






import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
def      a_ (      _A      ,   _A=0.999      ,   _A="cosine"      ,   )			->			List[str]:







				"""simple docstring"""
				if alpha_transform_type == "cosine":

								def alpha_bar_fn(_A  ):
												return math.cos((t + 0.008) / 1.008 * math.pi / 2  ) ** 2

				elif alpha_transform_type == "exp":

								def alpha_bar_fn(_A  ):
												return math.exp(t * -12.0  )

				else:
								raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}'''  )

				snake_case__									=     []
				for i in range(_A  ):
								snake_case__									=     i / num_diffusion_timesteps
								snake_case__									=     (i + 1) / num_diffusion_timesteps
								betas.append(min(1 - alpha_bar_fn(_A  ) / alpha_bar_fn(_A  )      ,   _A  )  )
				return torch.tensor(_A      ,   dtype=torch.floataa  )


class   __SCREAMING_SNAKE_CASE(	a_    ,  a_	):
							_UpperCAmelCase     =       [e.name for e in KarrasDiffusionSchedulers]
							_UpperCAmelCase     =       2
							@register_to_config
							def __init__(     self:      int       ,	UpperCamelCase:      int = 10_00       ,	UpperCamelCase:      float = 0.00_085       ,	UpperCamelCase:      float = 0.012       ,	UpperCamelCase:      str = "linear"       ,	UpperCamelCase:      Optional[Union[np.ndarray, List[float]]] = None       ,	UpperCamelCase:      str = "epsilon"       ,	UpperCamelCase:      str = "linspace"       ,	UpperCamelCase:      int = 0       ,	)		->		Dict:
											if trained_betas is not None:
															snake_case__									=     torch.tensor(UpperCamelCase       ,	dtype=torch.floataa						)
											elif beta_schedule == "linear":
															snake_case__									=     torch.linspace(UpperCamelCase       ,	UpperCamelCase       ,	UpperCamelCase       ,	dtype=torch.floataa						)
											elif beta_schedule == "scaled_linear":
															# this schedule is very specific to the latent diffusion model.
															snake_case__									=     (
															    torch.linspace(beta_start**0.5       ,	beta_end**0.5       ,	UpperCamelCase       ,	dtype=torch.floataa						) ** 2
															)
											elif beta_schedule == "squaredcos_cap_v2":
															# Glide cosine schedule
															snake_case__									=     betas_for_alpha_bar(UpperCamelCase						)
											else:
															raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''						)

											snake_case__									=     1.0 - self.betas
											snake_case__									=     torch.cumprod(self.alphas       ,	dim=0						)

											#  set all values
											self.set_timesteps(UpperCamelCase       ,	UpperCamelCase       ,	UpperCamelCase						)
							def lowerCAmelCase_ (     self:      Optional[int]       ,	UpperCamelCase:      Dict       ,	UpperCamelCase:      Any=None						)		->		Optional[Any]:
											if schedule_timesteps is None:
															snake_case__									=     self.timesteps

											snake_case__									=     (schedule_timesteps == timestep).nonzero()

											# The sigma index that is taken for the **very** first `step`
											# is always the second index (or the last index if there is only 1)
											# This way we can ensure we don't accidentally skip a sigma in
											# case we start in the middle of the denoising schedule (e.g. for image-to-image)
											if len(self._index_counter						) == 0:
															snake_case__									=     1 if len(UpperCamelCase						) > 1 else 0
											else:
															snake_case__									=     timestep.cpu().item() if torch.is_tensor(UpperCamelCase						) else timestep
															snake_case__									=     self._index_counter[timestep_int]

											return indices[pos].item()
							@property
							def lowerCAmelCase_ (     self:      Any						)		->		str:
											# standard deviation of the initial noise distribution
											if self.config.timestep_spacing in ["linspace", "trailing"]:
															return self.sigmas.max()

											return (self.sigmas.max() ** 2 + 1) ** 0.5
							def lowerCAmelCase_ (     self:      str       ,	UpperCamelCase:      torch.FloatTensor       ,	UpperCamelCase:      Union[float, torch.FloatTensor]       ,	)		->		torch.FloatTensor:
											snake_case__									=     self.index_for_timestep(UpperCamelCase						)

											if self.state_in_first_order:
															snake_case__									=     self.sigmas[step_index]
											else:
															snake_case__									=     self.sigmas_interpol[step_index]

											snake_case__									=     sample / ((sigma**2 + 1) ** 0.5)
											return sample
							def lowerCAmelCase_ (     self:      Dict       ,	UpperCamelCase:      int       ,	UpperCamelCase:      Union[str, torch.device] = None       ,	UpperCamelCase:      Optional[int] = None       ,	)		->		Dict:
											snake_case__									=     num_inference_steps

											snake_case__									=     num_train_timesteps or self.config.num_train_timesteps

											# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
											if self.config.timestep_spacing == "linspace":
															snake_case__									=     np.linspace(0       ,	num_train_timesteps - 1       ,	UpperCamelCase       ,	dtype=UpperCamelCase						)[::-1].copy()
											elif self.config.timestep_spacing == "leading":
															snake_case__									=     num_train_timesteps // self.num_inference_steps
															# creates integer timesteps by multiplying by ratio
															# casting to int to avoid issues when num_inference_step is power of 3
															snake_case__									=     (np.arange(0       ,	UpperCamelCase						) * step_ratio).round()[::-1].copy().astype(UpperCamelCase						)
															timesteps += self.config.steps_offset
											elif self.config.timestep_spacing == "trailing":
															snake_case__									=     num_train_timesteps / self.num_inference_steps
															# creates integer timesteps by multiplying by ratio
															# casting to int to avoid issues when num_inference_step is power of 3
															snake_case__									=     (np.arange(UpperCamelCase       ,	0       ,	-step_ratio						)).round().copy().astype(UpperCamelCase						)
															timesteps -= 1
											else:
															raise ValueError(
															    F'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''						)

											snake_case__									=     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
											snake_case__									=     torch.from_numpy(np.log(UpperCamelCase						)						).to(UpperCamelCase						)

											snake_case__									=     np.interp(UpperCamelCase       ,	np.arange(0       ,	len(UpperCamelCase						)						)       ,	UpperCamelCase						)
											snake_case__									=     np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
											snake_case__									=     torch.from_numpy(UpperCamelCase						).to(device=UpperCamelCase						)

											# interpolate sigmas
											snake_case__									=     sigmas.log().lerp(sigmas.roll(1						).log()       ,	0.5						).exp()

											snake_case__									=     torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2						), sigmas[-1:]]						)
											snake_case__									=     torch.cat(
											    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2						), sigmas_interpol[-1:]]						)

											if str(UpperCamelCase						).startswith('mps'						):
															# mps does not support float64
															snake_case__									=     torch.from_numpy(UpperCamelCase						).to(UpperCamelCase       ,	dtype=torch.floataa						)
											else:
															snake_case__									=     torch.from_numpy(UpperCamelCase						).to(UpperCamelCase						)

											# interpolate timesteps
											snake_case__									=     self.sigma_to_t(UpperCamelCase						).to(UpperCamelCase       ,	dtype=timesteps.dtype						)
											snake_case__									=     torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])       ,	dim=-1						).flatten()

											snake_case__									=     torch.cat([timesteps[:1], interleaved_timesteps]						)

											snake_case__									=     None

											# for exp beta schedules, such as the one for `pipeline_shap_e.py`
											# we need an index counter
											snake_case__									=     defaultdict(UpperCamelCase						)
							def lowerCAmelCase_ (     self:      Union[str, Any]       ,	UpperCamelCase:      Optional[int]						)		->		Tuple:
											# get log sigma
											snake_case__									=     sigma.log()

											# get distribution
											snake_case__									=     log_sigma - self.log_sigmas[:, None]

											# get sigmas range
											snake_case__									=     dists.ge(0						).cumsum(dim=0						).argmax(dim=0						).clamp(max=self.log_sigmas.shape[0] - 2						)
											snake_case__									=     low_idx + 1

											snake_case__									=     self.log_sigmas[low_idx]
											snake_case__									=     self.log_sigmas[high_idx]

											# interpolate sigmas
											snake_case__									=     (low - log_sigma) / (low - high)
											snake_case__									=     w.clamp(0       ,	1						)

											# transform interpolation to time range
											snake_case__									=     (1 - w) * low_idx + w * high_idx
											snake_case__									=     t.view(sigma.shape						)
											return t
							@property
							def lowerCAmelCase_ (     self:      str						)		->		str:
											return self.sample is None
							def lowerCAmelCase_ (     self:      Tuple       ,	UpperCamelCase:      Union[torch.FloatTensor, np.ndarray]       ,	UpperCamelCase:      Union[float, torch.FloatTensor]       ,	UpperCamelCase:      Union[torch.FloatTensor, np.ndarray]       ,	UpperCamelCase:      bool = True       ,	)		->		Union[SchedulerOutput, Tuple]:
											snake_case__									=     self.index_for_timestep(UpperCamelCase						)

											# advance index counter by 1
											snake_case__									=     timestep.cpu().item() if torch.is_tensor(UpperCamelCase						) else timestep
											self._index_counter[timestep_int] += 1

											if self.state_in_first_order:
															snake_case__									=     self.sigmas[step_index]
															snake_case__									=     self.sigmas_interpol[step_index + 1]
															snake_case__									=     self.sigmas[step_index + 1]
											else:
															# 2nd order / KDPM2's method
															snake_case__									=     self.sigmas[step_index - 1]
															snake_case__									=     self.sigmas_interpol[step_index]
															snake_case__									=     self.sigmas[step_index]

											# currently only gamma=0 is supported. This usually works best anyways.
											# We can support gamma in the future but then need to scale the timestep before
											# passing it to the model which requires a change in API
											snake_case__									=     0
											snake_case__									=     sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

											# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
											if self.config.prediction_type == "epsilon":
															snake_case__									=     sigma_hat if self.state_in_first_order else sigma_interpol
															snake_case__									=     sample - sigma_input * model_output
											elif self.config.prediction_type == "v_prediction":
															snake_case__									=     sigma_hat if self.state_in_first_order else sigma_interpol
															snake_case__									=     model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
															    sample / (sigma_input**2 + 1)
															)
											elif self.config.prediction_type == "sample":
															raise NotImplementedError('prediction_type not implemented yet: sample'						)
											else:
															raise ValueError(
															    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''						)

											if self.state_in_first_order:
															# 2. Convert to an ODE derivative for 1st order
															snake_case__									=     (sample - pred_original_sample) / sigma_hat
															# 3. delta timestep
															snake_case__									=     sigma_interpol - sigma_hat

															# store for 2nd order step
															snake_case__									=     sample
											else:
															# DPM-Solver-2
															# 2. Convert to an ODE derivative for 2nd order
															snake_case__									=     (sample - pred_original_sample) / sigma_interpol

															# 3. delta timestep
															snake_case__									=     sigma_next - sigma_hat

															snake_case__									=     self.sample
															snake_case__									=     None

											snake_case__									=     sample + derivative * dt

											if not return_dict:
															return (prev_sample,)

											return SchedulerOutput(prev_sample=UpperCamelCase						)
							def lowerCAmelCase_ (     self:      List[Any]       ,	UpperCamelCase:      torch.FloatTensor       ,	UpperCamelCase:      torch.FloatTensor       ,	UpperCamelCase:      torch.FloatTensor       ,	)		->		torch.FloatTensor:
											# Make sure sigmas and timesteps have the same device and dtype as original_samples
											snake_case__									=     self.sigmas.to(device=original_samples.device       ,	dtype=original_samples.dtype						)
											if original_samples.device.type == "mps" and torch.is_floating_point(UpperCamelCase						):
															# mps does not support float64
															snake_case__									=     self.timesteps.to(original_samples.device       ,	dtype=torch.floataa						)
															snake_case__									=     timesteps.to(original_samples.device       ,	dtype=torch.floataa						)
											else:
															snake_case__									=     self.timesteps.to(original_samples.device						)
															snake_case__									=     timesteps.to(original_samples.device						)

											snake_case__									=     [self.index_for_timestep(UpperCamelCase       ,	UpperCamelCase						) for t in timesteps]

											snake_case__									=     sigmas[step_indices].flatten()
											while len(sigma.shape						) < len(original_samples.shape						):
															snake_case__									=     sigma.unsqueeze(-1						)

											snake_case__									=     original_samples + noise * sigma
											return noisy_samples


							def __len__(     self:      str						)		->		Any:
											return self.config.num_train_timesteps












import qiskit
def      a_ (      _A = 2  )			->			qiskit.result.counts.Counts:







				"""simple docstring"""
				snake_case__									=     qubits

				# Using Aer's simulator
				snake_case__									=     qiskit.Aer.get_backend('aer_simulator'  )

				# Creating a Quantum Circuit acting on the q register
				snake_case__									=     qiskit.QuantumCircuit(_A      ,   _A  )

				# Adding a H gate on qubit 0 (now q0 in superposition)
				circuit.h(0  )

				for i in range(1      ,   _A  ):
								# Adding CX (CNOT) gate
								circuit.cx(i - 1      ,   _A  )

				# Mapping the quantum measurement to the classical bits
				circuit.measure(list(range(_A  )  )      ,   list(range(_A  )  )  )

				# Now measuring any one qubit would affect other qubits to collapse
				# their super position and have same state as the measured one.

				# Executing the circuit on the simulator
				snake_case__									=     qiskit.execute(_A      ,   _A      ,   shots=1000  )

				return job.result().get_counts(_A  )


if __name__ == "__main__":
							print(f'''Total count for various states are: {quantum_entanglement(3)}''')




