code: 
  
  
  
  
  
  '''simple docstring'''
  
  import qiskit
  from qiskit.providers import Backend
  
  
  
  
  
  def lowerCamelCase		(  __lowerCamelCase				:					int      , __lowerCamelCase				:					int					)		->tuple[qiskit.QuantumCircuit, str, str]:
      _SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE             =    bin(__lowerCamelCase					)[2:], bin(__lowerCamelCase					)[2:]  # Remove leading '0b'
  
      # Ensure that both strings are of the same length
      if len(__lowerCamelCase					) > len(__lowerCamelCase					):
          _SCREAMING_SNAKE_CASE             =    y.zfill(len(__lowerCamelCase					)					)
      else:
          _SCREAMING_SNAKE_CASE             =    x.zfill(len(__lowerCamelCase					)					)
  
      # We need (3 * number of bits in the larger number)+1 qBits
      # The second parameter is the number of classical registers, to measure the result
      _SCREAMING_SNAKE_CASE             =    qiskit.QuantumCircuit((len(__lowerCamelCase					) * 3) + 1      , len(__lowerCamelCase					) + 1					)
  
      # We are essentially "not-ing" the bits that are 1
      # Reversed because it's easier to perform ops on more significant bits
      for i in range(len(__lowerCamelCase					)					):
          if x[::-1][i] == "1":
              circuit.x(__lowerCamelCase					)
      for j in range(len(__lowerCamelCase					)					):
          if y[::-1][j] == "1":
              circuit.x(len(__lowerCamelCase					) + j					)
  
      return circuit, x, y
  
  
  
  
  
  def lowerCamelCase		(  __lowerCamelCase				:					qiskit.QuantumCircuit      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , )		->Optional[Any]:
      circuit.ccx(__lowerCamelCase      , __lowerCamelCase      , __lowerCamelCase					)
      circuit.cx(__lowerCamelCase      , __lowerCamelCase					)
      circuit.ccx(__lowerCamelCase      , __lowerCamelCase      , __lowerCamelCase					)
      circuit.cx(__lowerCamelCase      , __lowerCamelCase					)
      circuit.cx(__lowerCamelCase      , __lowerCamelCase					)
  
  
  
  
  
  def lowerCamelCase		(  __lowerCamelCase				:					int      , __lowerCamelCase				:					int      , __lowerCamelCase				:					Backend = qiskit.Aer.get_backend("""aer_simulator"""					)      , )		->int:
  
      if vala < 0 or vala < 0:
          raise ValueError("""Both Integers must be positive!"""					)
  
      # Store the Integers
      _SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE             =    store_two_classics(__lowerCamelCase      , __lowerCamelCase					)
      for i in range(len(__lowerCamelCase					)					):
          full_adder(__lowerCamelCase      , __lowerCamelCase      , len(__lowerCamelCase					) + i      , len(__lowerCamelCase					) + len(__lowerCamelCase					) + i      , len(__lowerCamelCase					) + len(__lowerCamelCase					) + i + 1					)
          circuit.barrier()  # Optional, just for aesthetics
  
      # Measure the resultant qBits
      for i in range(len(__lowerCamelCase					) + 1					):
          circuit.measure([(len(__lowerCamelCase					) * 2) + i]      , [i]					)
  
      _SCREAMING_SNAKE_CASE             =    qiskit.execute(__lowerCamelCase      , __lowerCamelCase      , shots=1					).result()
  
      # The result is in binary. Convert it back to int
      return int(list(res.get_counts()					)[0]      , 2					)
  
  
  if __name__ == "__main__":
        import doctest
  
        doctest.testmod()
  
  
  
  
style_context: 
  
  
  
  
  
  '''simple docstring'''
  
  # DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
  # and https://github.com/hojonathanho/diffusion
  
  from dataclasses import dataclass
  from typing import Optional, Tuple, Union
  
  import flax
  import jax.numpy as jnp
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from .scheduling_utils_flax import (
      CommonSchedulerState,
      FlaxKarrasDiffusionSchedulers,
      FlaxSchedulerMixin,
      FlaxSchedulerOutput,
      add_noise_common,
      get_velocity_common,
  )
  
  
  @flax.struct.dataclass
  class       a_  :
  
      '''simple docstring'''
      UpperCamelCase									=				42
      UpperCamelCase									=				42
  
      # setable values
      UpperCamelCase									=				42
      UpperCamelCase									=				42
      UpperCamelCase									=				None
  
  
      @classmethod
      def     snake_case_(	cls				,	A				,	A				,	A				,	A				,	)	->     List[Any]:
          return cls(
              common=A				,	final_alpha_cumprod=A				,	init_noise_sigma=A				,	timesteps=A				,	)
  
  
  
  
  @dataclass
  class       a_  (       snake_case_ ):
  
      '''simple docstring'''
      UpperCamelCase									=				42
  
  
  
  
  class       a_  (       snake_case_   ,					snake_case_ ):
  
      '''simple docstring'''
      UpperCamelCase									=				[e.name for e in FlaxKarrasDiffusionSchedulers]
  
      UpperCamelCase									=				42
  
  
      @property
      def     snake_case_(	self )	->     List[Any]:
          return True
  
  
      @register_to_config
      def __init__(	self				,	A = 1000				,	A = 0.0001				,	A = 0.02				,	A = "linear"				,	A = None				,	A = True				,	A = 0				,	A = "epsilon"				,	A = jnp.floataa				,	)	->     int:
          _SCREAMING_SNAKE_CASE             =    dtype
  
  
      def     snake_case_(	self				,	A = None )	->     DDIMSchedulerState:
          if common is None:
              _SCREAMING_SNAKE_CASE             =    CommonSchedulerState.create(self )
  
          # At every step in ddim, we are looking into the previous alphas_cumprod
          # For the final step, there is no previous alphas_cumprod because we are already at 0
          # `set_alpha_to_one` decides whether we set this parameter simply to one or
          # whether we use the final alpha of the "non-previous" one.
          _SCREAMING_SNAKE_CASE             =    (
              jnp.array(1.0				,	dtype=self.dtype ) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
          )
  
          # standard deviation of the initial noise distribution
          _SCREAMING_SNAKE_CASE             =    jnp.array(1.0				,	dtype=self.dtype )
  
          _SCREAMING_SNAKE_CASE             =    jnp.arange(0				,	self.config.num_train_timesteps ).round()[::-1]
  
          return DDIMSchedulerState.create(
              common=A				,	final_alpha_cumprod=A				,	init_noise_sigma=A				,	timesteps=A				,	)
  
  
      def     snake_case_(	self				,	A				,	A				,	A = None )	->     jnp.ndarray:
          return sample
  
  
      def     snake_case_(	self				,	A				,	A				,	A = () )	->     DDIMSchedulerState:
          _SCREAMING_SNAKE_CASE             =    self.config.num_train_timesteps // num_inference_steps
          # creates integer timesteps by multiplying by ratio
          # rounding to avoid issues when num_inference_step is power of 3
          _SCREAMING_SNAKE_CASE             =    (jnp.arange(0				,	A ) * step_ratio).round()[::-1] + self.config.steps_offset
  
          return state.replace(
              num_inference_steps=A				,	timesteps=A				,	)
  
  
      def     snake_case_(	self				,	A				,	A				,	A )	->     int:
          _SCREAMING_SNAKE_CASE             =    state.common.alphas_cumprod[timestep]
          _SCREAMING_SNAKE_CASE             =    jnp.where(
              prev_timestep >= 0				,	state.common.alphas_cumprod[prev_timestep]				,	state.final_alpha_cumprod )
          _SCREAMING_SNAKE_CASE             =    1 - alpha_prod_t
          _SCREAMING_SNAKE_CASE             =    1 - alpha_prod_t_prev
  
          _SCREAMING_SNAKE_CASE             =    (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
  
          return variance
  
  
      def     snake_case_(	self				,	A				,	A				,	A				,	A				,	A = 0.0				,	A = True				,	)	->     Union[FlaxDDIMSchedulerOutput, Tuple]:
          if state.num_inference_steps is None:
              raise ValueError(
                  """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler""" )
  
          # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
          # Ideally, read DDIM paper in-detail understanding
  
          # Notation (<variable name> -> <name in paper>
          # - pred_noise_t -> e_theta(x_t, t)
          # - pred_original_sample -> f_theta(x_t, t) or x_0
          # - std_dev_t -> sigma_t
          # - eta -> η
          # - pred_sample_direction -> "direction pointing to x_t"
          # - pred_prev_sample -> "x_t-1"
  
          # 1. get previous step value (=t-1)
          _SCREAMING_SNAKE_CASE             =    timestep - self.config.num_train_timesteps // state.num_inference_steps
  
          _SCREAMING_SNAKE_CASE             =    state.common.alphas_cumprod
          _SCREAMING_SNAKE_CASE             =    state.final_alpha_cumprod
  
          # 2. compute alphas, betas
          _SCREAMING_SNAKE_CASE             =    alphas_cumprod[timestep]
          _SCREAMING_SNAKE_CASE             =    jnp.where(prev_timestep >= 0				,	alphas_cumprod[prev_timestep]				,	A )
  
          _SCREAMING_SNAKE_CASE             =    1 - alpha_prod_t
  
          # 3. compute predicted original sample from predicted noise also called
          # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          if self.config.prediction_type == "epsilon":
              _SCREAMING_SNAKE_CASE             =    (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
              _SCREAMING_SNAKE_CASE             =    model_output
          elif self.config.prediction_type == "sample":
              _SCREAMING_SNAKE_CASE             =    model_output
              _SCREAMING_SNAKE_CASE             =    (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
          elif self.config.prediction_type == "v_prediction":
              _SCREAMING_SNAKE_CASE             =    (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
              _SCREAMING_SNAKE_CASE             =    (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
          else:
              raise ValueError(
                  f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or'
                  """ `v_prediction`""" )
  
          # 4. compute variance: "sigma_t(η)" -> see formula (16)
          # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
          _SCREAMING_SNAKE_CASE             =    self._get_variance(A				,	A				,	A )
          _SCREAMING_SNAKE_CASE             =    eta * variance ** 0.5
  
          # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          _SCREAMING_SNAKE_CASE             =    (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon
  
          # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
          _SCREAMING_SNAKE_CASE             =    alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction
  
          if not return_dict:
              return (prev_sample, state)
  
          return FlaxDDIMSchedulerOutput(prev_sample=A				,	state=A )
  
  
      def     snake_case_(	self				,	A				,	A				,	A				,	A				,	)	->     jnp.ndarray:
          return add_noise_common(state.common				,	A				,	A				,	A )
  
  
      def     snake_case_(	self				,	A				,	A				,	A				,	A				,	)	->     jnp.ndarray:
          return get_velocity_common(state.common				,	A				,	A				,	A )
  
  
  
  
  
      def __len__(	self )	->     Any:
          return self.config.num_train_timesteps
  
  
  
  