Hi Lars,

That feature of fitApplyMPO may not be working. However, I recently wrote a slightly different version of fitApplyMPO that does support a noise term and I am pasting it below. Could you look through it and give it a try and let me know if it works for you (perhaps with minor modifications if there's a minor bug somewhere)?

If it works well for you I may replace what's in the library with it:

```
namespace itensor {
template<typename T>
MPSt<T>
fitApplyOneSite(MPSt<T> const& psi,
MPOt<T> const& W,
Sweeps const& sweeps,
Args args = Args::global())
{
auto quiet = args.getBool("Quiet",true);
auto N = psi.N();
auto res = psi;
auto LR = std::vector<T>(N+2);
LR.at(N) = psi.A(N) * W.A(N) * dag(prime(res.A(N)));
for(auto j = N-1; j > 1; --j)
{
LR.at(j) = LR.at(j+1)*psi.A(j)*W.A(j)*dag(prime(res.A(j)));
}
for(auto sw : range1(sweeps.nsweep()))
{
args.add("Sweep",sw);
args.add("Cutoff",sweeps.cutoff(sw));
args.add("Minm",sweeps.minm(sw));
args.add("Maxm",sweeps.maxm(sw));
auto noise = sweeps.noise(sw);
for(int j = 1, ha = 1; ha <= 2; sweepnext1(j,ha,N))
{
if(not quiet) printfln("sw=%d j=%d ha=%d noise=%.3E",sw,j,ha,noise);
//
// Apply MPO
//
auto WA = psi.A(j);
if(LR.at(j-1)) WA *= LR.at(j-1);
WA *= W.A(j);
if(LR.at(j+1)) WA *= LR.at(j+1);
res.setA(j,noprime(WA));
if(not (ha==2 && j==1))
{
res.Anc(j) /= norm(res.A(j));
//
// Form density matrix
//
auto d = ha==1 ? +1 : -1;
auto li = linkInd(res,ha==1 ? j : j-1);
auto rho = li ? primeExcept(res.A(j),li) : prime(res.A(j));
rho *= dag(res.A(j));
//
// Form noise * density matrix perturbation
//
if(noise > 0.)
{
auto drho = psi.A(j);
if(LR.at(j-d)) drho *= LR.at(j-d);
drho *= W.A(j);
drho = dag(noprime(drho)) * drho;
rho += noise*drho;
}
//
// Diag density matrix
//
T U,D;
auto spec = diagHermitian(rho,U,D,args);
auto ci = commonIndex(U,D);
if(not quiet) printfln("m=%d truncerr=%.5E",ci.m(),spec.truncerr());
if(j+d <= N && j+d >= 1)
{
auto C = dag(U)*res.A(j);
res.setA(j,U);
res.setA(j+d,C*res.A(j+d));
}
LR.at(j) = LR.at(j-d) ? LR.at(j-d)*psi.A(j) : psi.A(j);
LR.at(j) *= W.A(j);
LR.at(j) *= dag(prime(res.A(j)));
}
}
}
return res;
}
} //namespace itensor
```

The above code is intended to go into a header file. You can put it into a .cc file too with using namespace itensor; above and just remove the namespace itensor { } part around it.

Best,

Miles