quantum-arrow-0.0.5: An embedding of quantum computation as a Haskell arrow

QuantumArrow.Quantum

Synopsis

# Documentation

data Quantum m b c Source

The Quantum arrow represents a quantum computation with observation. You can give a quantum computation a superposition of values, and it will operate over them, returning you a superposition back. If ever you observe (using the qLift or qLift_ functions), the system collapses to an eigenstate of what you observed.

``` x <- entangle -< [(1, 1 :+ 0), (2, 1 :+ 0)]
-- x is in state |1> + |2>; i.e. 1 or 2 with equal probability
let y = x + 1
-- y is in state |2> + |3>
qLift print -< y    -- will print either 2 or 3; let's say it printed 2
-- state collapses here, y in state |2>
qLift print -< x    -- prints 1 (assuming 2 was printed earlier)
```

So the variables become entangled with each other in order to maintain consistency of the computation.

Instances

 Monad m => Arrow (Quantum m) Monad m => ArrowChoice (Quantum m) Monad m => Category (Quantum m)

Representation of a probability amplitude

entangle :: Monad m => Quantum m [(a, Amp)] aSource

entangle takes as input a list of values and probability amplitudes and gives as output a superposition of the inputs. For example:

``` x <- entangle -< [(1, 1 :+ 0), (2, 0 :+ 1)]
-- x is now |1> + i|2>
qLift print -< x    -- prints 1 or 2 with equal probability
```

qLift :: (Eq a, MonadRandom m) => (a -> m b) -> Quantum m a bSource

`qLift f -< x` first collapses `x` to an eigenstate (using observe) then executes `f x` in the underlying monad. All conditionals up to this point are collapsed to an eigenstate (True or False) so a current branch of the computation is selected.

qLift_ :: MonadRandom m => m b -> Quantum m () bSource

qLift_ is just qIO which doesn't take an input. eg.

``` qLift_ \$ print "hello world" -< ()
```

All conditionals up to this point are collapsed to an eigenstate (True or False) so a current branch of the computation is selected.

observeWith :: MonadRandom m => (a -> a -> Bool) -> Quantum m a aSource

`observeWith f` takes an equivalence relation f, breaks the state space into eigenstates of that relation, and collapses to one. For example:

``` x <- entangle -< map (\s -> (s,1 :+ 0)) [1..20]
observeWith (\x y -> x `mod` 2 == y `mod` 2)
```

Will collapse `x` to be either even or odd, but make no finer decisions than that.

observe :: (Eq a, MonadRandom m) => Quantum m a aSource

observe is just observeWith on equality.

runQuantum :: Monad m => Quantum m a b -> [(a, Amp)] -> m [(b, Amp)]Source

runQuantum takes an input state vector, runs it through the given Quantum arrow, and returns a state vector of outputs.

execQuantum :: (Eq b, MonadRandom m) => Quantum m a b -> a -> m bSource

`execQuantum q x` passes the state |x> through q, collapses q's output to an eigenstate, and returns it.