Higher-Order Models

Sometimes it is nice to work with problems that are not restricted to quadratic interactions.

Binary Polynomials

class BinaryPolynomial(poly, vartype)

A polynomial with binary variables and real-valued coefficients.

Parameters

• poly (mapping/iterable) – Polynomial as a mapping of form {term: bias, …}, where term is a collection of variables and bias the associated bias. It can also be an iterable of 2-tuples (term, bias).

• vartype (Vartype/str/set) –

  Variable type for the binary quadratic model. Accepted input values:

  • SPIN, 'SPIN', {-1, 1}

  • BINARY, 'BINARY', {0, 1}

degree

Degree of the polynomial.

Type

int

variables

Variables of the polynomial.

Type

set

vartype

One of SPIN or BINARY.

Type

Vartype

Examples

Binary polynomials can be constructed in many different ways. The following are all equivalent

>>> poly = dimod.BinaryPolynomial({'a': -1, 'ab': 1}, dimod.SPIN)
>>> poly = dimod.BinaryPolynomial({('a',): -1, ('a', 'b'): 1}, dimod.SPIN)
>>> poly = dimod.BinaryPolynomial([('a', -1), (('a', 'b'), 1)], dimod.SPIN)
>>> poly = dimod.BinaryPolynomial({'a': -1, 'ab': .5, 'ba': .5}, dimod.SPIN)

Binary polynomials act a mutable mappings but the terms can be accessed with any sequence.

>>> poly = dimod.BinaryPolynomial({'a': -1, 'ab': 1}, dimod.BINARY)
>>> poly['ab']
1
>>> poly['ba']
1
>>> poly[{'a', 'b'}]
1
>>> poly[('a', 'b')]
1
>>> poly['cd'] = 4
>>> poly['dc']
4

Methods

BinaryPolynomial.copy()	Create a shallow copy.
BinaryPolynomial.energies(samples_like[, dtype])	Energies of the given samples.
BinaryPolynomial.energy(sample_like[, dtype])	Energy of the given sample.
BinaryPolynomial.from_hising(h, J[, offset])	Construct a binary polynomial from a higher-order Ising problem.
BinaryPolynomial.from_hubo(H[, offset])	Construct a binary polynomial from a higher-order unconstrained binary optimization (HUBO) problem.
BinaryPolynomial.normalize([bias_range, ...])	Normalize biases of the binary polynomial to fit the provided range(s).
BinaryPolynomial.relabel_variables(mapping)	Relabel variables of a binary polynomial as specified by mapping.
BinaryPolynomial.scale(scalar[, ignored_terms])	Multiply the polynomial by the given scalar.
BinaryPolynomial.to_binary([copy])	Return a binary polynomial over {0, 1} variables.
BinaryPolynomial.to_hising()	Construct a higher-order Ising problem from a binary polynomial.
BinaryPolynomial.to_hubo()	Construct a higher-order unconstrained binary optimization (HUBO) problem from a binary polynomial.
BinaryPolynomial.to_spin([copy])	Return a binary polynomial over {-1, +1} variables.

Functions

poly_energies(samples_like, poly)	Calculates energy of samples from a higher order polynomial.
poly_energy(sample_like, poly)	Calculate energy of a sample from a higher order polynomial.

Reducing to a Binary Quadratic Model

make_quadratic(poly, strength[, vartype, bqm])	Create a binary quadratic model from a higher order polynomial.
make_quadratic_cqm(poly[, vartype, cqm])	Create a constrained quadratic model from a higher order polynomial.
reduce_binary_polynomial(poly)	Reduce a binary polynomial to linear and quadratic terms, plus constraints.