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how to write milburn equation?

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reza hamzeh
reza hamzeh 2019-12-20
评论： reza hamzeh 2019-12-23
hi. i wanted to write milburn equation in matlab. but im not sure that i wrote it exactly. seems i made some mistakes because it didnt give me the correct answer.
this is the correct answer
1.jpg
and this is the milburn equation.
milburn.jpg
and this is the code that i wrote.(in my codes innerstate =p(0) and gamma=de)
clear;
syms x;
t=1;
de=50;
Haf=[x/2 0 0 0;0 -x/2 x 0;0 x -x/2 0;0 0 0 x/2];
innerstate=[1 1 0 0;1 1 1 1;1 1 1 0;1 0 1 0];
[vectors,values]=eig(Haf(x));
ro=zeros(size(innerstate,1));
for m=1:4
for n=1:4
ro=ro+exp(((-t/(2*de))*(values(n,n)-values(m,m))^2)-(1i*t)*(values(n,n)-values(m,m)))...
*((vectors(:,m)')*innerstate*vectors(:,n))*(vectors(:,m)*(vectors(:,n)'));
end
end
  2 个评论
David Goodmanson
David Goodmanson 2019-12-23
编辑：David Goodmanson 2019-12-23
Hi reza,
Is Haf the same as the H in the problem definition? And in the same basis used to express Haf, could you check that innerstate is as below? If all that is correct, then something seems to be wrong, as far as getting the proposed answer.
The most obvious indication is that the trace of rho(t) has to equal the trace of rho(0). This is true because the exponential factor = 1 whenever n=m. However, the trace of the proposed answer is 8, and the trace of innerstate is 3.
innerstate =
1 1 0 0
1 1 1 1
1 1 1 0
1 0 1 0
reza hamzeh
reza hamzeh 2019-12-23
hi. thank u. the problem is solved.

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