Created
May 17, 2013 15:57
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Unitary evolution code in Julia
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function expm_eigen(A::Matrix, t) | |
#Calculates expm(t*A) via eigenvalue decomposition and assuming Hermitian matrix | |
F = eigfact(Hermitian(A)) | |
# V * diagm(exp(t*D)) * V' | |
return scale(F[:vectors], exp(t*F[:values])) * F[:vectors]' | |
end | |
function evolution_unitary(Hnat::Matrix{Complex128}, controlHams::Array{Complex128, 3}, controlFields::Matrix{Float64}, controlFreqs::Vector{Float64}) | |
const timeStep = 0.01 | |
Uprop = eye(Complex128, size(Hnat,1)) | |
tmpH = similar(Hnat) | |
for timect = 1:size(controlFields,2) | |
tmpH[:] = Hnat | |
for controlct = 1:size(controlFields,1) | |
tmpH += controlFields[controlct, timect]*cos(2*pi*timeStep*timect*controlFreqs[controlct])*controlHams[:, :, controlct] | |
end | |
Uprop *= expm_eigen(tmpH, -1im*2*pi*timeStep) | |
end | |
return Uprop | |
end | |
function parallel_evolution_unitary(Hnat::Matrix{Complex128}, controlHams::Array{Complex128, 3}, controlFields::Matrix{Float64}, controlFreqs::Vector{Float64}) | |
const timeStep = 0.01 | |
tmpH = similar(Hnat) | |
Uprop = @parallel (*) for timect = 1:size(controlFields,2) | |
tmpH[:] = Hnat | |
for controlct = 1:size(controlFields,1) | |
tmpH += controlFields[controlct, timect]*cos(2*pi*timeStep*timect*controlFreqs[controlct])*controlHams[:, :, controlct] | |
end | |
expm_eigen(tmpH, -1im*2*pi*timeStep) | |
end | |
return Uprop | |
end | |
function sim_setup(dimension, numTimeSteps, numControls) | |
#Create a random natural hamiltonian | |
tmpMat = randn(dimension, dimension) + 1im*randn(dimension, dimension) | |
Hnat = tmpMat+tmpMat' | |
#Create random control Hamiltonians | |
controlHams = zeros(Complex128, (dimension, dimension, numControls)) | |
for ct = 1:numControls | |
tmpMat[:] = randn(dimension, dimension) + 1im*randn(dimension, dimension) | |
controlHams[:,:,ct] = tmpMat+tmpMat' | |
end | |
#Create random controlfields | |
controlFields = randn(numControls, numTimeSteps) | |
#Control frequencies | |
controlFreqs = randn(numControls) | |
return Hnat, controlHams, controlFields, controlFreqs | |
end | |
function run_sim() | |
evolution_unitary(Hnat, controlHams, controlFields, controlFreqs) | |
end | |
function run_parallel_sim() | |
parallel_evolution_unitary(Hnat, controlHams, controlFields, controlFreqs) | |
end | |
Hnat, controlHams, controlFields, controlFreqs = sim_setup(16, 2000, 4) |
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