ToySolver.QUBO

QUBO (quadratic unconstrained boolean optimization)

data Problem a

QUBO (quadratic unconstrained boolean optimization) problem.

Minimize \(\sum_{i\le j} Q_{i,j} x_i x_j\) where \(x_i \in \{0,1\}\) for \(i \in \{0 \ldots N-1\}\).

In the Solution type. 0 and 1 are represented as False and True respectively.

Constructors

Problem

Fields

• quboNumVars :: !Int

  Number of variables N. Variables are numbered from 0 to N-1.

• quboMatrix :: IntMap (IntMap a)

  Upper triangular matrix Q

Instances

Functor Problem

Defined in ToySolver.QUBO

Methods

fmap :: (a -> b) -> Problem a -> Problem b

(<$) :: a -> Problem b -> Problem a

Eq a => Eq (Problem a)

Defined in ToySolver.QUBO

Methods

(==) :: Problem a -> Problem a -> Bool

(/=) :: Problem a -> Problem a -> Bool

Show a => Show (Problem a)

Defined in ToySolver.QUBO

Methods

showsPrec :: Int -> Problem a -> ShowS

show :: Problem a -> String

showList :: [Problem a] -> ShowS

FileFormat (Problem Scientific)

Defined in ToySolver.QUBO

Methods

parse :: ByteString -> Either String (Problem Scientific)

render :: Problem Scientific -> Builder

type Solution = UArray Int Bool

eval :: Num a => Solution -> Problem a -> a

Ising Model

data IsingModel a

Ising model.

Minimize \(\sum_{i<j} J_{i,j} \sigma_i \sigma_j + \sum_i h_i \sigma_i\) where \(\sigma_i \in \{-1,+1\}\) for \(i \in \{0 \ldots N-1\}\).

In the Solution type. -1 and +1 are represented as False and True respectively.

Constructors

IsingModel

Fields

• isingNumVars :: !Int

  Number of variables N. Variables are numbered from 0 to N-1.

• isingInteraction :: IntMap (IntMap a)

  Interaction \(J_{i,j}\) with \(i < j\).

• isingExternalMagneticField :: IntMap a

  External magnetic field \(h_j\).

Instances

Eq a => Eq (IsingModel a)

Defined in ToySolver.QUBO

Methods

(==) :: IsingModel a -> IsingModel a -> Bool

(/=) :: IsingModel a -> IsingModel a -> Bool

Show a => Show (IsingModel a)

Defined in ToySolver.QUBO

Methods

showsPrec :: Int -> IsingModel a -> ShowS

show :: IsingModel a -> String

showList :: [IsingModel a] -> ShowS

evalIsingModel :: Num a => Solution -> IsingModel a -> a