from abc import abstractmethod
from typing import List, Tuple, Union
import numpy as np
import cvxpy as cp
from cvxpy.expressions.variable import Variable as CvxpyVariable
from cvxpy.expressions.expression import Expression as CvxpyExpression
from quara.objects.composite_system import CompositeSystem
from quara.loss_function.loss_function import (
LossFunction,
LossFunctionOption,
)
from quara.protocol.qtomography.standard.standard_qtomography import StandardQTomography
from quara.protocol.qtomography.standard.preprocessing import (
extract_nums_from_empi_dists,
extract_prob_dists_from_empi_dists,
calc_total_num,
calc_num_ratios,
type_standard_qtomography,
)
from quara.math.probability import validate_prob_dist
[docs]class CvxpyLossFunctionOption(LossFunctionOption):
def __init__(self, eps_prob_zero: np.float64 = 1e-12):
"""Constructor
Parameters
----------
eps_prob_zero : np.float64, optional
Threshold to truncate probability, by default 1e-12
"""
super().__init__()
self._eps_prob_zero = eps_prob_zero
@property
def eps_prob_zero(self) -> np.float64:
"""returns threshold to truncate probability
Returns
-------
np.float64
Threshold to truncate probability
"""
return self._eps_prob_zero
[docs]class CvxpyLossFunction(LossFunction):
def __init__(self, num_var: int = None):
"""Constructor
Parameters
----------
num_var : int, optional
number of variables, by default None
"""
super().__init__(num_var)
self._on_value = False
self._on_value_cvxpy: bool = False
self._eps_prob_zero = 1e-12
self._nums_data = None
self._num_data_total = None
self._num_data_ratios = None
self._prob_dists_data = None
self._on_prob_dists_data = False
self._sqt = None
self._type_estimate = None
self._option = None
@property
def on_value_cvxpy(self) -> bool:
"""returns whether or not to support value_cvxpy.
Returns
-------
bool
whether or not to support value_cvxpy.
"""
return self._on_value_cvxpy
@property
def eps_prob_zero(self) -> np.float64:
"""returns threshold to truncate probability
Returns
-------
np.float64
Threshold to truncate probability
"""
return self._eps_prob_zero
[docs] def set_from_option(self, option: CvxpyLossFunctionOption) -> None:
"""sets option from CvxpyLossFunctionOption.
Parameters
----------
option : CvxpyLossFunctionOption
option to set.
"""
self._eps_prob_zero = option.eps_prob_zero
self._option = option
@property
def sqt(self) -> StandardQTomography:
"""returns StandardQTomography for settings of loss function.
Returns
-------
StandardQTomography
StandardQTomography for settings of loss function.
"""
return self._sqt
[docs] def set_standard_qtomography(self, sqt: StandardQTomography) -> None:
"""sets StandardQTomography for settings of loss function.
Parameters
----------
sqt : StandardQTomography
StandardQTomography for settings of loss function.
Raises
------
ValueError
on_para_eq_constraint of StandardQTomography is False.
"""
if sqt.on_para_eq_constraint == False:
raise ValueError(
f"on_para_eq_constraint of StandardQTomography must be True."
)
self._sqt = sqt
self._type_estimate = type_standard_qtomography(sqt)
self._on_value = True
self._num_var = sqt.num_variables
@property
def type_estimate(self) -> str:
"""returns Type of QOperation. "state", "povm", "gate", or "mprocess".
type_estimate is set in `set_standard_qtomography` function.
Returns
-------
str
Type of QOperation.
"""
return self._type_estimate
@property
def nums_data(self) -> List[int]:
"""returns numbers of data.
nums_data is set in `set_prob_dists_data_from_empi_dists` function.
Returns
-------
List[int]
numbers of data.
"""
return self._nums_data
@property
def num_data_total(self) -> int:
"""returns number of total of data(sum of data).
num_data_total is set in `set_prob_dists_data_from_empi_dists` function.
Returns
-------
int
number of total of data.
"""
return self._num_data_total
@property
def num_data_ratios(self) -> List[np.float64]:
"""returns ratios of data.
num_data_ratios is set in `set_prob_dists_data_from_empi_dists` function.
Returns
-------
List[np.float64]
ratios of data.
"""
return self._num_data_ratios
[docs] def calc_average_num_data(self) -> np.float64:
"""calculates average of numbers of data.
Returns
-------
np.float64
average of numbers of data.
"""
arr = np.array(self.nums_data)
num_ave = np.mean(arr)
return num_ave
@property
def prob_dists_data(self) -> List[np.ndarray]:
"""returns probability distributions of data.
Returns
-------
List[np.ndarray]
probability distributions of data.
"""
return self._prob_dists_data
@property
def on_prob_dists_data(self) -> bool:
"""returns whether prob_dists_data is set.
Returns
-------
bool
whether prob_dists_data is set.
"""
return self._on_prob_dists_data
[docs] def set_prob_dists_data(self, ps: List[np.ndarray]) -> None:
"""sets probability distributions of data.
Parameters
----------
ps : List[np.ndarray]
probability distributions of data.
"""
q = ps
for i, pi in enumerate(ps):
validate_prob_dist(pi, eps=self.eps_prob_zero)
for x, pi_x in enumerate(pi):
if pi_x < self.eps_prob_zero:
q[i][x] = 0
elif pi_x > 1.0:
q[i][x] = 1
self._prob_dists_data = q
self._on_prob_dists_data = True
[docs] def erase_prob_dists_data(self) -> None:
"""erases probability distributions of data."""
self._prob_dists_data = None
self._on_prob_dists_data = False
[docs] def calc_prob_model(
self, i: int, x: int, var: Union[np.ndarray, CvxpyVariable]
) -> Union[np.float64, CvxpyExpression]:
"""calculates probability model.
Parameters
----------
i : int
schedule index.
x : int
measurement outcome index.
var : Union[np.ndarray, CvxpyVariable]
Variable of CVXPY
Returns
-------
Union[np.float64, CvxpyExpression]
probability model.
"""
pi_x = (
self.sqt.get_coeffs_1st_mat(i)[x] @ var + self.sqt.get_coeffs_0th_vec(i)[x]
)
return pi_x
[docs] def set_prob_dists_data_from_empi_dists(
self, empi_dists: List[Tuple[int, np.ndarray]]
) -> None:
"""sets probability distributions of data from empirical distributions.
Parameters
----------
empi_dists : List[Tuple[int, np.ndarray]]
empirical distributions.
"""
self._nums_data = extract_nums_from_empi_dists(empi_dists)
self._num_data_total = calc_total_num(self.nums_data)
self._num_data_ratios = calc_num_ratios(self.nums_data)
q = extract_prob_dists_from_empi_dists(empi_dists)
self.set_prob_dists_data(q)
@property
def composite_system(self) -> CompositeSystem:
"""returns CompositeSystem of type of estimate.
composite_system is set in `set_standard_qtomography` function.
Returns
-------
CompositeSystem
CompositeSystem of type of estimate
"""
t = self.type_estimate
if t == "state":
c_sys = self.sqt._experiment.povms[0]._composite_system
elif t == "povm":
c_sys = self.sqt._experiment.states[0]._composite_system
elif t == "gate":
c_sys = self.sqt._experiment.povms[0]._composite_system
elif t == "mprocess":
c_sys = self.sqt._experiment.povms[0]._composite_system
else:
c_sys = None
return c_sys
[docs] def dim_system(self) -> int:
"""returns dimension of CompositeSystem.
dim_system is set in `set_standard_qtomography` function.
Returns
-------
int
dimension of CompositeSystem.
"""
if self.composite_system is None:
return None
else:
return self.composite_system.dim
[docs] def num_outcomes_estimate(self) -> int:
"""returns number of outcomes of estimate.
num_outcomes_estimate is set in `set_standard_qtomography` function.
Returns
-------
int
number of outcomes of estimate.
Raises
------
ValueError
num_outcomes_estimate of StandardQTomography is neither 'povm' nor 'mprocess'.
"""
if self.type_estimate == "povm" or self.type_estimate == "mprocess":
return self.sqt.num_outcomes_estimate
else:
raise ValueError(
f"num_outcomes_estimate function is supported if type_estimate = 'povm' or 'mprocess'. type_estimate={self.type_estimate}"
)
[docs] def value(self, var: np.ndarray) -> np.float64:
"""returns the value of the loss function.
Parameters
----------
var : np.ndarray
np.ndarray of variables.
Returns
-------
np.float64
the value of the loss function.
"""
cvxvar = CvxpyVariable(len(var))
cvxvar.value = var
cvxval = self.value_cvxpy(cvxvar)
return cvxval.value
[docs] @abstractmethod
def value_cvxpy(self, var: CvxpyVariable) -> CvxpyExpression:
"""returns CvxpyExpression of the loss function.
Parameters
----------
var : CvxpyVariable
Variable of CVXPY
Returns
-------
CvxpyExpression
CvxpyExpression of the loss function.
Raises
------
NotImplementedError
this function does not be implemented in the subclass.
"""
raise NotImplementedError
[docs]class CvxpyRelativeEntropy(CvxpyLossFunction):
def __init__(self):
"""Constructor"""
super().__init__()
self._on_value = True
self._on_value_cvxpy = True
[docs] def is_option_sufficient(self) -> bool:
return True
[docs] def value_cvxpy(self, var: CvxpyVariable) -> CvxpyExpression:
"""returns the value of the loss function in the form of Expression of CVXPY.
Parameters
----------
var : np.ndarray
np.ndarray of variables.
Returns
-------
CvxpyExpression
the value of the loss function in the form of Expression of CVXPY.
Raises
------
ValueError
prob_dists_data is not set.
"""
if self.on_prob_dists_data is False:
raise ValueError(f"prob_dists_data is not set.")
const = 0.0
for i in range(self.sqt.num_schedules):
t = 0.0
for j in range(self.sqt.num_outcomes(i)):
qi_j = self.prob_dists_data[i][j]
if qi_j > self.eps_prob_zero:
t += qi_j * np.log(qi_j)
ci = self.num_data_ratios[i]
const += ci * t
expr = const
for i in range(self.sqt.num_schedules):
t = 0.0
for j in range(self.sqt.num_outcomes(i)):
qi_j = self.prob_dists_data[i][j]
if qi_j > self.eps_prob_zero:
pi_j = self.calc_prob_model(i, j, var)
t -= qi_j * cp.log(pi_j)
ci = self.num_data_ratios[i]
expr += ci * t
return expr
[docs]class CvxpyApproximateRelativeEntropyWithZeroProbabilityTerm(CvxpyLossFunction):
def __init__(self):
super().__init__()
self._on_value = True
self._on_value_cvxpy = True
[docs] def value_cvxpy(self, var: CvxpyVariable) -> CvxpyExpression:
"""returns the value of the loss function in the form of Expression of CVXPY.
Parameters
----------
var : np.ndarray
np.ndarray of variables.
Returns
-------
CvxpyExpression
the value of the loss function in the form of Expression of CVXPY.
Raises
------
ValueError
prob_dists_data is not set.
"""
if self.on_prob_dists_data is False:
raise ValueError(f"prob_dists_data is not set.")
expr = 0.0
for i in range(self.sqt.num_schedules):
t = 0.0
for j in range(self.sqt.num_outcomes(i)):
qi_j = self.prob_dists_data[i][j]
pi_j = self.calc_prob_model(i, j, var)
if qi_j > self.eps_prob_zero:
t += 0.50 * cp.quad_over_lin(pi_j - qi_j, pi_j)
else:
t += pi_j
ci = self.num_data_ratios[i]
expr += ci * t
return expr