openfermion.ops.SymbolicOperator

Base class for FermionOperator and QubitOperator.

openfermion.ops.SymbolicOperator(
    term=None, coefficient=1.0
)

A SymbolicOperator stores an object which represents a weighted sum of terms; each term is a product of individual factors of the form (index, action), where index is a nonnegative integer and the possible values for action are determined by the subclass. For instance, for the subclass FermionOperator, action can be 1 or 0, indicating raising or lowering, and for QubitOperator, action is from the set {'X', 'Y', 'Z'}. The coefficients of the terms are stored in a dictionary whose keys are the terms. SymbolicOperators of the same type can be added or multiplied together.

Adding SymbolicOperators is faster using += (as this is done by in-place addition). Specifying the coefficient during initialization is faster than multiplying a SymbolicOperator with a scalar.

actions tuple

A tuple of objects representing the possible actions. e.g. for FermionOperator, this is (1, 0).

action_strings tuple

A tuple of string representations of actions. These should be in one-to-one correspondence with actions and listed in the same order. e.g. for FermionOperator, this is ('^', '').

action_before_index bool

A boolean indicating whether in string representations, the action should come before the index.

different_indices_commute bool

A boolean indicating whether factors acting on different indices commute.

terms dict

key (tuple of tuples): A dictionary storing the coefficients of the terms in the operator. The keys are the terms. A term is a product of individual factors; each factor is represented by a tuple of the form (index, action), and these tuples are collected into a larger tuple which represents the term as the product of its factors.

constant The value of the constant term.

Methods

accumulate

View source

@classmethod
accumulate(
    operators, start=None
)

Sums over SymbolicOperators.

compress

View source

compress(
    abs_tol=EQ_TOLERANCE
)

Eliminates all terms with coefficients close to zero and removes small imaginary and real parts.

Args
abs_tol float

Absolute tolerance, must be at least 0.0

get_operator_groups

View source

get_operator_groups(
    num_groups
)

Gets a list of operators with a few terms.

Args
num_groups int

How many operators to get in the end.

Returns
operators [self.__class__]

A list of operators summing up to self.

get_operators

View source

get_operators()

Gets a list of operators with a single term.

Returns
operators [self.__class__]

A generator of the operators in self.

identity

View source

@classmethod
identity()

Returns: multiplicative_identity (SymbolicOperator): A symbolic operator u with the property that ux = xu = x for all operators x of the same class.

induced_norm

View source

induced_norm(
    order=1
)

Compute the induced p-norm of the operator.

If we represent an operator as \(\sum_{j} w_j H_j\) where \(w_j\) are scalar coefficients then this norm is \(\left(\sum_{j} \| w_j \|^p \right)^{\frac{1}{p} }\) where \(p\) is the order of the induced norm

Args
order int

the order of the induced norm.

isclose

View source

isclose(
    other, tol=EQ_TOLERANCE
)

Check if other (SymbolicOperator) is close to self.

Comparison is done for each term individually. Return True if the difference between each term in self and other is less than EQ_TOLERANCE

Args
other SymbolicOperator

SymbolicOperator to compare against.

many_body_order

View source

many_body_order()

Compute the many-body order of a SymbolicOperator.

The many-body order of a SymbolicOperator is the maximum length of a term with nonzero coefficient.

Returns
int

zero

View source

@classmethod
zero()

Returns: additive_identity (SymbolicOperator): A symbolic operator o with the property that o+x = x+o = x for all operators x of the same class.

__add__

View source

__add__(
    addend
)

Args: addend (SymbolicOperator): The operator to add.

Returns
sum (SymbolicOperator)

__div__

View source

__div__(
    divisor
)

For compatibility with Python 2.

__eq__

View source

__eq__(
    other
)

Approximate numerical equality (not true equality).

__iter__

View source

__iter__()

__mul__

View source

__mul__(
    multiplier
)

Return self * multiplier for a scalar, or a SymbolicOperator.

Args
multiplier A scalar, or a SymbolicOperator.

Returns
product (SymbolicOperator)

Raises
TypeError Invalid type cannot be multiply with SymbolicOperator.

__ne__

View source

__ne__(
    other
)

Return self!=value.

__neg__

View source

__neg__()

Returns: negation (SymbolicOperator)

__pow__

View source

__pow__(
    exponent
)

Exponentiate the SymbolicOperator.

Args
exponent int

The exponent with which to raise the operator.

Returns
exponentiated (SymbolicOperator)

Raises
ValueError Can only raise SymbolicOperator to non-negative integer powers.

__radd__

View source

__radd__(
    addend
)

Args: addend (SymbolicOperator): The operator to add.

Returns
sum (SymbolicOperator)

__rmul__

View source

__rmul__(
    multiplier
)

Return multiplier * self for a scalar.

We only define rmul for scalars because the left multiply exist for SymbolicOperator and left multiply is also queried as the default behavior.

Args
multiplier A scalar to multiply by.

Returns
product A new instance of SymbolicOperator.

Raises
TypeError Object of invalid type cannot multiply SymbolicOperator.

__rsub__

View source

__rsub__(
    subtrahend
)

Args: subtrahend (SymbolicOperator): The operator to subtract.

Returns
difference (SymbolicOperator)

__sub__

View source

__sub__(
    subtrahend
)

Args: subtrahend (SymbolicOperator): The operator to subtract.

Returns
difference (SymbolicOperator)

__truediv__

View source

__truediv__(
    divisor
)

Return self / divisor for a scalar.

Note
This is always floating point division.

Args
divisor A scalar to divide by.

Returns
A new instance of SymbolicOperator.

Raises
TypeError Cannot divide local operator by non-scalar type.