SE, LVN, LME types and integration

prop_eq_types.jl

using QuBase

import Base: start, next, done

abstract QuPropagatorMethod

abstract QuantumEquation

immutable SE{H<:QuBase.AbstractQuMatrix, V<:QuBase.AbstractQuVector} <: QuantumEquation
    hamiltonian::H
    initial_state::V
    SE(hamiltonian, initial_state) = new(hamiltonian, initial_state)
end

SE{H<:QuBase.AbstractQuMatrix, V<:QuBase.AbstractQuVector}(hamiltonian::H, initial_state::V) = SE{H,V}(hamiltonian, initial_state)

immutable LVN{H<:QuBase.AbstractQuMatrix} <: QuantumEquation
    hamiltonian::H
    initial_density_matrix::H
    LVN(hamiltonian, initial_density_matrix) = new(hamiltonian, initial_density_matrix)
end

LVN{H<:QuBase.AbstractQuMatrix}(hamiltonian::H, initial_density_matrix::H) = LVN{H}(hamiltonian, initial_density_matrix)

immutable QuPropagator{QPM<:QuPropagatorMethod, QE<:QuantumEquation}
    qu_equation::QE
    tlist
    method::QPM
    QuPropagator(qu_equation, tlist, method) = new(qu_equation, tlist, method)
end

QuPropagator{QPM<:QuPropagatorMethod, QE<:QuantumEquation}(qu_equation::QE, tlist, method::QPM) = QuPropagator{QPM, QE}(qu_equation, tlist, method)

immutable QuPropagatorState
    psi
    t
    t_state
end


function start_state(qu_eq::LVN)
    return qu_eq.initial_density_matrix
end

function start_state(qu_eq::SE)
    return qu_eq.initial_state
end

function Base.start(prob::QuPropagator)
    init_state = start_state(prob.qu_equation)
    t_state = start(prob.tlist)
    t,t_state = next(prob.tlist,t_state)
    return QuPropagatorState(init_state,t,t_state)
end

function op(qu_eq::LVN)
    return qu_eq.hamiltonian
end

function op(qu_eq::SE)
    return qu_eq.hamiltonian
end

function Base.next{QPM<:QuPropagatorMethod}(prob::QuPropagator{QPM}, qustate::QuPropagatorState)
    current_qustate = qustate.psi
    current_t = qustate.t
    t,t_state = next(prob.tlist, qustate.t_state)
    next_qustate = propagate(prob.method, t, current_t, current_qustate, prob.qu_equation)
    return (t, next_qustate), QuPropagatorState(next_qustate, t, t_state)
end

Base.done(prob::QuPropagator, qustate::QuPropagatorState) = done(prob.tlist, qustate.t_state)

immutable QuEuler <: QuPropagatorMethod
end

function propagate(prob::QuEuler, t, current_t, current_qustate, qu_eq::SE)
    dt = t - current_t
    return (eye(op(qu_eq))-im*op(qu_eq)*dt)*current_qustate
end

qv = normalize!(QuArray([0.5+0.1im, 0.2+0.2im]))
t = 0.:0.1:2*pi

se = SE(sigmax, qv)
println(se)
lvn = LVN(sigmax, sigmax)
println(lvn)
qe = QuPropagator(se, t, QuEuler())
println(qe)
start_qe = start(qe)
println(start_qe)
next_start_qe = next(qe, start_qe)
println(next_start_qe)

# Results in 
SE{QuArray{FiniteBasis{Orthonormal},Float64,2,Array{Float64,2}},QuArray{FiniteBasis{Orthonormal},Complex{Float64},1,Array{Complex{Float64},1}}}(2x2 QuMatrix in FiniteBasis{Orthonormal}:
...coefficients: Array{Float64,2}
[0.0 1.0
 1.0 0.0],2-element QuVector in FiniteBasis{Orthonormal}:
...coefficients: Array{Complex{Float64},1}
Complex{Float64}[0.8574929257125441 + 0.17149858514250882im,0.34299717028501764 + 0.34299717028501764im])

LVN{QuArray{FiniteBasis{Orthonormal},Float64,2,Array{Float64,2}}}(2x2 QuMatrix in FiniteBasis{Orthonormal}:
...coefficients: Array{Float64,2}
[0.0 1.0
 1.0 0.0],2x2 QuMatrix in FiniteBasis{Orthonormal}:
...coefficients: Array{Float64,2}
[0.0 1.0
 1.0 0.0])

QuPropagator{QuEuler,SE{QuArray{FiniteBasis{Orthonormal},Float64,2,Array{Float64,2}},QuArray{FiniteBasis{Orthonormal},Complex{Float64},1,Array{Complex{Float64},1}}}}(SE{QuArray{FiniteBasis{Orthonormal},Float64,2,Array{Float64,2}},QuArray{FiniteBasis{Orthonormal},Complex{Float64},1,Array{Complex{Float64},1}}}(2x2 QuMatrix in FiniteBasis{Orthonormal}:
...coefficients: Array{Float64,2}
[0.0 1.0
 1.0 0.0],2-element QuVector in FiniteBasis{Orthonormal}:
...coefficients: Array{Complex{Float64},1}
Complex{Float64}[0.8574929257125441 + 0.17149858514250882im,0.34299717028501764 + 0.34299717028501764im]),0.0:0.1:6.2,QuEuler())

QuPropagatorState(2-element QuVector in FiniteBasis{Orthonormal}:
...coefficients: Array{Complex{Float64},1}
Complex{Float64}[0.8574929257125441 + 0.17149858514250882im,0.34299717028501764 + 0.34299717028501764im],0.0,1)

((0.1,2-element QuVector in FiniteBasis{Orthonormal}:
...coefficients: Array{Complex{Float64},1}
Complex{Float64}[0.8917926427410459 + 0.13719886811400706im,0.3601470287992685 + 0.25724787771376323im]),QuPropagatorState(2-element QuVector in FiniteBasis{Orthonormal}:
...coefficients: Array{Complex{Float64},1}
Complex{Float64}[0.8917926427410459 + 0.13719886811400706im,0.3601470287992685 + 0.25724787771376323im],0.1,2))