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.
|Representation of a probability amplitude
entangle takes as input a list of values and probability
amplitudes and gives as output a superposition of the inputs.
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
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_ 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)
Will collapse x to be either even or odd, but make no finer
decisions than that.
|observe is just observeWith on equality.
|runQuantum takes an input state vector, runs it through the given
Quantum arrow, and returns a state vector of outputs.
|execQuantum q x passes the state |x> through q, collapses q's
output to an eigenstate, and returns it.
|Produced by Haddock version 2.3.0|