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Catalyst_Code-p=0.5-q=0.7.jl
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Catalyst_Code-p=0.5-q=0.7.jl
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#This function sorts the vector in descending order
function _vsort(p::Vector)
return sort(p,rev=true)
end
#This function pads to length d
function _vpad(d :: Int, p::Vector)
pad = zeros(d)
pad[1:length(p)] = p
return pad
end
#This function computes the classical fidelity of two vectors (i.e. Bhattacharya distance squared)
function _cFidelity(p::Vector, q::Vector)
if length(p) > length(q)
d = length(p)
q = _vpad(d,q)
elseif length(q) < length(p)
d = length(q)
p = _vpad(d,p)
else
d = length(q)
end
F = 0
for i in 1:d
F += sqrt(p[i]*q[i])
end
return F^2
end
#This returns the catalyst fidelity for a bernoulli catalyst
function _bernFidelity(p,q,r)
p = [p,1-p]
q = [q,1-q]
r = [r,1-r]
pr=_vsort(kron(p,r))
qr=_vsort(kron(q,r))
return _cFidelity(pr,qr)
end
#This generates a random distribution for a fixed dimension
function _randDist(dim)
distVect = rand(Float64,(dim,1))
return distVect/sum(distVect)
end
#Hardcode p and q at the start
pval = 0.5
qval = 0.7
println(_bernFidelity(pval,qval,0))
#d = 2
pvec = [pval,1-pval]
qvec = [qval,1-qval]
dim = 2
bestR= zeros(size(dim))
currentF = 0
maxF = 0
ctr = 0
step_size = 0.005
for r1 in [0:step_size:0.5;]
for r2 in [r1:step_size:0.5;]
r = [r1,r2]
if ctr % 100000 == 0
println("Now on ", r)
end
ctr += 1
if (r1+r2) == 1
pr=_vsort(kron(pvec,r))
qr=_vsort(kron(qvec,r))
currentF = _cFidelity(pr,qr)
if currentF > maxF
maxF = currentF
bestR = r
else
end
end
end
end
#d=3
pvec = [pval,1-pval]
qvec = [qval,1-qval]
dim = 3
bestR= zeros(size(dim))
currentF = 0
maxF = 0
ctr = 0
step_size = 0.005
for r1 in [0:step_size:0.4;]
for r2 in [r1:step_size:0.5;]
for r3 in [r2:step_size:0.5;]
r = [r1,r2,r3]
if ctr % 10^8 == 0
println("Now on ", r)
ctr = 0
end
ctr += 1
if (r1+r2+r3) == 1
pr=_vsort(kron(pvec,r))
qr=_vsort(kron(qvec,r))
currentF = _cFidelity(pr,qr)
if currentF > maxF
maxF = currentF
bestR = r
else
end
end
end
end
end
#d=4
pvec = [pval,1-pval]
qvec = [qval,1-qval]
dim = 4
bestR= zeros(size(dim))
currentF = 0
maxF = 0
ctr = 0
step_size = 0.005
for r1 in [0:step_size:0.4;]
for r2 in [r1:step_size:0.4;]
for r3 in [r2:step_size:0.5;]
for r4 in [r3:step_size:0.5;]
r = [r1,r2,r3,r4]
if ctr % 10^8 == 0
println("Now on ", r)
ctr = 0
end
ctr += 1
if (r1+r2+r3+r4) == 1
pr=_vsort(kron(pvec,r))
qr=_vsort(kron(qvec,r))
currentF = _cFidelity(pr,qr)
if currentF > maxF
maxF = currentF
bestR = r
else
end
end
end
end
end
end
#d=5
pvec = [pval,1-pval]
qvec = [qval,1-qval]
dim = 5
bestR= zeros(size(dim))
currentF = 0
maxF = 0
ctr = 0
step_size = 0.005
for r1 in [0:step_size:0.3;]
for r2 in [r1:step_size:0.4;]
for r3 in [r2:step_size:0.4;]
for r4 in [r3:step_size:0.5;]
for r5 in [r4:step_size:0.5;]
r = [r1,r2,r3,r4,r5]
if ctr % 10^8 == 0
println("Now on ", r)
ctr = 0
end
ctr += 1
if sum(r) == 1
pr=_vsort(kron(pvec,r))
qr=_vsort(kron(qvec,r))
currentF = _cFidelity(pr,qr)
if currentF > maxF
maxF = currentF
bestR = r
else
end
end
end
end
end
end
end
#d=6
pvec = [pval,1-pval]
qvec = [qval,1-qval]
dim = 6
bestR= zeros(size(dim))
currentF = 0
maxF = 0
ctr = 0
step_size = 0.005
for r1 in [0:step_size:0.3;]
for r2 in [r1:step_size:0.3;]
for r3 in [r2:step_size:0.4;]
for r4 in [r3:step_size:0.4;]
for r5 in [r4:step_size:0.5;]
for r6 in [r5:step_size:0.5;]
r = [r1,r2,r3,r4,r5,r6]
if ctr % 10^8 == 0
println("Now on ", r)
ctr = 0
end
ctr += 1
if sum(r) == 1
pr=_vsort(kron(pvec,r))
qr=_vsort(kron(qvec,r))
currentF = _cFidelity(pr,qr)
if currentF > maxF
maxF = currentF
bestR = r
else
end
end
end
end
end
end
end
end
#d=7
pvec = [pval,1-pval]
qvec = [qval,1-qval]
dim = 7
bestR= zeros(size(dim))
currentF = 0
maxF = 0
ctr = 0
step_size = 0.005
for r1 in [0.0:step_size:0.1;]
for r2 in [r1:step_size:0.1;]
for r3 in [r2:step_size:0.13;]
for r4 in [r3:step_size:0.16;]
for r5 in [r4:step_size:0.22;]
for r6 in [r5:step_size:0.3;]
for r7 in [r6:step_size:0.41;]
r = [r1, r2, r3, r4, r5, r6, r7]
if ctr % 10^8 == 0
println("Now on ", r)
ctr = 0
end
ctr += 1
if sum(r) == 1
pr=_vsort(kron(pvec,r))
qr=_vsort(kron(qvec,r))
currentF = _cFidelity(pr, qr)
if currentF > maxF
maxF = currentF
bestR = r
else
end
end
end
end
end
end
end
end
end
#d=8
pvec = [pval,1-pval]
qvec = [qval,1-qval]
dim = 8
bestR= zeros(size(dim))
currentF = 0
maxF = 0
ctr = 0
step_size = 0.005
for r1 in [0.0:step_size:0.08;]
for r2 in [r1:step_size:0.08;]
for r3 in [r2:step_size:0.1;]
for r4 in [r3:step_size:0.12;]
for r5 in [r4:step_size:0.16;]
for r6 in [r5:step_size:0.21;]
for r7 in [r6:step_size:0.29;]
for r8 in [r7:step_size:0.4;]
r = [r1,r2,r3,r4,r5,r6,r7,r8]
if ctr % 10^8 == 0
println("Now on ", r)
ctr = 0
end
ctr += 1
if sum(r) == 1
pr=_vsort(kron(pvec,r))
qr=_vsort(kron(qvec,r))
currentF = _cFidelity(pr,qr)
if currentF > maxF
maxF = currentF
bestR = r
else
end
end
end
end
end
end
end
end
end
end