[ITensors] [ENHANCEMENT] Add truncate keyword to the MPS constructor

[NuclearPowerNerd]

Hello!

Sometimes I create MPS and I want a "lossless" version of whatever field that MPS represents (i.e., no truncation). It is useful for code and algorithm validation purposes. I know I could achieve this thru maxdim and/or cutoff but I think it would be a simple matter to add a new keyword argument to the MPS constructor, called truncate, which skips the truncation step in the SVD algorithm at the low level (buried in NDTensors).

So then it would be possible to call the constructor like this

A = MPS(f, truncate=false). 

truncate would default to true so existing behavior would be maintained.

If everyone agrees I'd be happy to prepare the pull request. I've read the contributing guidelines here.

Please let me know what you think.

[mtfishman]

I assume you are talking about the function for converting an ITensor to an MPS? Are you sure that isn't already the behavior if you don't specify any truncation parameters? I see:

julia> using ITensors, ITensorMPS

julia> i, j = Index.((2, 2))
((dim=2|id=59), (dim=2|id=472))

julia> a = random_itensor(i, j)
ITensor ord=2 (dim=2|id=59) (dim=2|id=472)
NDTensors.Dense{Float64, Vector{Float64}}

julia> x = MPS(a, [i, j])
MPS
[1] ((dim=2|id=59), (dim=2|id=289|"Link,n=1"))
[2] ((dim=2|id=289|"Link,n=1"), (dim=2|id=472))


julia> @show x[1];
x[1] = ITensor ord=2
Dim 1: (dim=2|id=59)
Dim 2: (dim=2|id=289|"Link,n=1")
NDTensors.Dense{Float64, Vector{Float64}}
 2×2
 -0.5213970227157092  0.8533142121769648
  0.8533142121769648  0.5213970227157092

julia> @show x[2];
x[2] = ITensor ord=2
Dim 1: (dim=2|id=289|"Link,n=1")
Dim 2: (dim=2|id=472)
NDTensors.Dense{Float64, Vector{Float64}}
 2×2
 -1.7428604446123537  0.7202766240206115
  0.0                 1.9874308479155949

which looks like it is doing a QR decomposition (and therefore isn't truncating):

julia> q, r = qr(a, i);

julia> @show q;
q = ITensor ord=2
Dim 1: (dim=2|id=59)
Dim 2: (dim=2|id=950|"Link,qr")
NDTensors.Dense{Float64, Vector{Float64}}
 2×2
 -0.5213970227157092  0.8533142121769648
  0.8533142121769648  0.5213970227157092

julia> @show r;
r = ITensor ord=2
Dim 1: (dim=2|id=950|"Link,qr")
Dim 2: (dim=2|id=472)
NDTensors.Dense{Float64, Vector{Float64}}
 2×2
 -1.7428604446123537  0.7202766240206115
  0.0                 1.9874308479155949

[mtfishman]

If we are convinced that indeed by not setting any parameters it achieves the goal of your proposed truncate=false keyword argument interface, I don't think a new keyword argument is needed, but an action item could be to document the current behavior since it may be a bit hidden right now.

[NuclearPowerNerd]

Hey @mtfishman , sorry for not being clearer. In the example above f was meant to be a vector of Float64 (at least in my head that's how I was thinking about it). I will investigate and confirm what you say (check the behavior when no parameters are specified in the call to the constructor).

[mtfishman]

How would you make an MPS from just a Vector{Float64}? Wouldn't you need a set if ITensor Indices, i.e. to define the site Indices of the MPS?

[NuclearPowerNerd]

Right, not just Vector{Float64}. You would have had to create some indices probably using siteinds. So it would be something like MPS(f, sinds) where siteinds(d, N).

[NuclearPowerNerd]

I'd say go ahead and close this. I experimented a bit more and I am finding that I get agreement down to ~1E-15 whether I specify maxdim and cutoff or don't pass them at all. Thus, I think no truncate keyword is necessary.

[mtfishman]

Sounds good, thanks for following up.