sucks

open System.Numerics
open MathNet.Numerics
open MathNet.Numerics.LinearAlgebra

type Qregister = Qregister of Matrix<Complex>
let qreg n =
    let ket = matrix [[Complex (1.0, 0.0)]
                      [Complex (0.0, 0.0)]]
    let rec kronPow = function
    | 1 -> ket
    | n when n > 0 -> ket.KroneckerProduct (kronPow (n - 1))
    | _ -> failwith "degree must be greater than 0"

    Qregister (kronPow n)

type Gate =
    Gate of Matrix<Complex>
        static member (*) (Gate a, Gate b) = Gate (a.KroneckerProduct b)
        static member (><) (Gate a, Qregister s) = Qregister (a * s)
        static member (+) (a, b) = Binding [a; b]
and Binding =
    Binding of List<Gate>
        static member (+) (Binding a, Binding b) = Binding (List.append a b)

        static member (?-) (state, binding) =
            match binding with
            | Binding [] -> state
            | Binding (head::tail) -> (head >< state) ?- (Binding tail)

// lol

let I = matrix [[ Complex (1.0, 0.0); Complex (0.0, 0.0) ]
                [ Complex (0.0, 0.0); Complex (1.0, 0.0) ]] |> Gate
let H = (Complex (1.0/sqrt 2.0, 0.0)) *
        matrix [[ Complex (1.0, 0.0); Complex (1.0,  0.0)]
                [ Complex (1.0, 0.0); Complex (-1.0, 0.0)]] |> Gate

let PauliX = matrix [[Complex (0.0, 0.0); Complex (0.0, -1.0)]
                     [Complex (0.0, 1.0); Complex (0.0,  0.0)]] |> Gate

(qreg 2) ?- (I * H + H * I)
|> printfn "%A"