QIO.QioSyn

This module defines the Syntax of the Quantum IO Monad, which is an embedded language for writing quantum computations.

Documentation

type RR = Double

For Real numbers, we simply use the built in Double type

type CC = Complex RR

For Complex numbers, we use the built in Complex numbers, over our Real number type (i.e. Double)

amp :: CC -> RR

The amplitude of a complex number is the magnitude squared.

newtype Qbit

The type of Qubits in QIO are simply integer references.

Constructors

Qbit Int

Instances

Enum Qbit

Methods

succ :: Qbit -> Qbit

pred :: Qbit -> Qbit

toEnum :: Int -> Qbit

fromEnum :: Qbit -> Int

enumFrom :: Qbit -> [Qbit]

enumFromThen :: Qbit -> Qbit -> [Qbit]

enumFromTo :: Qbit -> Qbit -> [Qbit]

enumFromThenTo :: Qbit -> Qbit -> Qbit -> [Qbit]

Eq Qbit

Methods

(==) :: Qbit -> Qbit -> Bool

(/=) :: Qbit -> Qbit -> Bool

Num Qbit

Methods

(+) :: Qbit -> Qbit -> Qbit

(-) :: Qbit -> Qbit -> Qbit

(*) :: Qbit -> Qbit -> Qbit

negate :: Qbit -> Qbit

abs :: Qbit -> Qbit

signum :: Qbit -> Qbit

fromInteger :: Integer -> Qbit

Ord Qbit

Methods

compare :: Qbit -> Qbit -> Ordering

(<) :: Qbit -> Qbit -> Bool

(<=) :: Qbit -> Qbit -> Bool

(>) :: Qbit -> Qbit -> Bool

(>=) :: Qbit -> Qbit -> Bool

max :: Qbit -> Qbit -> Qbit

min :: Qbit -> Qbit -> Qbit

Show Qbit

We can display a qubit reference

Methods

showsPrec :: Int -> Qbit -> ShowS

show :: Qbit -> String

showList :: [Qbit] -> ShowS

Heap HeapMap

A HeapMap is an instance of the Heap type class, where the Heap functions can make use of the underlying Map functions.

Methods

initial :: HeapMap

update :: HeapMap -> Qbit -> Bool -> HeapMap

(?) :: HeapMap -> Qbit -> Maybe Bool

forget :: HeapMap -> Qbit -> HeapMap

hswap :: HeapMap -> Qbit -> Qbit -> HeapMap

Qdata Bool Qbit

The lowest-level instance of Qdata is the relation between Booleans and Qubits.

Methods

mkQ :: Bool -> QIO Qbit

measQ :: Qbit -> QIO Bool

letU :: Bool -> (Qbit -> U) -> U

condQ :: Qbit -> (Bool -> U) -> U

type Rotation = (Bool, Bool) -> CC

A rotation is in essence a two-by-two complex valued matrix

data U

The underlying data type of a U unitary operation

Constructors

UReturn

Rot Qbit Rotation U

Swap Qbit Qbit U

Cond Qbit (Bool -> U) U

Ulet Bool (Qbit -> U) U

Instances

Show U

We can display a representation of a unitary

Methods

showsPrec :: Int -> U -> ShowS

show :: U -> String

showList :: [U] -> ShowS

Monoid U

The type U forms a Monoid

Methods

mempty :: U

mappend :: U -> U -> U

mconcat :: [U] -> U

data QIO a

The underlying data type of a QIO Computation

Constructors

QReturn a

MkQbit Bool (Qbit -> QIO a)

ApplyU U (QIO a)

Meas Qbit (Bool -> QIO a)

Instances

Monad QIO

The QIO type forms a Monad

Methods

(>>=) :: QIO a -> (a -> QIO b) -> QIO b

(>>) :: QIO a -> QIO b -> QIO b

return :: a -> QIO a

fail :: String -> QIO a

Functor QIO

Methods

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

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

Applicative QIO

Methods

pure :: a -> QIO a

(<*>) :: QIO (a -> b) -> QIO a -> QIO b

(*>) :: QIO a -> QIO b -> QIO b

(<*) :: QIO a -> QIO b -> QIO a

rot :: Qbit -> Rotation -> U

Apply the given rotation to the given qubit

swap :: Qbit -> Qbit -> U

Swap the state of the two given qubits

cond :: Qbit -> (Bool -> U) -> U

Apply the conditional unitary, depending on the value of the given qubit

ulet :: Bool -> (Qbit -> U) -> U

Introduce an Ancilla qubit in the given state, for use in the sub-unitary

urev :: U -> U

Returns the inverse (or reverse) of the given unitary operation

unot :: Qbit -> U

Apply a not rotation to the given qubit

uhad :: Qbit -> U

Apply a hadamard rotation to the given qubit

uphase :: Qbit -> RR -> U

Apply a phase rotation (of the given angle) to the given qubit

mkQbit :: Bool -> QIO Qbit

Initialise a qubit in the given state (adding it to the overall quantum state)

applyU :: U -> QIO ()

Apply the given unitary operation to the current quantum state

measQbit :: Qbit -> QIO Bool

Measure the given qubit, and return the measurement outcome (note that this operation may affect the overall quantum state, as a measurement is destructive)

rid :: Rotation

The identity rotation

rnot :: Rotation

The not rotation

rhad :: Rotation

The hadamard rotation

rphase :: RR -> Rotation

The phase rotation

rrev :: Rotation -> Rotation

Returns the inverse (or reverse) of the given rotation

show' :: U -> Int -> Int -> String

A helper function for the show instance of U

spaces :: Int -> String

A helper function that returns a string of 4x spaces.

Orphan instances

Eq Rotation

Rotations can be compared for equality. They are equal if the define the same matrix.

Methods

(==) :: Rotation -> Rotation -> Bool

(/=) :: Rotation -> Rotation -> Bool

Show Rotation

We can display the matrix representation of a rotation

Methods

showsPrec :: Int -> Rotation -> ShowS

show :: Rotation -> String

showList :: [Rotation] -> ShowS