Safe Haskell	Safe-Inferred
Language	Haskell2010

Traq.Primitives.Simons.Prelude

Contents

Primitive

Synopsis

data FindXorPeriod sizeT precT = FindXorPeriod {
- n :: sizeT
- p_0 :: precT
}
newtype FindXorPeriodArg a = FindXorPeriodArg {
- fun :: a
}

Primitive

data FindXorPeriod sizeT precT #

Primitive to solve Simon's problem. Simon's Problem: Given a function f : {0, 1}^n -> {0, 1}^n, find an s : {0, 1}^n such that f(x) = f(x ^ s) for every x.

Promise of default variant: Either (1) f is two-to-one and there is exactly one such s, or (2) f is one-one.

Promise of Robust variant (used in the primitive below): f is allowed to have at most p_0 fraction of spurious collisions (i.e. f(x) = f(x') and x ^ x' /= s).

References: "On the Power of Quantum Computation" https://epubs.siam.org/doi/10.1137/S0097539796298637

Constructors

FindXorPeriod
Fields n :: sizeT p_0 :: precT

Instances

Instances details

(Read sizeT, Read precT) => Read (FindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods readsPrec :: Int -> ReadS (FindXorPeriod sizeT precT) # readList :: ReadS [FindXorPeriod sizeT precT] # readPrec :: ReadPrec (FindXorPeriod sizeT precT) # readListPrec :: ReadPrec [FindXorPeriod sizeT precT] #
(Show sizeT, Show precT) => Show (FindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods showsPrec :: Int -> FindXorPeriod sizeT precT -> ShowS # show :: FindXorPeriod sizeT precT -> String # showList :: [FindXorPeriod sizeT precT] -> ShowS #
(Eq sizeT, Eq precT) => Eq (FindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods (==) :: FindXorPeriod sizeT precT -> FindXorPeriod sizeT precT -> Bool # (/=) :: FindXorPeriod sizeT precT -> FindXorPeriod sizeT precT -> Bool #
Show sizeT => SerializePrim (FindXorPeriod sizeT Double) #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods primNames :: [Ident] # primNameOf :: FindXorPeriod sizeT Double -> Ident # parsePrimParams :: TokenParser () -> Ident -> Parser (FindXorPeriod sizeT Double) # printPrimParams :: FindXorPeriod sizeT Double -> [String] #
MapSize (FindXorPeriod size prec) #
Instance details Defined in Traq.Primitives.Simons.Prelude Associated Types type MappedSize (FindXorPeriod size prec) size' # Methods mapSize :: (size0 ~ SizeType (FindXorPeriod size prec), size' ~ SizeType ext', ext' ~ MappedSize (FindXorPeriod size prec) size') => (size0 -> size') -> FindXorPeriod size prec -> ext' #
(TypingReqs sizeT, Num precT, Ord precT, Show precT) => TypeCheckPrim (FindXorPeriod sizeT precT) sizeT #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods inferRetTypesPrim :: forall ext' shape m. (m ~ TypeChecker ext', sizeT ~ SizeType ext', shape ~ PrimFnShape (FindXorPeriod sizeT precT)) => FindXorPeriod sizeT precT -> shape (FnType sizeT) -> m [VarType sizeT] #
(FindXorPeriod sizeT precT) :<: (SimonsFindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Quantum Methods inject :: FindXorPeriod sizeT precT -> SimonsFindXorPeriod sizeT precT # project :: SimonsFindXorPeriod sizeT precT -> Maybe (FindXorPeriod sizeT precT) #
IsA (FindXorPeriod sizeT precT) (SimonsFindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Quantum Methods extract :: SimonsFindXorPeriod sizeT precT -> FindXorPeriod sizeT precT #
type PrecType (FindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Prelude type PrecType (FindXorPeriod sizeT precT) = precT
type SizeType (FindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Prelude type SizeType (FindXorPeriod sizeT precT) = sizeT
type PrimFnShape (FindXorPeriod sizeT precT) #
Instance details Defined in Traq.Primitives.Simons.Prelude type PrimFnShape (FindXorPeriod sizeT precT) = FindXorPeriodArg
type MappedSize (FindXorPeriod size prec) size' #
Instance details Defined in Traq.Primitives.Simons.Prelude type MappedSize (FindXorPeriod size prec) size' = FindXorPeriod size' prec

newtype FindXorPeriodArg a #

Constructors

FindXorPeriodArg
Fields fun :: a

Instances

Instances details

ValidPrimShape FindXorPeriodArg #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods listToShape :: [a] -> Either String (FindXorPeriodArg a) # shapeToList :: FindXorPeriodArg a -> [a] #
Show a => Show (FindXorPeriodArg a) #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods showsPrec :: Int -> FindXorPeriodArg a -> ShowS # show :: FindXorPeriodArg a -> String # showList :: [FindXorPeriodArg a] -> ShowS #
Eq a => Eq (FindXorPeriodArg a) #
Instance details Defined in Traq.Primitives.Simons.Prelude Methods (==) :: FindXorPeriodArg a -> FindXorPeriodArg a -> Bool # (/=) :: FindXorPeriodArg a -> FindXorPeriodArg a -> Bool #