Código fuente para qiskit_nature.second_q.operators.vibrational_op

# This code is part of a Qiskit project.
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# (C) Copyright IBM 2021, 2023.
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# This code is licensed under the Apache License, Version 2.0. You may
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# Any modifications or derivative works of this code must retain this
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"""The Vibrational Operator."""

from __future__ import annotations

import re
from collections import defaultdict
from collections.abc import Collection, Mapping
from typing import Iterator, Sequence, Tuple
import logging
import operator
import itertools

import numpy as np

from qiskit_nature.exceptions import QiskitNatureError

from ._bits_container import _BitsContainer
from .polynomial_tensor import PolynomialTensor
from .sparse_label_op import _TCoeff, SparseLabelOp, _to_number

logger = logging.getLogger(__name__)


[documentos]class VibrationalOp(SparseLabelOp): r"""N-mode vibrational operator. A ``VibrationalOp`` represents a weighted sum of vibrational creation/annihilation operator terms. These terms are encoded as sparse labels, strings consisting of a space-separated list of expressions. Each expression must look like :code:`[+-]_<mode_index>_<modal_index>`, where the :code:`<mode_index>` and :code:`<modal_index>` are non-negative integers representing the index of the vibrational mode and modal, respectively, where the ``+`` (creation) or ``-`` (annihilation) operation is to be performed. **Initialization** A ``VibrationalOp`` is initialized with a dictionary, mapping terms to their respective coefficients: .. code-block:: python from qiskit_nature.second_q.operators import VibrationalOp op = VibrationalOp( { "+_0_0 -_0_0": 1.0, "+_0_1 -_0_1": 1.0, "+_1_0 -_1_0": -1.0, "+_1_1 -_1_1": -1.0, }, num_modals=[2, 2] ) By default, this way of initializing will create a full copy of the dictionary of coefficients. If you have very restricted memory resources available, or would like to avoid the additional copy, the dictionary will be stored by reference if you disable ``copy`` like so: .. code-block:: python some_big_data = { "+_0_0 -_0_0": 1.0, "+_0_1 -_0_1": 1.0, # ... } op = VibrationalOp( some_big_data, num_modals=[2, 2], copy=False, ) .. note:: It is the users' responsibility, that in the above scenario, :code:`some_big_data` is not changed after initialization of the ``VibrationalOp``, since the operator contents are not guaranteed to remain unaffected by such changes. If :code:`num_modals` is not provided then the maximum :code:`modal_index` per mode will determine the :code:`num_modals` for that mode. .. code-block:: python from qiskit_nature.second_q.operators import VibrationalOp op = VibrationalOp( { "+_0_0 -_0_0": 1.0, "+_0_1 -_0_1": 1.0, "+_1_0 -_1_0": -1.0, "+_1_1 -_1_1": -1.0, }, ) **Algebra** This class supports the following basic arithmetic operations: addition, subtraction, scalar multiplication, operator multiplication, and adjoint. For example, Addition .. code-block:: python VibrationalOp({"+_1_0": 1}, num_modals=[2, 2]) + VibrationalOp({"+_0_0": 1}, num_modals=[2, 2]) Sum .. code-block:: python sum(VibrationalOp({label: 1}, num_modals=[1, 1, 1]) for label in ["+_0_0", "-_1_0", "+_2_0 -_2_0"]) Scalar multiplication .. code-block:: python 0.5 * VibrationalOp({"+_1_0": 1}, num_modals=[1, 1]) Operator multiplication .. code-block:: python op1 = VibrationalOp({"+_0_0 -_1_0": 1}, num_modals=[1, 1]) op2 = VibrationalOp({"-_0_0 +_0_0 +_1_0": 1}, num_modals=[1, 1]) print(op1 @ op2) Tensor multiplication .. code-block:: python op = VibrationalOp({"+_0_0 -_1_0": 1}, num_modals=[1, 1]) print(op ^ op) Adjoint .. code-block:: python VibrationalOp({"+_0_0 -_1_0": 1j}, num_modals=[1, 1]).adjoint() **Iteration** Instances of ``VibrationalOp`` are iterable. Iterating a ``VibrationalOp`` yields (term, coefficient) pairs describing the terms contained in the operator. .. note:: A VibrationalOp can contain :class:`qiskit.circuit.ParameterExpression` objects as coefficients. """ # a valid pattern consists of a single "+" or "-" operator followed by "_" and a mode index # followed by "_" and a modal index, possibly appearing multiple times and separated by a space _OPERATION_REGEX = re.compile(r"([\+\-]_\d+_\d+\s)*[\+\-]_\d+_\d+(?!\s)") def __init__( self, data: Mapping[str, _TCoeff], num_modals: Sequence[int] | None = None, *, copy: bool = True, validate: bool = True, ) -> None: """ Args: data: the operator data, mapping string-based keys to numerical values. num_modals: number of modals - described by a sequence of integers where each integer describes the number of modals in the corresponding mode; the total number of modals defines the ``register_length``. copy: when set to False the `data` will not be copied and the dictionary will be stored by reference rather than by value (which is the default; ``copy=True``). Note, that this requires you to not change the contents of the dictionary after constructing the operator. This also implies ``validate=False``. Use with care! validate: when set to False the ``data`` keys will not be validated. Note, that the SparseLabelOp base class, makes no assumption about the data keys, so will not perform any validation by itself. Only concrete subclasses are encouraged to implement a key validation method. Disable this setting with care! Raises: QiskitNatureError: when an invalid key is encountered during validation. """ self.num_modals = num_modals super().__init__(data, copy=copy, validate=validate) @property def num_modals(self) -> Sequence[int] | None: """The number of modals for each mode on which this operator acts. This is an optional sequence of integers which are considered lower bounds. That means that mathematical operations acting on two or more operators will result in a new operator with the maximum number of modals for each mode involved in any of the operators. """ # to ensure future flexibility, the type here is Sequence. However, the current # implementation ensures it will always be a list. return self._num_modals @num_modals.setter def num_modals(self, num_modals: Sequence[int] | None): self._num_modals = list(num_modals) if num_modals is not None else None @property def register_length(self) -> int: if self._num_modals is None: num_modals: list[int] = [] for key in self._data: for term in key.split(): _, mode_index_str, modal_index_str = term.split("_") mode_index = int(mode_index_str) modal_index = int(modal_index_str) if mode_index + 1 > len(num_modals): num_modals += [0] * (mode_index + 1 - len(num_modals)) if modal_index > num_modals[mode_index] - 1: num_modals[mode_index] = modal_index + 1 return sum(num_modals) return sum(self.num_modals) def _new_instance( self, data: Mapping[str, _TCoeff], *, other: VibrationalOp | None = None ) -> VibrationalOp: num_modals = self.num_modals if other is not None: other_num_modals = other.num_modals def pad_to_length(a, b): if len(a) < len(b): a, b = b, a return a, b + [0] * (len(a) - len(b)) def elementwise_max(a, b): return [max(i, j) for i, j in zip(*pad_to_length(a, b))] if num_modals is not None and other_num_modals is not None: num_modals = elementwise_max(num_modals, other_num_modals) return self.__class__(data, copy=False, num_modals=num_modals) def _validate_keys(self, keys: Collection[str]) -> None: super()._validate_keys(keys) num_modals = self._num_modals if self._num_modals is not None else [] for key in keys: # 0. explicitly allow the empty key if key == "": continue # Validate overall key structure if not re.fullmatch(VibrationalOp._OPERATION_REGEX, key): raise QiskitNatureError(f"{key} is not a valid VibrationalOp label.") coeff_labels_split = key.split() for label in coeff_labels_split: _, mode_index_str, modal_index_str = label.split("_") mode_index = int(mode_index_str) modal_index = int(modal_index_str) if mode_index + 1 > len(num_modals): num_modals += [0] * (mode_index + 1 - len(num_modals)) if modal_index > num_modals[mode_index] - 1: num_modals[mode_index] = modal_index + 1 self.num_modals = num_modals @classmethod def _validate_polynomial_tensor_key(cls, keys: Collection[str]) -> None: allowed = re.compile(r"(_\+\-)*") for key in keys: if not re.fullmatch(allowed, key): raise QiskitNatureError( f"The key '{key}' is invalid. PolynomialTensor keys must be multiples of the " "'_+-' character sequence, for them to be expandable into a VibrationalOp." )
[documentos] @classmethod def from_polynomial_tensor(cls, tensor: PolynomialTensor) -> VibrationalOp: cls._validate_polynomial_tensor_key(tensor.keys()) data: dict[str, _TCoeff] = {} def _reshape_index(index): new_index = [] for idx in range(0, len(index), 3): new_index.extend([index[idx], index[idx + 1], index[idx], index[idx + 2]]) return new_index for key in tensor: if key == "": data[""] = tensor[key].item() continue mat = tensor[key] label_template = mat.label_template.format(*key.replace("_", "")) for value, index in mat.coord_iter(): data[label_template.format(*_reshape_index(index))] = value return cls(data)
def __repr__(self) -> str: data_str = f"{dict(self.items())}" return "VibrationalOp(" f"{data_str}, " f"num_modals={self.num_modals}, " ")" def __str__(self) -> str: pre = ( "Vibrational Operator\n" f"number modes={len(self.num_modals)}, number modals={self.num_modals}, " f"number terms={len(self)}\n" ) ret = " " + "\n+ ".join( [f"{coeff} * ( {label} )" if label else f"{coeff}" for label, coeff in self.items()] ) return pre + ret
[documentos] def terms(self) -> Iterator[tuple[list[tuple[str, int]], _TCoeff]]: """Provides an iterator analogous to :meth:`items` but with the labels already split into pairs of operation characters and indices. Yields: A tuple with two items; the first one being a list of pairs of the form (char, int) where char is either ``+`` or ``-`` and the integer corresponds to the vibrational mode and modal index on which the operator gets applied; the second item of the returned tuple is the coefficient of this term. """ num_modals = self.num_modals partial_sum_modals = [0] + list(itertools.accumulate(num_modals, operator.add)) for label in iter(self): if not label: yield ([], self[label]) continue terms = [self._build_register_label(lbl, partial_sum_modals) for lbl in label.split()] yield (terms, self[label])
[documentos] @classmethod def from_terms(cls, terms: Sequence[tuple[list[tuple[str, int]], _TCoeff]]) -> VibrationalOp: raise NotImplementedError()
def _permute_term( self, term: list[tuple[str, int]], permutation: Sequence[int] ) -> list[tuple[str, int]]: raise NotImplementedError() def _build_register_label(self, label: str, partial_sum_modals: list[int]) -> tuple[str, int]: op, mode_index, modal_index = label.split("_") index = partial_sum_modals[int(mode_index)] + int(modal_index) return (op, index)
[documentos] def compose(self, other: VibrationalOp, qargs=None, front: bool = False) -> VibrationalOp: if not isinstance(other, VibrationalOp): raise TypeError( f"Unsupported operand type(s) for *: 'VibrationalOp' and '{type(other).__name__}'" ) if front: return self._tensor(self, other, offset=False) else: return self._tensor(other, self, offset=False)
[documentos] def tensor(self, other: VibrationalOp) -> VibrationalOp: return self._tensor(self, other)
[documentos] def expand(self, other: VibrationalOp) -> VibrationalOp: return self._tensor(other, self)
@classmethod def _tensor(cls, a: VibrationalOp, b: VibrationalOp, *, offset: bool = True) -> VibrationalOp: shift = len(a.num_modals) if offset else 0 new_data: dict[str, _TCoeff] = {} for a_labels, a_coeff in a.items(): for b_labels, b_coeff in b.items(): if b_labels == "": new_label = a_labels else: b_terms = [lbl.split("_") for lbl in b_labels.split()] new_b_label = " ".join(f"{op}_{int(i)+shift}_{j}" for op, i, j in b_terms) new_label = f"{a_labels} {new_b_label}".strip() if new_label in new_data: new_data[new_label] += a_coeff * b_coeff else: new_data[new_label] = a_coeff * b_coeff new_op = a._new_instance(new_data, other=b) if offset: new_op.num_modals = [*a.num_modals, *b.num_modals] return new_op
[documentos] def transpose(self) -> VibrationalOp: data = {} trans = "".maketrans("+-", "-+") for label, coeff in self.items(): data[" ".join(lbl.translate(trans) for lbl in reversed(label.split()))] = coeff return self._new_instance(data)
[documentos] def normal_order(self) -> VibrationalOp: """Convert to the equivalent operator in normal order. The normal order for this operator is defined as follows: - creation (``+``) operations are applied before annihilation (``-``) ones - operators are ordered by index within each of the operator type groups Returns a new operator (the original operator is not modified). .. note:: The operations encoded by a ``VibrationalOp`` are fully commutative, which means that re-ordering of individual terms does **not** result in a phase shift. Returns: The normal ordered operator. """ ordered_op = VibrationalOp.zero() for label, coeff in self.items(): terms = [] for lbl in label.split(): char, mode, modal = lbl.split("_") terms.append((char, int(mode), int(modal))) ordered_op += self._normal_order(terms, coeff) # after successful normal ordering, we remove all zero coefficients return self._new_instance( { label: coeff for label, coeff in ordered_op.items() if not np.isclose(_to_number(coeff), 0.0, atol=self.atol) } )
def _normal_order(self, terms: list[tuple[str, int, int]], coeff: _TCoeff) -> VibrationalOp: if not terms: return self._new_instance({"": coeff}) ordered_op = VibrationalOp.zero() # perform insertion sorting for i in range(1, len(terms)): for j in range(i, 0, -1): right = terms[j] left = terms[j - 1] if right[0] == "+" and left[0] == "-": # swap terms where an annihilation operator is left of a creation operator terms[j - 1] = right terms[j] = left if right[1] == left[1] and right[2] == left[2]: # if their indices are identical, we incur an additional term because of: # a_i a_i^\dagger = 1 + a_i^\dagger a_i new_terms = terms[: (j - 1)] + terms[(j + 1) :] # we can do so by recursion on this method ordered_op += self._normal_order(new_terms, coeff) elif right[0] == left[0]: # when we have identical neighboring operators, differentiate two cases: # on identical index, this is an invalid operation which evaluates to # zero: e.g. +_0_0 +_0_0 = 0 if right[1] == left[1] and right[2] == left[2]: # thus, we bail on this recursion call return ordered_op # otherwise, if the left index is higher than the right one, swap the terms elif left[1] > right[1] or (left[1] == right[1] and left[2] > right[2]): terms[j - 1] = right terms[j] = left new_label = " ".join(f"{term[0]}_{term[1]}_{term[2]}" for term in terms) ordered_op += self._new_instance({new_label: coeff}) return ordered_op
[documentos] def index_order(self) -> VibrationalOp: """Convert to the equivalent operator with the terms of each label ordered by index. Returns a new operator (the original operator is not modified). .. note:: You can use this method to achieve the most aggressive simplification of an operator without changing the operation order per index. :meth:`simplify` does *not* reorder the terms and, thus, cannot deduce ``-_0_0 +_1_0`` and ``+_1_0 -_0_0 +_0_0 -_0_0`` to be identical labels. Calling this method will reorder the latter label to ``-_0_0 +_0_0 -_0_0 +_1_0``, after which :meth:`simplify` will be able to correctly collapse these two labels into one. Returns: The index ordered operator. """ data = defaultdict(complex) # type: dict[str, _TCoeff] for label, coeff in self.items(): terms = [] for lbl in label.split(): char, mode, modal = lbl.split("_") terms.append((char, int(mode), int(modal))) label, coeff = self._index_order(terms, coeff) data[label] += coeff # after successful index ordering, we remove all zero coefficients return self._new_instance( { label: coeff for label, coeff in data.items() if not np.isclose(_to_number(coeff), 0.0, atol=self.atol) } )
def _index_order( self, terms: list[tuple[str, int, int]], coeff: _TCoeff ) -> tuple[str, _TCoeff]: if not terms: return "", coeff # perform insertion sorting for i in range(1, len(terms)): for j in range(i, 0, -1): right = terms[j] left = terms[j - 1] if left[1] > right[1] or (left[1] == right[1] and left[2] > right[2]): terms[j - 1] = right terms[j] = left new_label = " ".join(f"{term[0]}_{term[1]}_{term[2]}" for term in terms) return new_label, coeff
[documentos] def simplify(self, atol: float | None = None) -> VibrationalOp: """Simplify the operator. The simplifications implemented by this method should be: - to eliminate terms whose coefficients are close (w.r.t. ``atol``) to 0. - to combine the coefficients which correspond to equivalent terms (see also the note below) .. note:: :meth:`simplify` should be used to simplify terms whose coefficients are close to zero, up to the specified numerical tolerance. It still differs slightly from :meth:`chop` because that will chop real and imaginary part components individually. .. note:: The meaning of "equivalence" between multiple terms depends on the specific operator subclass. As a restriction this method is required to preserve the order of appearance of the different components within a term. This avoids some possibly unexpected edge cases. However, this also means that some equivalencies cannot be detected. Check for other methods of a specific subclass which may affect the order of terms and can allow for further simplifications to be implemented. For example, check out :meth:`index_order`. This method returns a new operator (the original operator is not modified). Args: atol: Absolute numerical tolerance. The default behavior is to use ``self.atol``. Returns: The simplified operator. """ atol = self.atol if atol is None else atol data = defaultdict(complex) # type: dict[str, _TCoeff] # TODO: use parallel_map to make this more efficient (?) for label, coeff in self.items(): label, coeff = self._simplify_label(label, coeff) data[label] += coeff simplified_data = { label: coeff for label, coeff in data.items() if not np.isclose(_to_number(coeff), 0.0, atol=self.atol) } return self._new_instance(simplified_data)
def _simplify_label(self, label: str, coeff: _TCoeff) -> tuple[str, _TCoeff]: bits = _BitsContainer[Tuple[int, int]]() # Since Python 3.7, dictionaries are guaranteed to be insert-order preserving. We use this # to our advantage, to implement an ordered set, which allows us to preserve the label order # and only remove canceling terms. new_label: dict[str, None] = {} for lbl in label.split(): char, mode_index, modal_index = lbl.split("_") idx = (int(mode_index), int(modal_index)) char_b = char == "+" if idx not in bits: # we store all relevant information for each register index in 4 bits: # 1. True if a `+` has been applied on this index # 2. True if a `-` has been applied on this index # 3. True if a `+` was applied first, False if a `-` was applied first # 4. True if the last added operation on this index was `+`, False if `-` bits[idx] = int(f"{char_b:b}{not char_b:b}{char_b:b}{char_b:b}", base=2) # and we insert the encountered label into our ordered set new_label[lbl] = None elif bits.get_last(idx) == char_b: # we bail, if we apply the same operator as the last one return "", 0 elif bits.get_plus(idx) and bits.get_minus(idx): # If both, `+` and `-`, have already been applied, we cancel the opposite to the # current one (i.e. `+` will cancel `-` and vice versa). # 1. we construct the reversed label which is the key we need to pop pop_lbl = f"{'-' if char_b else '+'}_{idx[0]}_{idx[1]}" # 2. we perform the information update by: # a) popping the key we just canceled out new_label.pop(pop_lbl) # b) updating the bits container bits.set_plus_or_minus(idx, not char_b, False) # c) and updating the last bit to the current char bits.set_last(idx, char_b) else: # else, we simply set the bit of the currently applied char bits.set_plus_or_minus(idx, char_b, True) # and track it in our ordered set new_label[lbl] = None # we also update the last bit to the current char bits.set_last(idx, char_b) return " ".join(new_label), coeff
[documentos] @staticmethod def build_dual_index(num_modals: Sequence[int], index: int) -> str: r"""Convert a single expanded index into a dual mode and modal index string. Args: num_modals: The number of modals - described by a list of integers where each integer describes the number of modals in the corresponding mode; the total number of modals defines the ``register_length``. index: The expanded (register) index. Returns: The dual index label. Raises: ValueError: If the index is greater than the sum of num_modals. """ for mode_index, num_modals_per_mode in enumerate(num_modals): if index < num_modals_per_mode: return f"{mode_index}_{index}" else: index -= num_modals_per_mode raise ValueError("Invalid index: index > sum(num_modals) - 1.")