- data Quantum m b c
- type Amp = Complex Double
- entangle :: Monad m => Quantum m [(a, Amp)] a
- qLift :: (Eq a, MonadRandom m) => (a -> m b) -> Quantum m a b
- qLift_ :: MonadRandom m => m b -> Quantum m () b
- observeWith :: MonadRandom m => (a -> a -> Bool) -> Quantum m a a
- observe :: (Eq a, MonadRandom m) => Quantum m a a
- runQuantum :: Monad m => Quantum m a b -> [(a, Amp)] -> m [(b, Amp)]
- execQuantum :: (Eq b, MonadRandom m) => Quantum m a b -> a -> m b
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.
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 f -< x first collapses
x to an eigenstate (using observe) then
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_ 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 f takes an equivalence relation f, breaks the state
space into eigenstates of that relation, and collapses to one.
x <- entangle -< map (\s -> (s,1 :+ 0)) [1..20] observeWith (\x y -> x `mod` 2 == y `mod` 2)
x to be either even or odd, but make no finer
decisions than that.
runQuantum takes an input state vector, runs it through the given Quantum arrow, and returns a state vector of outputs.