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Operators : Squeeze, displaceop. Addition : expm, full #25

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Apr 21, 2015
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Operators : Squeeze, displaceop. Addition : expm, full #25

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8 changes: 7 additions & 1 deletion src/arrays/arraymath.jl
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Expand Up @@ -59,7 +59,7 @@ function *{B<:OrthonormalBasis}(qm1::QuMatrix{B}, qm2::QuMatrix{B})
bases(qm2,2))
end

*(dm1::DualMatrix, dm2::DualMatrix) = (dm1.qarr*dm2.qarr)'
*(dm1::DualMatrix, dm2::DualMatrix) = (dm2.qarr*dm1.qarr)'

function +{B<:OrthonormalBasis,N}(qarr1::AbstractQuArray{B,N}, qarr2::AbstractQuArray{B,N})
if bases(qarr1) == bases(qarr2)
Expand Down Expand Up @@ -90,6 +90,12 @@ Base.scale(qarr::Union(QuArray,CTranspose), num::Number) = scale(num, qarr)
*(qarr::Union(QuArray,CTranspose), num::Number) = scale(qarr, num)
/(qarr::Union(QuArray,CTranspose), num::Number) = scale(1/num, qarr)

# sparse to dense
Base.full(qarr::AbstractQuMatrix) = QuArray(full(coeffs(qarr)),bases(qarr))

# exponential of dense matrix
Base.expm(qarr::AbstractQuMatrix) = QuArray(expm(full(coeffs(qarr))),bases(qarr))

# normalization
Base.norm(qarr::Union(QuArray,CTranspose)) = vecnorm(rawcoeffs(qarr))

Expand Down
19 changes: 18 additions & 1 deletion src/arrays/constructors.jl
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Expand Up @@ -16,4 +16,21 @@
one_at_ind!(arr, i) = setindex!(arr, one(eltype(arr)), i)
single_coeff(i, lens...) = one_at_ind!(zeros(lens), i)

export statevec
# Reference :
# Section - 1.1, http://cds.cern.ch/record/331607/files/9708012.pdf
function coherentstatevec_inf(n::Int,alpha::Number)
s = zeros(typeof(float(alpha)),n)
s[1] = one(alpha)
for i in [2:n]
s[i] = alpha/sqrt(i-1)*s[i-1]
end
z = QuArray(s)
return scale!(exp(-abs2(alpha)/2),z)
end

# Reference :
# 2nd Defintion : http://en.wikipedia.org/wiki/Coherent_states#Mathematical_features_of_the_canonical_coherent_states
coherentstatevec(n::Int, alpha::Number) = displaceop(n,alpha)*statevec(1,FiniteBasis(n))
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I don't think we need both versions and for now I would prefer the second one. There might actually be a problem having both, because they only differ in the keywords and I am not sure how Julia handles this. You can check by calling

@which coherentstatevec(20,1,method = "direct")
@which coherentstatevec(20,1)

To see which versions are actually called.

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I have tried this out

println(@which coherentstatevec(10,1,method="direct"))
println(coherentstatevec(10,1,method="direct"))
println(@which coherentstatevec(10,1))
println(coherentstatevec(10,1))

# gives out 

coherentstatevec(n::Int64,alpha::Number) at QuBase.jl/src/arrays/constructors.jl:28
10-element QuVector in FiniteBasis{Orthonormal,1}:
...coefficients: Array{Float64,1}
[0.6065306597126334,0.6065306597126334,0.4288819424803534,0.24761510494160166,0.12380755247080083,0.05536842069051653,0.02260406309258736,0.008543532794657104,0.0030205949871958465,0.001006864995731949]
coherentstatevec(n::Int64,alpha::Number) at QuBase.jl/src/arrays/constructors.jl:28
10-element QuVector in FiniteBasis{Orthonormal,1}:
...coefficients: Array{Float64,1}
[0.6065306597114603,0.6065306597355303,0.4288819421804789,0.24761510797604577,0.12380752738214919,0.05536859516814174,0.02260302507996636,0.008548870306885925,0.0029967233467164565,0.0011000726308558629]

The output is different though they point to the same method which is reflected by the @which

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To be sure you can put a println statement in one of the functions ...

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I gave in a println for the rand(n) and this is the output ... seems like the method is being called but is not reflected by @which

coherentstatevec(n::Int64,alpha::Number) at QuBase.jl/src/arrays/constructors.jl:28

# printing rand(n)

[0.019244684430714143,0.3719091096873184,0.9047165798455694,0.6866397480495858,0.5561245580875909,0.14391135614954487,0.6180840544733457,0.002417775152962154,0.9427717780056364,0.20641868199486169]

# returning the output 

10-element QuVector in FiniteBasis{Orthonormal,1}:
...coefficients: Array{Float64,1}
[0.6065306597126334,0.6065306597126334,0.4288819424803534,0.24761510494160166,0.12380755247080083,0.05536842069051653,0.02260406309258736,0.008543532794657104,0.0030205949871958465,0.001006864995731949]


coherentstatevec(n::Int64,alpha::Number) at QuBase.jl/src/arrays/constructors.jl:28
10-element QuVector in FiniteBasis{Orthonormal,1}:
...coefficients: Array{Float64,1}
[0.6065306597114603,0.6065306597355303,0.4288819421804789,0.24761510797604577,0.12380752738214919,0.05536859516814174,0.02260302507996636,0.008548870306885925,0.0029967233467164565,0.0011000726308558629]


export statevec,
coherentstatevec
10 changes: 9 additions & 1 deletion src/arrays/ladderops.jl
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Expand Up @@ -37,7 +37,15 @@ function momentumop(n::Int)
return scale(im/sqrt(2.), cop-cop')
end

squeeze_construct(a::AbstractQuMatrix,b::AbstractQuMatrix, z::Number) = scale!(0.5,(scale!(z',a*b)-scale!(z,a'*b')))
squeezingop(a::AbstractQuMatrix, b::AbstractQuMatrix, z::Number) = expm(squeeze_construct(a,b,z))
squeezingop(n::Int,z::Number) = squeezingop(lowerop(n),lowerop(n),z)

displaceop(n::Int,alpha::Number) = expm(scale(alpha,lowerop(n)')-scale(alpha',lowerop(n)))

export raiseop,
lowerop,
positionop,
momentumop
momentumop,
squeezingop,
displaceop
2 changes: 1 addition & 1 deletion test/multest.jl
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Expand Up @@ -30,4 +30,4 @@ qv = QuArray(v)
@test_approx_eq rawcoeffs(normalize(qv)) rawcoeffs(qv)/norm(v)

# a simple test of the `==` operator
@assert qm*3im == scale!(3im, copy(qm))
@assert qm*3im == scale!(3im, copy(qm))
17 changes: 14 additions & 3 deletions test/operatortest.jl
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Expand Up @@ -10,11 +10,22 @@

@assert coeffs(commutator(sigma_x, sigma_x)) == spzeros(2,2)

######################################
# Position & Momentum Operators Test #
######################################
####################################################
# Position, Displacement & Momentum Operators Test #
####################################################

p = positionop(2)
m = momentumop(2)
@assert coeffs(commutator(sigma_x, p)) == spzeros(2,2)
@assert coeffs(commutator(sigma_y, m)) == spzeros(2,2)

coherentstate_inf = QuBase.coherentstatevec_inf(20,1)
coherentstate = displaceop(20,1)*statevec(1,FiniteBasis(20))
@test_approx_eq_eps coeffs(coherentstate_inf)[1] coeffs(coherentstate)[1] 1e-8

############################
# Squeezing Operators Test #
############################

@assert squeezingop(2,1.0)== QuArray(eye(2))
@test_approx_eq coeffs(squeezingop(lowerop(2), QuArray(eye(2)), 2.0)') coeffs(displaceop(2,1.0))