MPS and MPO interface updates

[mtfishman]

Here are some proposals for improving the MPS and MPO algebra interface:

• Introduce a function product that wraps contract(::MPO, ::MPS) that attempts to return the output site indices to the original MPS site indices (for example, with a simple call to replace_siteinds!). This is called product since it is very similar to the ProjMPO product function, and you could imagine this operation being used in a global Krylov method using MPS/MPO.
• Introduce a function product(A::MPO, B::MPO) that works like matmul(::ITensor, ::ITensor) where the two MPOs have the same pairs of site indices, and returns an MPO with the same pairs of site indices as the input. It would do the operation mapprime(prime(A)*B,2,1).
• Introduce add(::MPS, ::MPS, ::MPS...) for summing many MPS, with the fancier algorithm use in sum(::Vector{MPS}).
• Make contract(::MPS, ::MPS) that is like inner/dot but does not dag the first MPS, and doesn't match the site indices by default (a more literal MPS * MPS contraction).
• Rename mul(::MPO, ::MPS)/applympo(::MPO, ::MPS) to contract(::MPO, ::MPS), with an alias *. We can also provide contract(H::MPS, psi::MPO) = contract(psi, H).
• Rename mul(::MPO, ::MPO)/multmpo to contract(::MPO, ::MPO).
• Change the name of sum(::MPS, ::MPS) to add/+.

And for other miscellaneous improvements:

• Add reverse_sites!(::Union{MPS,MPO}) to reverse the site ordering of the MPS/MPO (useful for some quantum computing applications, where you might want to reverse the qubit ordering).
• Add Vector(::MPS) and Matrix(::MPO) conversion which converts an MPS/MPO into the equivalent exponentially large Vector or Matrix (useful for ED comparisons).
• Provide an MPO(sites) function that fills with Empty ITensors.
• Add versions of MPO(...) constructors that accept an element type.
• In *(x::Number, ::AbstractMPS), instead of multiplying the middle tensor by x, instead multiply the tensors between the left and right orthogonality center by x^(1/N) where N is the distance between llim and rlim.
• Add norm for MPS/MPO.
• Add lognorm and loginner/logdot for MPS/MPO (proposed here).
• MPS(sites) where length(sites) == 1 doesn't work right now.
• Add more priming and tagging functions.
• Add an "unsafe" version of setindex! that does not change the orthogonality center, for operations that you know will not affect the orthogonality center.

[mtfishman]

Some of these have been implemented in #290, at least the breaking changes. The rest would be new features and can be implemented after v0.1.

[emstoudenmire]

@mtfishman ok to remove the 0.1 Milestone tag from this, then, if the rest of these will be post 0.1 changes?

[mtfishman]

Yes, all of these are non-breaking. Just removed.

[GTorlai]

It would be useful to have a function returning the normalization of an MPS with large N without a gauge center (e.g. for gradient-based optimizations of randomly initialized MPS). Depending on the initial MPS parameters, a direct calculation of the normalization typically becomes unstable for large N. The following function fixes the problem by computing the log-normalization:

function lognormalization(psi::MPS)                                   
  blob = dag(psi[1]) * prime(psi[1], "Link")
  localZ = real((dag(blob)*blob)[])
  logZ = 0.5*log(localZ)
  blob /= sqrt(localZ)

  for j in 2:length(psi)-1
    blob = blob * dag(psi[j]);
    blob = blob * prime(psi[j], "Link")
    localZ = real((dag(blob)*blob)[])
    logZ += 0.5*log(localZ)
    blob /= sqrt(localZ)
  end

  blob = blob * dag(psi[length(psi)]);
  blob = blob * prime(psi[length(psi)],"Link")
  logZ += log(real(blob[]))
  return logZ
end;

[emstoudenmire]

Yes, I really like this idea. I would call it `lognorm`. It might be good to avoid doing the contraction on the line `localZ = real((dag(blob)*blob)[])` if possible though, since that's doing extra work. Would it not be enough to just pull out the norm of `blob` itself at each step? Thanks for suggesting; we should add this.

…

On Thu, 21 May 2020 at 11:12, Giacomo Torlai ***@***.***> wrote: It would be useful to have a function returning the normalization of an MPS with large N without a gauge center (e.g. for gradient-based optimizations of randomly initialized MPS). Depending on the initial MPS parameters, a direct calculation of the normalization typically becomes unstable for large N. The following function fixes the problem by computing the log-normalization: function lognormalization(psi::MPS) # Site 1 blob = dag(psi[1]) * prime(psi[1], "Link") localZ = real((dag(blob)*blob)[]) logZ = 0.5*log(localZ) blob /= sqrt(localZ) for j in 2:length(psi)-1 blob = blob * dag(psi[j]); blob = blob * prime(psi[j], "Link") localZ = real((dag(blob)*blob)[]) logZ += 0.5*log(localZ) blob /= sqrt(localZ) end blob = blob * dag(psi[length(psi)]); blob = blob * prime(psi[length(psi)],"Link") logZ += log(real(blob[])) return logZend; — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#285 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAHJ3RNFD6EKZ2MFEXD4BKDRSVAELANCNFSM4MKAPZOQ> .

-- -=Miles Stoudenmire=- miles.stoudenmire@gmail.com mstoudenmire@flatironinstitute.org http://itensor.org/miles/

[GTorlai]

Yes, good point, that would be enough.

[mtfishman]

I'm working on this right now, by the way.