register = QuantumRegister(self._nbits, name='v')
        self._circuit = QuantumCircuit(self._variable_register, self._output_register)

        if self._esops:
            num_ancillae, self._ancillary_register = 0, None
            for i, e in enumerate(self._esops):
                num_ancillae = max(num_ancillae, e.compute_num_ancillae(self._mct_mode))
            if num_ancillae > 0:
                self._ancillary_register = QuantumRegister(num_ancillae, name='a')
                self._circuit.add_register(self._ancillary_register)

            for i, e in enumerate(self._esops):
                if e is not None:
                    e.construct_circuit(
                        circuit=self._circuit,
                        variable_register=self._variable_register,
                        output_register=self._output_register,
                        output_idx=i,
                        ancillary_register=self._ancillary_register,
                        mct_mode=self._mct_mode
                    )

        else:
            self._ancillary_register = None
        return self._circuit

    def evaluate_classically(self, measurement):
        """ evaluate classical """
        assignment = [(var + 1) * (int(tf) * 2 - 1) for tf, var in zip(measurement[::-1],
                                                                       range(len(measurement)))]
        ret = [bitmap[int(measurement, 2)] == '1' for bitmap in self._bitmaps]
        if self._num_outputs == 1:
            return ret[0], assignment
        else:
            return ret, assignment


def get_prime_implicants(ones=None, dcs=None):
    """
    Compute all prime implicants for a truth table using the Quine-McCluskey Algorithm

    Args:
        ones (list of int): The list of integers corresponding to '1' outputs
        dcs (list of int): The list of integers corresponding to don't-cares

    Return:
        list: list of lists of int, representing all prime implicants
    """

    def combine_terms(terms, num1s_dict=None):
        if num1s_dict is None:
            num1s_dict = {}
            for num in terms:
                num1s = bin(num).count('1')
                if num1s not in num1s_dict:
                    num1s_dict[num1s] = [num]
                else:
                    num1s_dict[num1s].append(num)

        new_implicants = {}
        new_num1s_dict = {}
        prime_dict = {mt: True for mt in sorted(terms)}
        cur_num1s, max_num1s = min(num1s_dict.keys()), max(num1s_dict.keys())
        while cur_num1s < max_num1s:
            if cur_num1s in num1s_dict and (cur_num1s + 1) in num1s_dict:
                for cur_term in sorted(num1s_dict[cur_num1s]):
                    for next_term in sorted(num1s_dict[cur_num1s + 1]):
                        if isinstance(cur_term, int):
                            diff_mask = dc_mask = cur_term ^ next_term
                            implicant_mask = cur_term & next_term
                        elif isinstance(cur_term, tuple):
                            if terms[cur_term][1] == terms[next_term][1]:
                                diff_mask = terms[cur_term][0] ^ terms[next_term][0]
                                dc_mask = diff_mask | terms[cur_term][1]
                                implicant_mask = terms[cur_term][0] & terms[next_term][0]
                            else:
                                continue
                        else:
                            raise AquaError('Unexpected type: {}.'.format(type(cur_term)))
                        if bin(diff_mask).count('1') == 1:
                            prime_dict[cur_term] = False
                            prime_dict[next_term] = False
                            if isinstance(cur_term, int):
                                cur_implicant = (cur_term, next_term)
                            elif isinstance(cur_term, tuple):
                                cur_implicant = tuple(sorted((*cur_term, *next_term)))
                            else:
                                raise AquaError('Unexpected type: {}.'.format(type(cur_term)))
                            new_implicants[cur_implicant] = (
                                implicant_mask,
                                dc_mask
                            )
                            num1s = bin(implicant_mask).count('1')
                            if num1s not in new_num1s_dict:
                                new_num1s_dict[num1s] = [cur_implicant]
                            else:
                                if cur_implicant not in new_num1s_dict[num1s]:
                                    new_num1s_dict[num1s].append(cur_implicant)
            cur_num1s += 1
        return new_implicants, new_num1s_dict, prime_dict

    terms = ones + dcs
    cur_num1s_dict = None

    prime_implicants = []

    while True:
        next_implicants, next_num1s_dict, cur_prime_dict = combine_terms(terms,
                                                                         num1s_dict=cur_num1s_dict)
        for implicant in cur_prime_dict:
            if cur_prime_dict[implicant]:
                if isinstance(implicant, int):
                    if implicant not in dcs:
                        prime_implicants.append((implicant,))
                else:
                    if not set.issubset(set(implicant), dcs):
                        prime_implicants.append(implicant)
        if next_implicants:
            terms = next_implicants
            cur_num1s_dict = next_num1s_dict
        else:
            break

    return prime_implicants


def get_exact_covers(cols, rows, num_cols=None):
    """
    Use Algorithm X to get all solutions to the exact cover problem

    https://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X

    Args:
          cols (list[int]): A list of integers representing the columns to be covered
          rows (list[list[int]]): A list of lists of integers representing the rows
          num_cols (int): The total number of columns

    Returns:
        list: All exact covers
    """
    if num_cols is None:
        num_cols = max(cols) + 1
    ec = DLX([(c, 0 if c in cols else 1) for c in range(num_cols)])
    ec.appendRows([[c] for c in cols])
    ec.appendRows(rows)
    exact_covers = []
    for s in ec.solve():
        cover = []
        for i in s:
            cover.append(ec.getRowList(i))
        exact_covers.append(cover)
    return exact_covers