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:

  • Vartype.SPIN, 'SPIN', {-1, 1}
  • Vartype.BINARY, 'BINARY', {0, 1}

degree

The degree of the polynomial.

Type:int

variables

The variables.

Type:set

vartype

One of Vartype.SPIN or Vartype.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])	The energies of the given samples.
BinaryPolynomial.energy(sample_like[, dtype])	The 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, …])	Normalizes the biases of the binary polynomial such that they fall in 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.

Reducing to a Binary Quadratic Model

make_quadratic(poly, strength[, vartype, bqm])

Create a binary quadratic model from a higher order polynomial.