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

Eq Qbit

Num Qbit

Ord Qbit

Show Qbit

We can display a qubit reference

Heap HeapMap

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

Qdata Bool Qbit

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

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

Monoid U

The type U forms a Monoid

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

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.