# Copyright (C) Unitary Fund
#
# This source code is licensed under the GPL license (v3) found in the
# LICENSE file in the root directory of this source tree.
"""Classes corresponding to different zero-noise extrapolation methods."""
import warnings
from abc import ABC, abstractmethod
from copy import deepcopy
from typing import (
Any,
Callable,
Dict,
List,
Optional,
Sequence,
Tuple,
Union,
cast,
)
import matplotlib.pyplot as plt
import numpy as np
import numpy.typing as npt
from cirq import Circuit
from matplotlib.figure import Figure
from numpy.lib.polynomial import RankWarning
from scipy.optimize import OptimizeWarning, curve_fit
from mitiq import QPROGRAM, QuantumResult
from mitiq.executor import Executor
from mitiq.interface import accept_any_qprogram_as_input
from mitiq.observable import Observable
from mitiq.zne.scaling import fold_gates_at_random
ExtrapolationResult = Union[
float, # The zero-noise value.
Tuple[
float, # The zero-noise value.
Optional[float], # The (estimated) error on the zero-noise value.
List[float], # Optimal parameters found during fitting.
Optional[np.ndarray], # Covariance of fitting parameters.
Callable[[float], float], # Function that was fit.
],
]
_EXTR_ERR = (
"The extrapolation fit failed to converge."
" The problem may be solved by switching to a more stable"
" extrapolation model such as `LinearFactory`."
)
_EXTR_WARN = (
"The extrapolation fit may be ill-conditioned."
" Likely, more data points are necessary to fit the parameters"
" of the model."
)
DATA_MISSING_ERR = (
"Data is either ill-defined or not enough to evaluate the required"
" information. Please make sure that the 'run' and 'reduce' methods"
" have been called and that enough expectation values have been measured."
)
[docs]
class ConvergenceWarning(Warning):
"""Warning raised by :class:`.Factory` objects when
their `run_classical` method fails to converge.
"""
pass
@accept_any_qprogram_as_input
def _check_circuit_length(circuit: Circuit) -> None:
"""Raises a warning if the circuit is too short."""
if len(list(circuit.all_operations())) < 5:
warnings.warn(
"The input circuit is very short. "
"This may reduce the accuracy of noise scaling."
)
[docs]
def mitiq_curve_fit(
ansatz: Callable[..., float],
scale_factors: Sequence[float],
exp_values: Sequence[float],
init_params: Optional[List[float]] = None,
) -> Tuple[List[float], npt.NDArray[np.float64]]:
"""Fits the ansatz to the (scale factor, expectation value) data using
``scipy.optimize.curve_fit``, returning the optimal parameters and
covariance matrix of the parameters.
Args:
ansatz: The model function used for zero-noise extrapolation. The first
argument is the noise scale variable, the remaining arguments are
the parameters to fit.
scale_factors: The array of noise scale factors.
exp_values: The array of expectation values.
init_params: Initial guess for the parameters. If None, the initial
values are set to 1.
Returns:
The array of optimal parameters and the covariance matrix of the
parameters. If the fit is ill-conditioned, the covariance matrix may
contain np.inf elements.
Raises:
ExtrapolationError: If the extrapolation fit fails.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
"""
try:
with warnings.catch_warnings(record=True) as warn_list:
opt_params, params_cov = curve_fit(
ansatz, scale_factors, exp_values, p0=init_params
)
for warn in warn_list:
# replace OptimizeWarning with ExtrapolationWarning
if warn.category is OptimizeWarning:
warn.category = ExtrapolationWarning
warn.message = _EXTR_WARN
# re-raise all warnings
warnings.warn_explicit(
warn.message, warn.category, warn.filename, warn.lineno
)
except RuntimeError:
raise ExtrapolationError(_EXTR_ERR) from None
return list(opt_params), params_cov
[docs]
def mitiq_polyfit(
scale_factors: Sequence[float],
exp_values: Sequence[float],
deg: int,
weights: Optional[Sequence[float]] = None,
) -> Tuple[List[float], Optional[npt.NDArray[np.float64]]]:
"""Fits the ansatz to the (scale factor, expectation value) data using
``numpy.polyfit``, returning the optimal parameters and covariance matrix
of the parameters.
Args:
scale_factors: The array of noise scale factors.
exp_values: The array of expectation values.
deg: The degree of the polynomial fit.
weights: Optional array of weights for each sampled point.
This is used to make a weighted least squares fit.
Returns:
The optimal parameters and covariance matrix of the parameters.
If there is not enough data to estimate the covariance matrix, it is
returned as None.
Raises:
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
"""
with warnings.catch_warnings(record=True) as warn_list:
try:
opt_params, params_cov = np.polyfit(
scale_factors, exp_values, deg, w=weights, cov=True
)
except (ValueError, np.linalg.LinAlgError):
opt_params = np.polyfit(scale_factors, exp_values, deg, w=weights)
params_cov = None
for warn in warn_list:
# replace RankWarning with ExtrapolationWarning
if warn.category is RankWarning:
warn.category = ExtrapolationWarning
warn.message = _EXTR_WARN
# re-raise all warnings
warnings.warn_explicit(
warn.message, warn.category, warn.filename, warn.lineno
)
return list(opt_params), params_cov
[docs]
class Factory(ABC):
"""Abstract base class which performs the classical parts of zero-noise
extrapolation. This minimally includes:
* scaling circuits,
* sending jobs to execute,
* collecting the results,
* fitting the collected data,
* Extrapolating to the zero-noise limit.
If all scale factors are set a priori, the jobs can be batched. This is
handled by a BatchedFactory.
If the next scale factor depends on the previous history of results,
jobs are run sequentially. This is handled by an AdaptiveFactory.
"""
def __init__(self) -> None:
self._instack: List[Dict[str, float]] = []
self._outstack: List[float] = []
self._opt_params: Optional[List[float]] = None
self._params_cov: Optional[npt.NDArray[np.float64]] = None
self._zne_limit: Optional[float] = None
self._zne_error: Optional[float] = None
self._zne_curve: Optional[Callable[[float], float]] = None
self._already_reduced = False
self._options: Dict[str, Optional[float]] = {}
[docs]
def get_scale_factors(self) -> List[float]:
"""Returns the scale factors at which the factory has computed
expectation values.
"""
return [params.get("scale_factor", 0.0) for params in self._instack]
[docs]
def get_expectation_values(self) -> List[float]:
"""Returns the expectation values computed by the factory."""
return self._outstack
[docs]
def get_optimal_parameters(self) -> List[float]:
"""Returns the optimal model parameters produced by the extrapolation
fit.
"""
if self._opt_params is None:
raise ValueError(DATA_MISSING_ERR)
return self._opt_params
[docs]
def get_parameters_covariance(self) -> npt.NDArray[np.float64]:
"""Returns the covariance matrix of the model parameters produced by
the extrapolation fit.
"""
if self._params_cov is None:
raise ValueError(DATA_MISSING_ERR)
return self._params_cov
[docs]
def get_zero_noise_limit(self) -> float:
"""Returns the last evaluation of the zero-noise limit
computed by the factory. To re-evaluate
its value, the method 'reduce' should be called first.
"""
if self._zne_limit is None:
raise ValueError(DATA_MISSING_ERR)
return self._zne_limit
[docs]
def get_zero_noise_limit_error(self) -> float:
"""Returns the extrapolation error representing the uncertainty
affecting the zero-noise limit. It is deduced by error propagation
from the covariance matrix associated to the fit parameters.
Note: this quantity is only related to the ability of the model
to fit the measured data. Therefore, it may underestimate the
actual error existing between the zero-noise limit and the
true ideal expectation value.
"""
if self._zne_error is None:
raise ValueError(DATA_MISSING_ERR)
return self._zne_error
[docs]
@abstractmethod
def run(
self,
qp: QPROGRAM,
executor: Union[Executor, Callable[..., QuantumResult]],
observable: Optional[Observable] = None,
scale_noise: Callable[
[QPROGRAM, float], QPROGRAM
] = fold_gates_at_random, # type: ignore [has-type]
num_to_average: int = 1,
) -> "Factory":
"""Calls the executor function on noise-scaled quantum circuit and
stores the results.
Args:
qp: Quantum circuit to scale noise in.
executor: A ``mitiq.Executor`` or a function which inputs a (list
of) quantum circuits and outputs a (list of)
``mitiq.QuantumResult`` s.
observable: Observable to compute the expectation value of. If
None, the `executor` must return an expectation value.
Otherwise, the `QuantumResult` returned by `executor` is used
to compute the expectation of the observable.
scale_noise: Function which inputs a quantum circuit and outputs
a noise-scaled quantum circuit.
num_to_average: Number of times the executor function is called
on each noise-scaled quantum circuit.
"""
raise NotImplementedError
[docs]
@abstractmethod
def run_classical(
self,
scale_factor_to_expectation_value: Callable[..., float],
) -> "Factory":
"""Calls the function scale_factor_to_expectation_value at each scale
factor of the factory, and stores the results.
Args:
scale_factor_to_expectation_value: A function which inputs a scale
factor and outputs an expectation value. This does not have to
involve a quantum processor making this a "classical analogue"
of the run method.
"""
raise NotImplementedError
@abstractmethod
def reduce(self) -> float:
raise NotImplementedError
[docs]
def push(
self, instack_val: Dict[str, float], outstack_val: float
) -> "Factory":
"""Appends "instack_val" to "self._instack" and "outstack_val" to
"self._outstack". Each time a new expectation value is computed this
method should be used to update the internal state of the Factory.
"""
if self._already_reduced:
warnings.warn(
"You are pushing new data into a factory object despite its "
".reduce() method has already been called. Please make "
"sure your intention is to append new data to the stack of "
"previous data. Otherwise, the method .reset() can be used "
"to clean the internal state of the factory.",
ExtrapolationWarning,
)
self._instack.append(instack_val)
self._outstack.append(outstack_val)
return self
[docs]
def plot_data(self) -> Figure:
"""Returns a figure which is a scatter plot of (x, y) data where x are
scale factors at which expectation values have been computed, and y are
the associated expectation values.
Returns:
fig: A 2D scatter plot described above.
"""
fig = plt.figure(figsize=(7, 5))
ax = plt.gca()
plt.plot(
self.get_scale_factors(),
self.get_expectation_values(),
"o",
markersize=10,
markeredgecolor="black",
alpha=0.8,
label="Data",
)
ax.grid(True)
plt.xlabel("Noise scale factor")
plt.ylabel("Expectation value")
return fig
[docs]
def plot_fit(self) -> Figure:
"""Returns a figure which plots the experimental data as well as the
best fit curve.
Returns:
fig: A figure which plots the best fit curve as well as the data.
"""
fig = self.plot_data()
smooth_scale_factors = np.linspace(0, self.get_scale_factors()[-1], 20)
smooth_expectations = [
self.get_extrapolation_curve()(scale_factor)
for scale_factor in smooth_scale_factors
]
plt.xlim(left=0)
fig.axes[0].plot(
smooth_scale_factors,
smooth_expectations,
"--",
lw=2,
color="black",
label="Best fit",
)
return fig
[docs]
def reset(self) -> "Factory":
"""Resets the internal state of the Factory."""
self._instack = []
self._outstack = []
self._opt_params = None
self._params_cov = None
self._zne_limit = None
self._zne_error = None
self._already_reduced = False
return self
[docs]
class BatchedFactory(Factory, ABC):
"""Abstract class of a non-adaptive Factory initialized with a
pre-determined set of scale factors.
Specific (non-adaptive) extrapolation algorithms are derived from this
class by defining the `reduce` method.
"""
def __init__(
self,
scale_factors: Sequence[float],
shot_list: Optional[List[int]] = None,
) -> None:
"""Constructs a BatchedFactory.
Args:
scale_factors: Sequence of noise scale factors at which expectation
values should be measured.
shot_list: Optional sequence of integers corresponding to the
number of samples taken for each expectation value. If this
argument is explicitly passed to the factory, it must have the
same length of scale_factors and the executor function must
accept "shots" as a valid keyword argument.
Raises:
ValueError: If the number of scale factors is less than 2.
TypeError: If shot_list is provided and has any non-integer values.
"""
if len(scale_factors) < 2:
raise ValueError("At least 2 scale factors are necessary.")
if shot_list and (
not isinstance(shot_list, Sequence)
or not all([isinstance(shots, int) for shots in shot_list])
):
raise TypeError(
"The optional argument shot_list must be None "
"or a valid iterator of integers."
)
if shot_list and (len(scale_factors) != len(shot_list)):
raise IndexError(
"The arguments scale_factors and shot_list"
" must have the same length."
f" But len(scale_factors) is {len(scale_factors)}"
f" and len(shot_list) is {len(shot_list)}."
)
self._scale_factors = scale_factors
self._shot_list = shot_list
super(BatchedFactory, self).__init__()
[docs]
def reduce(self) -> float:
"""Evaluates the zero-noise limit found by fitting according to
the factory's extrapolation method.
Returns:
The zero-noise limit.
"""
(
self._zne_limit,
self._zne_error,
self._opt_params,
self._params_cov,
self._zne_curve,
) = self.extrapolate( # type: ignore
self.get_scale_factors(),
self.get_expectation_values(),
full_output=True,
**self._options,
)
self._already_reduced = True
return self._zne_limit
[docs]
def run(
self,
qp: QPROGRAM,
executor: Union[Executor, Callable[..., QuantumResult]],
observable: Optional[Observable] = None,
scale_noise: Callable[
[QPROGRAM, float], QPROGRAM
] = fold_gates_at_random, # type: ignore [has-type]
num_to_average: int = 1,
) -> "BatchedFactory":
"""Computes the expectation values at each scale factor and stores them
in the factory. If the executor returns a single expectation value, the
circuits are run sequentially. If the executor is batched and returns
a list of expectation values (one for each circuit), then the circuits
are sent to the backend as a single job. To detect if an executor is
batched, it must be annotated with a return type that is one of the
following:
* Iterable[float]
* List[float]
* Sequence[float]
* Tuple[float]
* numpy.ndarray
Args:
qp: Quantum circuit to run.
executor: A ``mitiq.Executor`` or a function which inputs a (list
of) quantum circuits and outputs a (list of)
``mitiq.QuantumResult`` s.
observable: Observable to compute the expectation value of. If
None, the `executor` must return an expectation value.
Otherwise, the `QuantumResult` returned by `executor` is used
to compute the expectation of the observable.
scale_noise: Noise scaling function.
num_to_average: The number of circuits executed for each noise
scale factor. This parameter can be used to increase the
precision of the "executor" or to average the effect of a
non-deterministic "scale_noise" function.
"""
self.reset()
self._batch_populate_instack()
_check_circuit_length(qp)
# Get all noise-scaled circuits to run.
to_run = self._generate_circuits(qp, scale_noise, num_to_average)
# Run all circuits.
if not isinstance(executor, Executor):
executor = Executor(executor)
# Get the list of keywords associated to each circuit in "to_run".
kwargs_list = self._get_keyword_args(num_to_average)
# If there are different keyword args, run each circuit individually.
# https://stackoverflow.com/questions/1151658/python-hashable-dicts.
class HashableDict(Dict[Any, Any]):
def __hash__(self) -> int: # type: ignore[override]
return hash(tuple(sorted(self.items())))
if len(set(HashableDict(kwargs) for kwargs in kwargs_list)) != 1:
res = []
for circuit, kwargs in zip(to_run, kwargs_list):
res.extend(
executor.evaluate(
circuit, observable, force_run_all=True, **kwargs
)
)
else:
# Else, run all circuits.
res = executor.evaluate(
to_run, observable, force_run_all=True, **kwargs_list[0]
)
# Reshape "res" to have "num_to_average" columns
reshaped = np.array(res).reshape((-1, num_to_average))
# Average the "num_to_average" columns
self._outstack = np.average(reshaped, axis=1).tolist()
return self
[docs]
def run_classical(
self, scale_factor_to_expectation_value: Callable[..., float]
) -> "BatchedFactory":
"""Computes expectation values by calling the input function at each
scale factor.
Args:
scale_factor_to_expectation_value: Function mapping a noise scale
factor to an expectation value. If shot_list is not None,
"shots" must be an argument of this function.
"""
self.reset()
self._batch_populate_instack()
kwargs_list = self._get_keyword_args(num_to_average=1)
self._outstack = [
scale_factor_to_expectation_value(scale_factor, **kwargs)
for scale_factor, kwargs in zip(self._scale_factors, kwargs_list)
]
return self
def _generate_circuits(
self,
circuit: QPROGRAM,
scale_noise: Callable[[QPROGRAM, float], QPROGRAM],
num_to_average: int = 1,
) -> List[QPROGRAM]:
"""Returns all noise-scaled circuits to run.
Args:
circuit: Base circuit to scale noise in.
scale_noise: Noise scaling function.
num_to_average: Number of times to call scale_noise at each scale
factor.
"""
to_run = []
for scale_factor in self.get_scale_factors():
for _ in range(num_to_average):
to_run.append(scale_noise(circuit, scale_factor))
return to_run
def _batch_populate_instack(self) -> None:
"""Populates the instack with all computed values."""
if self._shot_list:
self._instack = [
{"scale_factor": scale, "shots": shots}
for scale, shots in zip(self._scale_factors, self._shot_list)
]
else:
self._instack = [
{"scale_factor": scale} for scale in self._scale_factors
]
def _get_keyword_args(self, num_to_average: int) -> List[Dict[str, Any]]:
"""Returns a list of keyword dictionaries to be used for
executing the circuits generated by the method "_generate_circuits".
Args:
num_to_average: The number of times the same keywords are used
for each scale factor. This should correspond to the number
of circuits executed for each scale factor.
Returns:
The output list of keyword dictionaries.
"""
params = deepcopy(self._instack)
for d in params:
_ = d.pop("scale_factor")
# Repeat each keyword num_to_average times
return [k for k in params for _ in range(num_to_average)]
[docs]
class AdaptiveFactory(Factory, ABC):
"""Abstract class designed to adaptively produce a new noise scaling
parameter based on a historical stack of previous noise scale parameters
("self._instack") and previously estimated expectation values
("self._outstack").
Specific zero-noise extrapolation algorithms which are adaptive are derived
from this class.
"""
[docs]
@abstractmethod
def next(self) -> Dict[str, float]:
"""Returns a dictionary of parameters to execute a circuit at."""
raise NotImplementedError
[docs]
@abstractmethod
def is_converged(self) -> bool:
"""Returns True if all needed expectation values have been computed,
else False.
"""
raise NotImplementedError
[docs]
@abstractmethod
def reduce(self) -> float:
"""Returns the extrapolation to the zero-noise limit."""
raise NotImplementedError
[docs]
def run_classical(
self,
scale_factor_to_expectation_value: Callable[..., float],
max_iterations: int = 100,
) -> "AdaptiveFactory":
"""Evaluates a sequence of expectation values until enough
data is collected (or iterations reach "max_iterations").
Args:
scale_factor_to_expectation_value: Function mapping a noise scale
factor to an expectation value. If shot_list is not None,
"shots" must be an argument of this function.
max_iterations: Maximum number of iterations (optional).
Default: 100.
Raises:
ConvergenceWarning: If iteration loop stops before convergence.
"""
# Reset the instack, outstack, and optimal parameters
self.reset()
counter = 0
while not self.is_converged() and counter < max_iterations:
next_in_params = self.next()
next_exec_params = deepcopy(next_in_params)
# Get next scale factor and remove it from next_exec_params
scale_factor = next_exec_params.pop("scale_factor")
next_expval = scale_factor_to_expectation_value(
scale_factor, **next_exec_params
)
self.push(next_in_params, next_expval)
counter += 1
if counter == max_iterations:
warnings.warn(
"Factory iteration loop stopped before convergence. "
f"Maximum number of iterations ({max_iterations}) "
"was reached.",
ConvergenceWarning,
)
return self
[docs]
def run(
self,
qp: QPROGRAM,
executor: Union[Executor, Callable[..., QuantumResult]],
observable: Optional[Observable] = None,
scale_noise: Callable[
[QPROGRAM, float], QPROGRAM
] = fold_gates_at_random, # type: ignore [has-type]
num_to_average: int = 1,
max_iterations: int = 100,
) -> "AdaptiveFactory":
"""Evaluates a sequence of expectation values by executing quantum
circuits until enough data is collected (or iterations reach
"max_iterations").
Args:
qp: Circuit to mitigate.
executor: A ``mitiq.Executor`` or a function which inputs a (list
of) quantum circuits and outputs a (list of)
``mitiq.QuantumResult`` s.
observable: Observable to compute the expectation value of. If
None, the `executor` must return an expectation value.
Otherwise, the `QuantumResult` returned by `executor` is used
to compute the expectation of the observable.
scale_noise: Function that scales the noise level of a quantum
circuit.
num_to_average: Number of times expectation values are computed by
the executor after each call to scale_noise, then averaged.
max_iterations: Maximum number of iterations (optional).
"""
_check_circuit_length(qp)
if not isinstance(executor, Executor):
executor = Executor(executor)
def scale_factor_to_expectation_value(
scale_factor: float, **exec_params: Any
) -> float:
"""Evaluates the quantum expectation value for a given
scale_factor and other executor parameters."""
to_run = [
scale_noise(qp, scale_factor) for _ in range(num_to_average)
]
expectation_values = executor.evaluate( # type: ignore[union-attr]
to_run, observable, force_run_all=True, **exec_params
)
return cast(float, np.average(expectation_values))
return self.run_classical(
scale_factor_to_expectation_value, max_iterations
)
[docs]
class PolyFactory(BatchedFactory):
"""Factory object implementing a zero-noise extrapolation algorithm based
on a polynomial fit.
Args:
scale_factors: Sequence of noise scale factors at which
expectation values should be measured.
order: Extrapolation order (degree of the polynomial fit).
It cannot exceed len(scale_factors) - 1.
shot_list: Optional sequence of integers corresponding to the number
of samples taken for each expectation value. If this
argument is explicitly passed to the factory, it must have
the same length of scale_factors and the executor function
must accept "shots" as a valid keyword argument.
Raises:
ValueError: If data is not consistent with the extrapolation model.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
Note:
RichardsonFactory and LinearFactory are special cases of PolyFactory.
"""
def __init__(
self,
scale_factors: Sequence[float],
order: int,
shot_list: Optional[List[int]] = None,
) -> None:
"""Instantiates a new object of this Factory class."""
if order > len(scale_factors) - 1:
raise ValueError(
"The extrapolation order cannot exceed len(scale_factors) - 1."
)
super(PolyFactory, self).__init__(scale_factors, shot_list)
self._options = {"order": order}
[docs]
class RichardsonFactory(BatchedFactory):
"""Factory object implementing Richardson extrapolation.
Args:
scale_factors: Sequence of noise scale factors at which
expectation values should be measured.
shot_list: Optional sequence of integers corresponding to the number
of samples taken for each expectation value. If this
argument is explicitly passed to the factory, it must have
the same length of scale_factors and the executor function
must accept "shots" as a valid keyword argument.
Raises:
ValueError: If data is not consistent with the extrapolation model.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
"""
[docs]
class FakeNodesFactory(BatchedFactory):
"""Factory object implementing a modified version [De2020polynomial]_ of
Richardson extrapolation. In this version the original set of scale factors
is mapped to a new set of fake nodes, known as Chebyshev-Lobatto points.
This method may give a better interpolation for particular types of curves
and if the number of scale factors is large (> 10). One should be aware
that, in many other cases, the fake nodes extrapolation method is usually
not superior to standard Richardson extrapolation.
Args:
scale_factors: Sequence of noise scale factors at which
expectation values should be measured.
shot_list: Optional sequence of integers corresponding to the number
of samples taken for each expectation value. If this
argument is explicitly passed to the factory, it must have
the same length of scale_factors and the executor function
must accept "shots" as a valid keyword argument.
Raises:
ValueError: If data is not consistent with the extrapolation model.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
.. [De2020polynomial] : S.De Marchia. F. Marchetti, E.Perracchionea
and D.Poggialia,
"Polynomial interpolation via mapped bases without resampling,"
*Journ of Comp. and App. Math.* **364**, 112347 (2020),
(https://www.sciencedirect.com/science/article/abs/pii/S0377042719303449).
"""
@staticmethod
def _map_to_fake_nodes(
x: Sequence[float], a: float, b: float
) -> Sequence[float]:
"""
A function that maps inputs to Chebyshev-Lobatto points. Based on
the function [De2020polynomial]_:
S(x) = (a - b)/2 * cos(pi * (x - a)/(b - a)) + (a + b)/2.
Where a and b are the endpoints of the interval [a, b] of CL points
we are mapping to.
Args:
x: Sequence[float]: Set of values to be mapped to CL points.
a: A float representing the interval starting at a.
b: A float representing the interval ending at b.
Returns:
A new sequence of fake nodes (Chebyshev-Lobatto points).
.. [De2020polynomial]: S.De Marchia. F. Marchetti, E.Perracchionea
and D.Poggialia,
"Polynomial interpolation via mapped bases without resampling,"
*Journ of Comp. and App. Math.* **364**, 112347 (2020),
(https://www.sciencedirect.com/science/article/abs/pii/S0377042719303449).
"""
# The mapping function
def mapping(_x: float) -> float:
return (a - b) / 2 * np.cos(np.pi * (_x - a) / (b - a)) + (
a + b
) / 2
return [mapping(y) for y in x]
@staticmethod
def _is_equally_spaced(arr: Sequence[float]) -> bool:
"""Checks if the sequence is equally spaced."""
diff_arr = np.diff(np.sort(arr))
return np.allclose(diff_arr, diff_arr[0])
[docs]
class LinearFactory(BatchedFactory):
"""
Factory object implementing zero-noise extrapolation based
on a linear fit.
Args:
scale_factors: Sequence of noise scale factors at which
expectation values should be measured.
shot_list: Optional sequence of integers corresponding to the number
of samples taken for each expectation value. If this
argument is explicitly passed to the factory, it must have
the same length of scale_factors and the executor function
must accept "shots" as a valid keyword argument.
Raises:
ValueError: If data is not consistent with the extrapolation model.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
"""
[docs]
class ExpFactory(BatchedFactory):
"""
Factory object implementing a zero-noise extrapolation algorithm assuming
an exponential ansatz y(x) = a + b * exp(-c * x), with c > 0.
If y(x->inf) is unknown, the ansatz y(x) is fitted with a non-linear
optimization.
If y(x->inf) is given and avoid_log=False, the exponential
model is mapped into a linear model by a logarithmic transformation.
Args:
scale_factors: Sequence of noise scale factors at which expectation
values should be measured.
asymptote: Infinite-noise limit (optional argument).
avoid_log: If set to True, the exponential model is not linearized
with a logarithm and a non-linear fit is applied even if asymptote
is not None. The default value is False.
shot_list: Optional sequence of integers corresponding to the number
of samples taken for each expectation value. If this argument is
explicitly passed to the factory, it must have the same length of
scale_factors and the executor function must accept "shots" as a
valid keyword argument.
Raises:
ValueError: If data is not consistent with the extrapolation model.
ExtrapolationError: If the extrapolation fit fails.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
"""
def __init__(
self,
scale_factors: Sequence[float],
asymptote: Optional[float] = None,
avoid_log: bool = False,
shot_list: Optional[List[int]] = None,
) -> None:
"""Instantiate an new object of this Factory class."""
super(ExpFactory, self).__init__(scale_factors, shot_list)
if not (asymptote is None or isinstance(asymptote, float)):
raise ValueError(
"The argument 'asymptote' must be either a float or None"
)
self._options = {
"asymptote": asymptote,
"avoid_log": avoid_log,
}
[docs]
class PolyExpFactory(BatchedFactory):
"""
Factory object implementing a zero-noise extrapolation algorithm assuming
an (almost) exponential ansatz with a non linear exponent
y(x) = a + sign * exp(z(x)), where z(x) is a polynomial of a given order.
The parameter "sign" is a sign variable which can be either 1 or -1,
corresponding to decreasing and increasing exponentials, respectively.
The parameter "sign" is automatically deduced from the data.
If y(x->inf) is unknown, the ansatz y(x) is fitted with a non-linear
optimization.
If y(x->inf) is given and avoid_log=False, the exponential
model is mapped into a polynomial model by logarithmic transformation.
Args:
scale_factors: Sequence of noise scale factors at which
expectation values should be measured.
order: Extrapolation order (degree of the polynomial z(x)).
It cannot exceed len(scale_factors) - 1.
If asymptote is None, order cannot exceed
len(scale_factors) - 2.
asymptote: The infinite-noise limit y(x->inf) (optional argument).
avoid_log: If set to True, the exponential model is not linearized
with a logarithm and a non-linear fit is applied even
if asymptote is not None. The default value is False.
shot_list: Optional sequence of integers corresponding to the number
of samples taken for each expectation value. If this
argument is explicitly passed to the factory, it must have
the same length of scale_factors and the executor function
must accept "shots" as a valid keyword argument.
Raises:
ValueError: If data is not consistent with the extrapolation model.
ExtrapolationError: If the extrapolation fit fails.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
"""
def __init__(
self,
scale_factors: Sequence[float],
order: int,
asymptote: Optional[float] = None,
avoid_log: bool = False,
shot_list: Optional[List[int]] = None,
) -> None:
"""Instantiates a new object of this Factory class."""
super(PolyExpFactory, self).__init__(scale_factors, shot_list)
if not (asymptote is None or isinstance(asymptote, float)):
raise ValueError(
"The argument 'asymptote' must be either a float or None"
)
self._options = {
"order": order,
"asymptote": asymptote,
"avoid_log": avoid_log,
}
# Keep a log of the optimization process storing:
# noise value(s), expectation value(s), parameters, and zero limit
OptimizationHistory = List[
Tuple[List[Dict[str, float]], List[float], List[float], float]
]
[docs]
class AdaExpFactory(AdaptiveFactory):
"""Factory object implementing an adaptive zero-noise extrapolation
algorithm assuming an exponential ansatz y(x) = a + b * exp(-c * x),
with c > 0.
The noise scale factors are are chosen adaptively at each step,
depending on the history of collected results.
If y(x->inf) is unknown, the ansatz y(x) is fitted with a non-linear
optimization.
If y(x->inf) is given and avoid_log=False, the exponential
model is mapped into a linear model by logarithmic transformation.
Args:
steps: The number of optimization steps. At least 3 are necessary.
scale_factor: The second noise scale factor (the first is always 1.0).
Further scale factors are adaptively determined.
asymptote: The infinite-noise limit y(x->inf) (optional argument).
avoid_log: If set to True, the exponential model is not linearized
with a logarithm and a non-linear fit is applied even if asymptote
is not None. The default value is False.
max_scale_factor: Maximum noise scale factor. Default is 6.0.
Raises:
ValueError: If data is not consistent with the extrapolation model.
ExtrapolationError: If the extrapolation fit fails.
ExtrapolationWarning: If the extrapolation fit is ill-conditioned.
"""
_SHIFT_FACTOR = 1.27846
_EPSILON = 1.0e-9
def __init__(
self,
steps: int,
scale_factor: float = 2.0,
asymptote: Optional[float] = None,
avoid_log: bool = False,
max_scale_factor: float = 6.0,
) -> None:
"""Instantiate a new object of this Factory class."""
super(AdaExpFactory, self).__init__()
if not (asymptote is None or isinstance(asymptote, float)):
raise ValueError(
"The argument 'asymptote' must be either a float or None"
)
if scale_factor <= 1:
raise ValueError(
"The argument 'scale_factor' must be strictly larger than one."
)
if steps < 3 + int(asymptote is None):
raise ValueError(
"The argument 'steps' must be an integer"
" greater or equal to 3. "
"If 'asymptote' is None, 'steps' must be"
" greater or equal to 4."
)
if max_scale_factor <= 1:
raise ValueError(
"The argument 'max_scale_factor' must be"
" strictly larger than one."
)
self._steps = steps
self._scale_factor = scale_factor
self.asymptote = asymptote
self.avoid_log = avoid_log
self.max_scale_factor = max_scale_factor
self.history: OptimizationHistory = []
[docs]
def next(self) -> Dict[str, float]:
"""Returns a dictionary of parameters to execute a circuit at."""
# The 1st scale factor is always 1
if len(self._instack) == 0:
return {"scale_factor": 1.0}
# The 2nd scale factor is self._scale_factor
if len(self._instack) == 1:
return {"scale_factor": self._scale_factor}
# If asymptote is None we use 2 * scale_factor as third noise parameter
if (len(self._instack) == 2) and (self.asymptote is None):
return {"scale_factor": 2 * self._scale_factor}
with warnings.catch_warnings():
# This is an intermediate fit, so we suppress its warning messages
warnings.simplefilter("ignore", ExtrapolationWarning)
# Call reduce() to fit the exponent and save it in self.history
self.reduce()
# The next line avoids warnings after intermediate extrapolations
self._already_reduced = False
# Get the most recent fitted parameters from self.history
_, _, params, _ = self.history[-1]
# The exponent parameter is the 3rd element of params
exponent = params[2]
# Further noise scale factors are determined with
# an adaptive rule which depends on self.exponent
next_scale_factor = min(
1.0 + self._SHIFT_FACTOR / np.abs(exponent + self._EPSILON),
self.max_scale_factor,
)
return {"scale_factor": next_scale_factor}
[docs]
def is_converged(self) -> bool:
"""Returns True if all the needed expectation values have been
computed, else False.
"""
if len(self._outstack) != len(self._instack):
raise IndexError(
f"The length of 'self._instack' ({len(self._instack)}) "
f"and 'self._outstack' ({len(self._outstack)}) must be equal."
)
return len(self._outstack) == self._steps
[docs]
def reduce(self) -> float:
"""Returns the zero-noise limit found by fitting an exponential
model to the internal data stored in the factory.
Returns:
The zero-noise limit.
"""
(
self._zne_limit,
self._zne_error,
self._opt_params,
self._params_cov,
self._zne_curve,
) = self.extrapolate( # type: ignore [misc]
self.get_scale_factors(),
self.get_expectation_values(),
asymptote=self.asymptote,
avoid_log=self.avoid_log,
full_output=True,
)
# Update optimization history
self.history.append(
(self._instack, self._outstack, self._opt_params, self._zne_limit)
)
self._already_reduced = True
return self._zne_limit
