text: # This code is part of Qiskit.
  #
  # (C) Copyright IBM 2020, 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.
  
  """ DictStateFn Class """
  
  from typing import Optional, Union, Set, Dict, cast, List
  import itertools
  import numpy as np
  from scipy import sparse
  
  from qiskit.result import Result
  from qiskit.circuit import ParameterExpression
  from qiskit.utils import algorithm_globals
  
  from ..exceptions import OpflowError
  from ..operator_base import OperatorBase
  from .state_fn import StateFn
  from ..list_ops.list_op import ListOp
  from .vector_state_fn import VectorStateFn
  
  
  class DictStateFn(StateFn):
      """ A class for state functions and measurements which are defined by a lookup table,
      stored in a dict.
      """
  
      # TODO allow normalization somehow?
      def __init__(self,
                   primitive: Union[str, dict, Result] = None,
                   coeff: Union[int, float, complex, ParameterExpression] = 1.0,
                   is_measurement: bool = False) -> None:
          """
              Args:
                  primitive: The dict, single bitstring (if defining a basis sate), or Qiskit
                      Result, which defines the behavior of the underlying function.
                  coeff: A coefficient by which to multiply the state function.
                  is_measurement: Whether the StateFn is a measurement operator.
  
              Raises:
                  TypeError: invalid parameters.
          """
          # If the initial density is a string, treat this as a density dict
          # with only a single basis state.
          if isinstance(primitive, str):
              primitive = {primitive: 1}
  
          # NOTE:
          # 1) This is not the same as passing in the counts dict directly, as this will
          # convert the shot numbers to
          # probabilities, whereas passing in the counts dict will not.
          # 2) This will extract counts for both shot and statevector simulations.
          # To use the statevector,
          # simply pass in the statevector.
          # 3) This will only extract the first result.
          if isinstance(primitive, Result):
              counts = primitive.get_counts()
              # NOTE: Need to square root to take correct Pauli measurements!
              primitive = {bstr: (shots / sum(counts.values()))**.5 for
                           (bstr, shots) in counts.items()}
  
          if not isinstance(primitive, dict):
              raise TypeError(
                  'DictStateFn can only be instantiated with dict, '
                  'string, or Qiskit Result, not {}'.format(type(primitive)))
  
          super().__init__(primitive, coeff=coeff, is_measurement=is_measurement)
  
      def primitive_strings(self) -> Set[str]:
          return {'Dict'}
  
      @property
      def num_qubits(self) -> int:
          return len(list(self.primitive.keys())[0])
  
      def add(self, other: OperatorBase) -> OperatorBase:
          if not self.num_qubits == other.num_qubits:
              raise ValueError(
                  'Sum over statefns with different numbers of qubits, {} and {}, is not well '
                  'defined'.format(self.num_qubits, other.num_qubits))
  
          # Right now doesn't make sense to add a StateFn to a Measurement
          if isinstance(other, DictStateFn) and self.is_measurement == other.is_measurement:
              # TODO add compatibility with vector and Operator?
              if self.primitive == other.primitive:
                  return DictStateFn(self.primitive,
                                     coeff=self.coeff + other.coeff,
                                     is_measurement=self.is_measurement)
              else:
                  new_dict = {b: (v * self.coeff) + (other.primitive.get(b, 0) * other.coeff)
                              for (b, v) in self.primitive.items()}
                  new_dict.update({b: v * other.coeff for (b, v) in other.primitive.items()
                                   if b not in self.primitive})
                  return StateFn(new_dict, is_measurement=self._is_measurement)
          # pylint: disable=cyclic-import,import-outside-toplevel
          from ..list_ops.summed_op import SummedOp
          return SummedOp([self, other])
  
      def adjoint(self) -> OperatorBase:
          return DictStateFn({b: np.conj(v) for (b, v) in self.primitive.items()},
                             coeff=self.coeff.conjugate(),
                             is_measurement=(not self.is_measurement))
  
      def permute(self, permutation: List[int]) -> 'DictStateFn':
          new_num_qubits = max(permutation) + 1
          if self.num_qubits != len(permutation):
              raise OpflowError("New index must be defined for each qubit of the operator.")
  
          # helper function to permute the key
          def perm(key):
              list_key = ['0'] * new_num_qubits
              for i, k in enumerate(permutation):
                  list_key[k] = key[i]
              return ''.join(list_key)
  
          new_dict = {perm(key): value for key, value in self.primitive.items()}
          return DictStateFn(new_dict, coeff=self.coeff, is_measurement=self.is_measurement)
  
      def _expand_dim(self, num_qubits: int) -> 'DictStateFn':
          pad = '0'*num_qubits
          new_dict = {key + pad: value for key, value in self.primitive.items()}
          return DictStateFn(new_dict, coeff=self.coeff, is_measurement=self.is_measurement)
  
      def tensor(self, other: OperatorBase) -> OperatorBase:
          # Both dicts
          if isinstance(other, DictStateFn):
              new_dict = {k1 + k2: v1 * v2 for ((k1, v1,), (k2, v2)) in
                          itertools.product(self.primitive.items(), other.primitive.items())}
              return StateFn(new_dict,
                             coeff=self.coeff * other.coeff,
                             is_measurement=self.is_measurement)
          # pylint: disable=cyclic-import,import-outside-toplevel
          from ..list_ops.tensored_op import TensoredOp
          return TensoredOp([self, other])
  
      def to_density_matrix(self, massive: bool = False) -> np.ndarray:
          OperatorBase._check_massive('to_density_matrix', True, self.num_qubits, massive)
          states = int(2 ** self.num_qubits)
          return self.to_matrix(massive=massive) * np.eye(states) * self.coeff
  
      def to_matrix(self, massive: bool = False) -> np.ndarray:
          OperatorBase._check_massive('to_matrix', False, self.num_qubits, massive)
          states = int(2 ** self.num_qubits)
          probs = np.zeros(states) + 0.j
          for k, v in self.primitive.items():
              probs[int(k, 2)] = v
          vec = probs * self.coeff
  
          # Reshape for measurements so np.dot still works for composition.
          return vec if not self.is_measurement else vec.reshape(1, -1)
  
      def to_spmatrix(self) -> sparse.spmatrix:
          """
          Same as to_matrix, but returns csr sparse matrix.
  
          Returns:
              CSR sparse matrix representation of the State function.
  
          Raises:
              ValueError: invalid parameters.
          """
  
          indices = [int(v, 2) for v in self.primitive.keys()]
          vals = np.array(list(self.primitive.values())) * self.coeff
          spvec = sparse.csr_matrix((vals, (np.zeros(len(indices), dtype=int), indices)),
                                    shape=(1, 2**self.num_qubits))
          return spvec if not self.is_measurement else spvec.transpose()
  
      def to_circuit_op(self) -> OperatorBase:
          """ Return ``StateFnCircuit`` corresponding to this StateFn."""
          from .circuit_state_fn import CircuitStateFn
          csfn = CircuitStateFn.from_dict(self.primitive) * self.coeff  # type: ignore
          return csfn.adjoint() if self.is_measurement else csfn
  
      def __str__(self) -> str:
          prim_str = str(self.primitive)
          if self.coeff == 1.0:
              return "{}({})".format('DictStateFn' if not self.is_measurement
                                     else 'DictMeasurement', prim_str)
          else:
              return "{}({}) * {}".format('DictStateFn' if not self.is_measurement
                                          else 'DictMeasurement',
                                          prim_str,
                                          self.coeff)
  
      # pylint: disable=too-many-return-statements
      def eval(self,
               front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
               ) -> Union[OperatorBase, float, complex]:
          if front is None:
              vector_state_fn = self.to_matrix_op().eval()
              vector_state_fn = cast(OperatorBase, vector_state_fn)
              return vector_state_fn
  
          if not self.is_measurement and isinstance(front, OperatorBase):
              raise ValueError(
                  'Cannot compute overlap with StateFn or Operator if not Measurement. Try taking '
                  'sf.adjoint() first to convert to measurement.')
  
          if isinstance(front, ListOp) and front.distributive:
              return front.combo_fn([self.eval(front.coeff * front_elem)  # type: ignore
                                     for front_elem in front.oplist])
  
          # For now, always do this. If it's not performant, we can be more granular.
          if not isinstance(front, OperatorBase):
              front = StateFn(front)
  
          # pylint: disable=cyclic-import,import-outside-toplevel
          from ..operator_globals import EVAL_SIG_DIGITS
  
          # If the primitive is a lookup of bitstrings,
          # we define all missing strings to have a function value of
          # zero.
          if isinstance(front, DictStateFn):
              return np.round(
                  cast(float, sum([v * front.primitive.get(b, 0) for (b, v) in
                                   self.primitive.items()]) * self.coeff * front.coeff),
                  decimals=EVAL_SIG_DIGITS)
  
          # All remaining possibilities only apply when self.is_measurement is True
  
          if isinstance(front, VectorStateFn):
              # TODO does it need to be this way for measurement?
              # return sum([v * front.primitive.data[int(b, 2)] *
              # np.conj(front.primitive.data[int(b, 2)])
              return np.round(
                  cast(float, sum([v * front.primitive.data[int(b, 2)] for (b, v) in
                                   self.primitive.items()]) * self.coeff),
                  decimals=EVAL_SIG_DIGITS)
  
          from .circuit_state_fn import CircuitStateFn
          if isinstance(front, CircuitStateFn):
              # Don't reimplement logic from CircuitStateFn
              return np.conj(
                  front.adjoint().eval(self.adjoint().primitive)) * self.coeff  # type: ignore
  
          from .operator_state_fn import OperatorStateFn
          if isinstance(front, OperatorStateFn):
              return cast(Union[OperatorBase, float, complex], front.adjoint().eval(self.adjoint()))
  
          # All other OperatorBases go here
          return front.adjoint().eval(self.adjoint().primitive).adjoint() * self.coeff  # type: ignore
  
      def sample(self,
                 shots: int = 1024,
                 massive: bool = False,
                 reverse_endianness: bool = False) -> dict:
          probs = np.square(np.abs(np.array(list(self.primitive.values()))))
          unique, counts = np.unique(algorithm_globals.random.choice(list(self.primitive.keys()),
                                                                     size=shots,
                                                                     p=(probs / sum(probs))),
                                     return_counts=True)
          counts = dict(zip(unique, counts))
          if reverse_endianness:
              scaled_dict = {bstr[::-1]: (prob / shots) for (bstr, prob) in counts.items()}
          else:
              scaled_dict = {bstr: (prob / shots) for (bstr, prob) in counts.items()}
          return dict(sorted(scaled_dict.items(), key=lambda x: x[1], reverse=True))
  