Implement an MPS method initializing the tensors to identity (copy-tensors) #218

Todorbsc · 2024-10-09T13:14:23Z

Closes #165

mofeing

Thanks! But could you clarify a lil bit how it works?

mofeing · 2024-10-09T13:25:32Z

test/MPS_test.jl

+    dispatch_arraysdims = [
+        ([2, 4], [5, 4, 3], [2, 3]),
+        [(2, 4), (5, 4, 3), (2, 3)],
+        ((2, 4), (5, 4, 3), (2, 3)),
+        [[2, 4], [5, 4, 3], [2, 3]],
+    ]
+    for arraysdims in dispatch_arraysdims
+        ψ = MPS(arraysdims) # Default order (:o, :l, :r)
+        @test size(tensors(ψ; at=site"1")) == (2, 4)
+        @test size(tensors(ψ; at=site"2")) == (5, 4, 3)
+        @test size(tensors(ψ; at=site"3")) == (2, 3)
+        t1 = tensors(ψ; at=site"1")
+        @test t1[1, 1] == t1[2, 2] == 1
+        @test sum(t1) == 2
+        t2 = tensors(ψ; at=site"2")
+        @test t2[1, 1, 1] == t2[2, 2, 2] == t2[3, 3, 3] == 1
+        @test sum(t2) == 3
+        t3 = tensors(ψ; at=site"3")
+        @test t3[1, 1] == t3[2, 2] == 1
+        @test sum(t3) == 2
+    end
+


Wrap this into a @testset

mofeing · 2024-10-09T13:45:57Z

src/Ansatz/MPS.jl

+MPS(arraysdims::NTuple{N,<:Vector{Int}}; order=defaultorder(MPS)) where {N} = MPS(collect(arraysdims); order=order)
+MPS(arraysdims::Vector{<:Tuple{Vararg{Int}}}; order=defaultorder(MPS)) = MPS(collect.(arraysdims); order=order)
+function MPS(arraysdims::NTuple{N,Tuple{Vararg{Int}}}; order=defaultorder(MPS)) where {N}
+    return MPS(collect(collect.(arraysdims)); order=order)
+end


I would currently just delete these methods for now...

Suggested change

MPS(arraysdims::NTuple{N,<:Vector{Int}}; order=defaultorder(MPS)) where {N} = MPS(collect(arraysdims); order=order)

MPS(arraysdims::Vector{<:Tuple{Vararg{Int}}}; order=defaultorder(MPS)) = MPS(collect.(arraysdims); order=order)

function MPS(arraysdims::NTuple{N,Tuple{Vararg{Int}}}; order=defaultorder(MPS)) where {N}

return MPS(collect(collect.(arraysdims)); order=order)

end

I removed them

mofeing · 2024-10-09T13:47:39Z

src/Ansatz/MPS.jl

+function MPS(arraysdims::NTuple{N,Tuple{Vararg{Int}}}; order=defaultorder(MPS)) where {N}
+    return MPS(collect(collect.(arraysdims)); order=order)
+end
+function MPS(arraysdims::Vector{<:Vector{Int}}; order=defaultorder(MPS))


I would use Base.identity, not a constructor since you're not passing arrays.

Suggested change

function MPS(arraysdims::Vector{<:Vector{Int}}; order=defaultorder(MPS))

function Base.identity(::Type{MPS}, arraysdims; order=defaultorder(MPS))

This was one possibility along with the one @jofrevalles suggested below of using ones. I replaced the constructor by identity as I think it fits better than ones.

jofrevalles

Thanks @Todorbsc

jofrevalles · 2024-10-09T13:52:29Z

src/Ansatz/MPS.jl

+MPS(arraysdims::NTuple{N,<:Vector{Int}}; order=defaultorder(MPS)) where {N} = MPS(collect(arraysdims); order=order)
+MPS(arraysdims::Vector{<:Tuple{Vararg{Int}}}; order=defaultorder(MPS)) = MPS(collect.(arraysdims); order=order)
+function MPS(arraysdims::NTuple{N,Tuple{Vararg{Int}}}; order=defaultorder(MPS)) where {N}
+    return MPS(collect(collect.(arraysdims)); order=order)
+end
+function MPS(arraysdims::Vector{<:Vector{Int}}; order=defaultorder(MPS))
+    @assert length(arraysdims[1]) == 2 "First array must have 2 dimensions"
+    @assert all(==(3) ∘ length, arraysdims[2:(end - 1)]) "All arrays must have 3 dimensions"
+    @assert length(arraysdims[end]) == 2 "Last array must have 2 dimensions"
+    issetequal(order, defaultorder(MPS)) ||
+        throw(ArgumentError("order must be a permutation of $(String.(defaultorder(MPS)))"))
+
+    return MPS(
+        map(arraysdims) do arrdims
+            mindim = minimum(arrdims)
+            arr = zeros(ComplexF64, arrdims...)
+            deltas = ntuple(x -> ntuple(_ -> x, length(arrdims)), mindim)
+            broadcast(delta -> arr[delta...] = 1.0, deltas)
+            arr
+        end;
+        order=order,
+    )
+end
+


I would not create another constructor for MPS, since that may be misleading to the user who wants to directly create an MPS with some specific arrays. Instead, you could extend the function ones or one similiar, to make that when we call ones(MPS, arraydims ... ) we get this kind of MPS. Something similar to the things we do with rand.

As I said above, I agree it is better to not implement another constructor. The option that fits the best for me is Base.identity, check it out :)

Yeah, in general I agree with @jofrevalles but I think ones might be misleading since it could mean you're initializing the MPS to a $\ket{11\dots 1}$ state.

I think identity is better because contracting against another "identity" MPS gives you 1, all the tensors are just COPY-tensors and "identity initialization" is how is known in some packages (it's also known as eye-initialization but eye is how the identity is known on those languages).

jofrevalles · 2024-10-09T13:54:58Z

Also note that, as we discussed, we should add a docstring to every new function we make, since we lack a lot of documentation. :)

Todorbsc · 2024-10-09T16:59:29Z

Thanks! But could you clarify a lil bit how it works?

Sure! The point is to create an identity MPS where the tensors will have some user-provided dimensions (arraysdims). Thus, what Base.identity(::Type{MPS}, arraysdims; order) would do is create zero-initialized tensors with the specified dimensions and then assign to the unit those tensor elements that have the same index in all of its dimensions.
For example: In a tensor of shape (3,4,5), the constraint is the lowest dimension of the tensor, i.e. 3, doing the unit assignment to the tensors elements (1,1,1), (2,2,2) and (3,3,3).

mofeing · 2024-10-09T18:45:26Z

Sure! The point is to create an identity MPS where the tensors will have some user-provided dimensions (arraysdims). Thus, what Base.identity(::Type{MPS}, arraysdims; order) would do is create zero-initialized tensors with the specified dimensions and then assign to the unit those tensor elements that have the same index in all of its dimensions. For example: In a tensor of shape (3,4,5), the constraint is the lowest dimension of the tensor, i.e. 3, doing the unit assignment to the tensors elements (1,1,1), (2,2,2) and (3,3,3).

Thanks for clarifying but I think having custom dimensions is not so relevant and can be tedious for the user to generate all the tuples...

IMO it would be better to accept a signature like

Base.identity(::Type{MPS}, n; maxdim=2^(n ÷ 2), physdim=2)

where n is the number of sites and maxdim is the $\chi$ and is the maximum bond dimensions. The size of the virtual dims would then increase exponentially fast until arriving to maxdim.

Todorbsc · 2024-10-10T13:51:14Z

maxdim=2^(n ÷ 2), physdim=2

@mofeing What happens in the case where $\chi$ (maxdim) is reached before the middle of the MPS?
For instance, a 7-site MPS with maxdim=4: the 1st virtual index would be 2-dimensional and the 2nd one would be 4-dimensional (where the maxdim is reached). Would the 3rd one (reaching to the half of the chain) also be 4-dimensional?
This would give the following bond dimensions [2, 4, 4, 4, 4, 2]. Is this right?

mofeing · 2024-10-10T14:11:42Z

@mofeing What happens in the case where χ (maxdim) is reached before the middle of the MPS? For instance, a 7-site MPS with maxdim=4: the 1st virtual index would be 2-dimensional and the 2nd one would be 4-dimensional (where the maxdim is reached). Would the 3rd one (reaching to the half of the chain) also be 4-dimensional? This would give the following bond dimensions [2, 4, 4, 4, 4, 2]. Is this right?

the order or num dims of the tensors is not affected. just the size of the virtual indices is upper bounded. so yeah, [2, 4, 4, 4, 4, 2] is correct.

you can use this code in here to compute the virtual index sizes for an open MPS

Tenet.jl/src/Ansatz/Chain.jl

Lines 233 to 239 in 4c16d2f

    
           χl, χr = let after_mid = i > n ÷ 2, i = (n + 1 - abs(2i - n - 1)) ÷ 2 
        
               χl = min(χ, p^(i - 1)) 
        
               χr = min(χ, p^i) 
        
               # swap bond dims after mid and handle midpoint for odd-length MPS 
        
               (isodd(n) && i == n ÷ 2 + 1) ? (χl, χl) : (after_mid ? (χr, χl) : (χl, χr)) 
        
           end

…sions

Todorbsc · 2024-10-10T16:56:50Z

@mofeing What happens in the case where χ (maxdim) is reached before the middle of the MPS? For instance, a 7-site MPS with maxdim=4: the 1st virtual index would be 2-dimensional and the 2nd one would be 4-dimensional (where the maxdim is reached). Would the 3rd one (reaching to the half of the chain) also be 4-dimensional? This would give the following bond dimensions [2, 4, 4, 4, 4, 2]. Is this right?

the order or num dims of the tensors is not affected. just the size of the virtual indices is upper bounded. so yeah, [2, 4, 4, 4, 4, 2] is correct.

you can use this code in here to compute the virtual index sizes for an open MPS

Tenet.jl/src/Ansatz/Chain.jl

Lines 233 to 239 in 4c16d2f

χl, χr = let after_mid = i > n ÷ 2, i = (n + 1 - abs(2i - n - 1)) ÷ 2

χl = min(χ, p^(i - 1))

χr = min(χ, p^i)

# swap bond dims after mid and handle midpoint for odd-length MPS

(isodd(n) && i == n ÷ 2 + 1) ? (χl, χl) : (after_mid ? (χr, χl) : (χl, χr))

end

Perfect, thanks!
Actually, I had written my own method for the bond dimensions before reading this, check it out and I can change it if you wish.

jofrevalles

Nice! I would add some empty lines to make the testset clearer, but this is ready to merge soon.

test/MPS_test.jl

Co-authored-by: Jofre Vallès Muns <[email protected]>

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Todorbsc linked an issue Oct 10, 2024 that may be closed by this pull request

Implement identity initialization of Chain #165

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Todorbsc changed the title ~~Implement a MPS constructor that initializes the tensors to identity~~ Implement an MPS method initializing the tensors to identity (copy-tensors) Oct 11, 2024

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Implement an MPS method initializing the tensors to identity (copy-tensors) #218

Implement an MPS method initializing the tensors to identity (copy-tensors) #218

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	function MPS(arraysdims::Vector{<:Vector{Int}}; order=defaultorder(MPS))
	function Base.identity(::Type{MPS}, arraysdims; order=defaultorder(MPS))

Implement an MPS method initializing the tensors to identity (copy-tensors) #218

Are you sure you want to change the base?

Implement an MPS method initializing the tensors to identity (copy-tensors) #218

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