Safe Haskell	Safe-Inferred
Language	Haskell2010

Traq.Primitives.Simons.Prelude

Contents

Primitive

Synopsis

data FindXorPeriod size prec = FindXorPeriod {
- n :: size
- p_0 :: prec
}
newtype FindXorPeriodArg a = FindXorPeriodArg {
- fun :: a
}

Primitive

data FindXorPeriod size prec #

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 :: size p_0 :: prec

Instances

Instances details

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