openfermion.ops.BinaryPolynomial

The BinaryPolynomial class provides an analytic representation of non-linear binary functions.

openfermion.ops.BinaryPolynomial(
    term=None
)

Used in the notebooks

Used in the tutorials

An instance of this class describes a term of binary variables (variables of the values {0,1}, indexed by integers like w0, w1, w2 and so on) that is considered to be evaluated modulo 2. This implies the following set of rules:

the binary addition w1 + w1 = 0, binary multiplication w2 * w2 = w2 and power rule w3 ^ 0 = 1, where raising to every other integer power than zero reproduces w3.

Of course, we can also add a non-trivial constant, which is 1. Due to these binary rules, every function available will be a multinomial like e.g.

1 + w1 w2 + w0 w1 .

These binary functions are used for non-linear binary codes in order to decompress qubit bases back into fermion bases. In that instance, one BinaryPolynomial object characterizes the occupation of single orbital given a multi-qubit state in configuration |w0> |w1> |w2> ... .

For initialization, the preferred data types is either a string of the multinomial, where each variable and constant is to be well separated by a whitespace, or in its native form of tuples, 1 + w1 w2 + w0 w1 is represented as [(_SYMBOLIC_ONE,),(1,2),(0,1)]

After initialization,BinaryPolynomial terms can be manipulated with the overloaded signs +, * and ^, according to the binary rules mentioned.

.. code-block:: python

bin_fun = BinaryPolynomial('1 + w1 w2 + w0 w1')

Equivalently

bin_fun = BinaryPolynomial(1) + BinaryPolynomial([(1,2),(0,1)])

Equivalently

bin_fun = BinaryPolynomial([(_SYMBOLIC_ONE,),(1,2),(0,1)])

term str, list, tuple

used for initializing a BinaryPolynomial

ValueError when term is not a string,list or tuple

terms list

a list of tuples. Each tuple represents a summand of the BinaryPolynomial term and each summand can contain multiple tuples representing the factors.

Methods

enumerate_qubits

View source

enumerate_qubits()

Enumerates all qubits indexed in a given BinaryPolynomial.

Returns (list): a list of qubits

evaluate

View source

evaluate(
    binary_list
)

Evaluates a BinaryPolynomial

Args
binary_list list, array, str

a list of binary values corresponding each binary variable (in order of their indices) in the expression

Returns (int, 0 or 1): result of the evaluation

Raises
BinaryPolynomialError Length of list provided must match the number of qubits indexed in BinaryPolynomial

identity

View source

@classmethod
identity()

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

shift

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shift(
    const
)

Shift all qubit indices by a given constant.

Args
const int

the constant to shift the indices by

Raises
TypeError const must be integer

zero

View source

@classmethod
zero()

Returns: additive_identity (BinaryPolynomial): 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
)

Left addition of BinaryPolynomial.

Args
addend int or BinaryPolynomial

The operator or int to add.

Returns
sum BinaryPolynomial

the sum of terms

__mul__

View source

__mul__(
    multiplier
)

Return self * multiplier for int, or a BinaryPolynomial.

Args
multiplier (int or BinaryPolynomial): the multiplier of the BinaryPolynomial object

Returns
product BinaryPolynomial

result of the multiplication

Raises
TypeError Invalid type cannot be multiply with BinaryPolynomial.

__pow__

View source

__pow__(
    exponent
)

Exponentiate the BinaryPolynomial.

Args
exponent int

The exponent with which to raise the operator.

Returns
exponentiated BinaryPolynomial

Exponentiated symbolicBinary

Raises
TypeError Can only raise BinaryPolynomial to non-negative integer powers.

__radd__

View source

__radd__(
    addend
)

Method for right addition to BinaryPolynomial.

Args
addend int or BinaryPolynomial

The operator to add.

Returns
sum BinaryPolynomial

the sum of terms

Raises
TypeError Cannot add invalid type.

__rmul__

View source

__rmul__(
    multiplier
)

Return multiplier * self for a scalar or BinaryPolynomial.

Args
multiplier int or BinaryPolynomial

the multiplier of the BinaryPolynomial object

Returns
product BinaryPolynomial

A new instance of BinaryPolynomial.

Raises
TypeError Object of invalid type cannot multiply BinaryPolynomial.