Implementation of the Quantum Monad, which promotes an arbitrary data type to a quantum state.

Whenever a value of type Quantum a is modified, the modification is propagated to all possible states of the underlying type. Each possible state is weighted by a complex amplitude and the individual amplitudes can interfere when the state undergoes a transformation. This allows (in theory) the simulation of any discrete quantum process.

The Quantum Monad is analogous to the Probability Monad used for probabalistic programming. The main difference is in the normalization of states: While using the L1 norm leads to probabalistic states, the L2 norm is responsible for quantum states.

Analogously, one can say that this package implements the concept of quantum programming.

The following code defines a Quantum Int that is in a superposition of |0> and |1>, performs a unitary variant of addition and prints the resulting measurement probabilities. Non-unitary transformations currently lead to a runtime error.

import Control.Quantum

state :: Quantum Int
state = quantize [(0, 1 / sqrt 2 ), (1, 1 / sqrt 2)]

-- All quantum transformations have to be unitary (i.e. reversible)
transform :: Quantum Int -> Quantum Int -> Quantum (Int,  Int)
transform qx qy = do
  x <- qx
  y <- qy
  return (x, x + y)

main = print $ measurements $ transform state state
-- [((0,0),0.25),((0,1),0.25),((1,1),0.25),((1,2),0.25)]