# openfermion.ops.SymbolicOperator

Base class for FermionOperator and QubitOperator.

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.

action_before_index Whether action comes before index in string representations.

Example: For QubitOperator, the actions are ('X', 'Y', 'Z') and the string representations look something like 'X0 Z2 Y3'. So the action comes before the index, and this function should return True. For FermionOperator, the string representations look like '0^ 1 2^ 3'. The action comes after the index, so this function should return False.

action_strings The string representations of the allowed actions.

Returns a tuple containing string representations of the possible actions, in the same order as the actions property.

actions The allowed actions.

Returns a tuple of objects representing the possible actions.

constant The value of the constant term.
different_indices_commute Whether factors acting on different indices commute.

## Methods

### accumulate

View source

Sums over SymbolicOperators.

### compress

View source

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

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

Gets a list of operators with a single term.

Returns
operators([self.class]): A generator of the operators in self.

### identity

View source

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

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

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

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

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

Returns
sum (SymbolicOperator)

### __div__

View source

For compatibility with Python 2.

### __eq__

View source

Approximate numerical equality (not true equality).

View source

### __mul__

View source

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

Return self!=value.

### __neg__

View source

Returns: negation (SymbolicOperator)

### __pow__

View source

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

Returns
sum (SymbolicOperator)

### __rmul__

View source

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

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

Returns
difference (SymbolicOperator)

### __sub__

View source

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

Returns
difference (SymbolicOperator)

### __truediv__

View source

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.

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