BosonicOp#

class BosonicOp(data, num_modes=None, *, copy=True, validate=True)[ソース]#

ベースクラス: SparseLabelOp

N-mode Bosonic operator.

A BosonicOp represents a weighted sum of bosonic creation/annihilation operator terms. These terms are encoded as sparse labels, which are strings consisting of a space-separated list of expressions. Each expression must look like [+-]_<index>, where the <index> is a non-negative integer representing the index of the bosonic mode where the + (creation) or - (annihilation) operation is to be performed. The value of index is bound by the number of modes (num_modes) of the operator (Note: since Python indices are 0-based, the maximum value an index can take is given by num_modes-1).

Initialization

A BosonicOp is initialized with a dictionary, mapping terms to their respective coefficients:

from qiskit_nature.second_q.operators import BosonicOp

op = BosonicOp(
    {
        "+_0 -_0": 1.0,
        "+_1 -_1": -1.0,
    },
    num_modes=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:

some_big_data = {
    "+_0 -_0": 1.0,
    "+_1 -_1": -1.0,
    # ...
}

op = BosonicOp(
    some_big_data,
    num_modes=2,
    copy=False,
)

注釈

It is the users』 responsibility, that in the above scenario, some_big_data is not changed after initialization of the BosonicOp, since the operator contents are not guaranteed to remain unaffected by such changes.

Algebra

This class supports the following basic arithmetic operations: addition, subtraction, scalar multiplication, operator multiplication, and adjoint. For example,

Addition

BosonicOp({"+_1": 1}, num_modes=2) + BosonicOp({"+_0": 1}, num_modes=2)

Sum

sum(BosonicOp({label: 1}, num_modes=3) for label in ["+_0", "-_1", "+_2 -_2"])

Scalar multiplication

0.5 * BosonicOp({"+_1": 1}, num_modes=2)

Operator multiplication

op1 = BosonicOp({"+_0 -_1": 1}, num_modes=2)
op2 = BosonicOp({"-_0 +_0 +_1": 1}, num_modes=2)
print(op1 @ op2)

Tensor multiplication

op = BosonicOp({"+_0 -_1": 1}, num_modes=2)
print(op ^ op)

Adjoint

BosonicOp({"+_0 -_1": 1j}, num_modes=2).adjoint()

Iteration

Instances of BosonicOp are iterable. Iterating a BosonicOp yields (term, coefficient) pairs describing the terms contained in the operator.

num_modes#

the number of modes on which this operator acts. This is considered a lower bound, which means that mathematical operations acting on two or more operators will result in a new operator with the maximum number of modes of any of the involved operators.

Type:

int | None

注釈

A BosonicOp can contain qiskit.circuit.ParameterExpression objects as coefficients. However, a BosonicOp containing parameters does not support the following methods:

  • is_hermitian

パラメータ:

  • data (Mapping[str, _TCoeff]) – the operator data, mapping string-based keys to numerical values.

  • num_modes (int | None) – the number of modes on which this operator acts.

  • copy (bool) – 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 (bool) – 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!

例外:

QiskitNatureError – when an invalid key is encountered during validation.

Attributes

atol = 1e-08#
register_length#
rtol = 1e-05#

Methods

adjoint()#

Return the adjoint of the Operator.

戻り値の型:

Self

argsort(*, weight=False)#

Returns the keys which sort this operator.

パラメータ:

weight (bool) – when True, the returned keys will sort this operator according to the coefficient weights of the stored terms; when False, the keys will sort the operator by its keys (i.e. lexicographically).

戻り値:

The sequence of keys which sort this operator.

戻り値の型:

Sequence[str]

assign_parameters(parameters)#

Assign parameters to new parameters or values.

パラメータ:

parameters (Mapping[ParameterExpression, complex | ParameterExpression]) – The mapping from parameters to new parameters or values.

戻り値:

A new operator with the parameters assigned.

戻り値の型:

SparseLabelOp

chop(atol=None)#

Chops the real and imaginary parts of the operator coefficients.

This function separately chops the real and imaginary parts of all coefficients to the provided tolerance. Parameters are chopped only if they are exactly zero.

パラメータ:

atol (float | None) – the tolerance to which to chop. If None, atol will be used.

戻り値:

The chopped operator.

戻り値の型:

SparseLabelOp

compose(other, qargs=None, front=False)[ソース]#

Returns the operator composition with another operator.

パラメータ:

  • other (BosonicOp) – the other operator.

  • qargs – UNUSED.

  • front (bool) – If True composition uses right operator multiplication, otherwise left multiplication is used (the default).

戻り値:

The operator resulting from the composition.

戻り値の型:

BosonicOp

注釈

Composition (&) by default is defined as left matrix multiplication for matrix operators, while @ (equivalent to dot()) is defined as right matrix multiplication. This means that A & B == A.compose(B) is equivalent to B @ A == B.dot(A) when A and B are of the same type.

Setting the front=True keyword argument changes this to right matrix multiplication which is equivalent to the dot() method A.dot(B) == A.compose(B, front=True).

conjugate()#

Returns the conjugate of the SparseLabelOp.

戻り値:

The complex conjugate of the starting SparseLabelOp.

戻り値の型:

SparseLabelOp

dot(other, qargs=None)#

Return the right multiplied operator self * other.

パラメータ:

  • other (Operator) – an operator object.

  • qargs (list or None) – Optional, a list of subsystem positions to apply other on. If None apply on all subsystems (default: None).

戻り値:

The right matrix multiplied Operator.

戻り値の型:

Operator

注釈

The dot product can be obtained using the @ binary operator. Hence a.dot(b) is equivalent to a @ b.

equiv(other, *, atol=None, rtol=None)#

Check equivalence of two SparseLabelOp instances up to an accepted tolerance.

パラメータ:

  • other (SparseLabelOp) – the second SparseLabelOp to compare with this instance.

  • atol (float | None) – Absolute numerical tolerance. The default behavior is to use self.atol.

  • rtol (float | None) – Relative numerical tolerance. The default behavior is to use self.rtol.

戻り値:

True if operators are equivalent, False if not.

例外:

ValueError – Raised if either operator contains parameters

戻り値の型:

bool

expand(other)[ソース]#

Returns the reverse-order tensor product with another operator.

パラメータ:

other (BosonicOp) – the other operator.

戻り値:

The operator resulting from the tensor product, \(othr \otimes self\).

戻り値の型:

BosonicOp

classmethod from_polynomial_tensor(tensor)[ソース]#

Constructs the operator from a PolynomialTensor.

パラメータ:

tensor (PolynomialTensor) – the PolynomialTensor to be expanded.

戻り値:

The constructed operator.

戻り値の型:

BosonicOp

classmethod from_terms(terms)[ソース]#

Constructs a new SparseLabelOp from a sequence returned by terms().

パラメータ:

terms (Sequence[tuple[list[tuple[str, int]], Union[complex, qiskit.circuit.parameterexpression.ParameterExpression]]]) – a sequence as returned by terms().

戻り値:

The constructed operator.

戻り値の型:

BosonicOp

get(k[, d]) → D[k] if k in D, else d.  d defaults to None.#
index_order()[ソース]#

Convert to the equivalent operator with the terms of each label ordered by index.

戻り値:

A new index ordered BosonicOp (the original operator is not modified).

戻り値の型:

BosonicOp

注釈

You can use this method to achieve the most aggressive simplification of an operator without changing the operation order per index. simplify() does not reorder the terms and, thus, cannot deduce -_0 +_1 and +_1 -_0 to be identical labels. Calling this method will reorder the latter label to -_0 +_1, correctly collapsing these two labels into one.

induced_norm(order=1)#

Returns the p-norm induced by the operator coefficients.

If the operator is represented as a sum of terms

\[\sum_i w_i H_i\]

then the induced \(p\)-norm is

\[\left(\sum_i |w_i|^p \right)^{1/p}\]

This is the standard \(p\)-norm of the operator coefficients considered as a vector (see https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm). Note that this method does not normal-order or simplify the operator before computing the norm; performing either of those operations can affect the result.

パラメータ:

order (int) – Order \(p\) of the norm. The default value is 1.

戻り値:

The induced norm.

戻り値の型:

float

例外:

ValueError – Operator contains parameters.

戻り値の型:

float

is_hermitian(atol=None)[ソース]#

Checks whether the operator is hermitian.

パラメータ:

atol (float | None) – Absolute numerical tolerance. The default behavior is to use self.atol.

戻り値:

True if the operator is hermitian up to numerical tolerance, False otherwise.

例外:

ValueError – Operator contains parameters.

戻り値の型:

bool

is_parameterized()#

Returns whether the operator contains any parameters.

戻り値の型:

bool

is_zero(tol=None)#

Returns true if operator length is zero or all coefficients have value zero.

パラメータ:

tol (int | None) – tolerance for checking coefficient values. If this is None, atol will be used instead.

戻り値:

If operator length is zero or all coefficients are zero.

戻り値の型:

bool

items() → a set-like object providing a view on D's items#
keys() → a set-like object providing a view on D's keys#
normal_order()[ソース]#

Convert to the equivalent operator in normal order.

The normal order for bosons is defined [here](https://en.wikipedia.org/wiki/Normal_order#Bosons).

戻り値:

A new normal ordered BosonicOp (the original operator is not modified).

戻り値の型:

BosonicOp

注釈

This method implements the transformation of an operator to the normal ordered operator. The transformation is calculated by considering all commutation relations between the operators. For example, for the case \(\colon b_0 b_0^\dagger\colon\) where \(b_0\) is an annihilation operator, this method returns \(1 + b_0^\dagger b_0\) due to commutation relations. See the reference: [here](https://en.wikipedia.org/wiki/Normal_order#Multiple_bosons).

classmethod one()#

Constructs a unity-operator.

戻り値:

The unity-operator of the given length.

戻り値の型:

SparseLabelOp

parameters()#

Returns a list of the parameters in the operator.

戻り値:

A list of the parameters in the operator.

戻り値の型:

list[qiskit.circuit.parameterexpression.ParameterExpression]

permute_indices(permutation)#

Permutes the indices of the operator.

This method applies the provided index permutation to all labels of this operator. The provided permutation must be a sequence of integers whose length is equal to the register_length of the operator. The integer at any given index of the sequence indicates the new index which that location will be permuted to. For example:

op = SparseLabelOp({"+_0 -_1 +_2 -_3": 1.0})
permuted_op = op.permute_indices([3, 1, 0, 2])
assert permuted_op == SparseLabelOp({"+_3 -_1 +_0 -_2": 1.0})

警告

This permutation utility is very powerful. Be mindful of the implications such a permutation might have on other components of the stack. To name an example, the builtin two-qubit reduction of the ParityMapper might not yield the expected results when used on permuted operator.

パラメータ:

permutation (Sequence[int]) – a sequence of integers indicating the permutation to be applied. See above for an example.

戻り値:

A new operator instance with the permuted indices.

例外:

ValueError – if the length of the permutation argument does not equal register_length.

戻り値の型:

SparseLabelOp

power(n)#

Return the compose of a operator with itself n times.

パラメータ:

n (int) – the number of times to compose with self (n>0).

戻り値:

the n-times composed operator.

戻り値の型:

Clifford

例外:

QiskitError – if the input and output dimensions of the operator are not equal, or the power is not a positive integer.

round(decimals=0)#

Rounds the operator coefficients to a specified number of decimal places.

パラメータ:

decimals (int) – the number of decimal places to round coefficients to. By default this will round to the nearest integer value.

戻り値:

The rounded operator.

戻り値の型:

SparseLabelOp

simplify(atol=None)[ソース]#

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)

注釈

simplify() should be used to simplify terms whose coefficients are close to zero, up to the specified numerical tolerance. It still differs slightly from chop() because that will chop real and imaginary part components individually.

注釈

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 index_order().

注釈

simplify() is not allowed to simplify the labels +_0 -_0 or -_0 +_0. The former corresponds to the boson number operator, and when it is applied to a state yields the number of bosons in that state \(n\). Similarly, the latter yields \(1 + n\). As a consequence, the label +_0 -_0 -_1 +_0 will remain untouched by this method. This is in contrast to how FermionicOp.simplify() works, because it exploits that \(n\) can be either \(0\) or \(1\).

This method returns a new operator (the original operator is not modified).

パラメータ:

atol (float | None) – Absolute numerical tolerance. The default behavior is to use self.atol.

戻り値:

The simplified operator.

戻り値の型:

BosonicOp

sort(*, weight=False)#

Returns a new sorted operator.

パラメータ:

weight (bool) – when True, the returned keys will sort this operator according to the coefficient weights of the stored terms; when False, the keys will sort the operator by its keys (i.e. lexicographically).

戻り値:

A new operator instance with its contents sorted.

戻り値の型:

SparseLabelOp

tensor(other)[ソース]#

Returns the tensor product with another SparseLabelOp.

パラメータ:

other (BosonicOp) – the other SparseLabelOp.

戻り値:

The operator resulting from the tensor product, \(self \otimes other\).

戻り値の型:

BosonicOp

注釈

The tensor product can be obtained using the ^ binary operator. Hence a.tensor(b) is equivalent to a ^ b.

terms()[ソース]#

Provides an iterator analogous to items() but with the labels already split into pairs of operation characters and indices.

列挙:

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 bosonic mode index on which the operator gets applied; the second item of the returned tuple is the coefficient of this term.

戻り値の型:

Iterator[tuple[list[tuple[str, int]], Union[complex, qiskit.circuit.parameterexpression.ParameterExpression]]]

transpose()[ソース]#

Returns the transpose of the operator.

戻り値:

The transpose of the operator.

戻り値の型:

BosonicOp

values() → an object providing a view on D's values#
classmethod zero()#

Constructs a zero-operator.

戻り値:

The zero-operator of the given length.

戻り値の型:

SparseLabelOp