[ITensors] Support for MPO*MPO contraction by densitymatrix method

[shinaoka]

Description

Based on discussions with Miles.

This small patch allows contracting an MPO and an MPS with a dangling bond at each site. This is intended to be a minimal and tentative patch that will eventually be replaced by ITensorNetworks.jl.

Minimal demonstration of previous behavior

using ITensors

R = 3
sites = [Index(2, "Qubit,n=$n") for n in 1:R]
a = replaceprime(randomMPO(sites), 0 => 1, 1 => 2)
b = randomMPO(sites)
ab_ref = contract(a, b; alg="naive")
ab = contract(a, b; alg="densitymatrix")

ERROR: MethodError: no method matching contract(::NDTensors.Algorithm{:densitymatrix}, ::MPO, ::MPO)

Closest candidates are:
  contract(::NDTensors.Algorithm{:naive}, ::MPO, ::MPO; kwargs...)
   @ ITensors ~/.julia/packages/ITensors/HjjU3/src/mps/mpo.jl:801
  contract(::NDTensors.Algorithm{:densitymatrix}, ::MPO, ::MPS; kwargs...)
   @ ITensors ~/.julia/packages/ITensors/HjjU3/src/mps/mpo.jl:678
  contract(::NDTensors.Algorithm{:zipup}, ::MPO, ::MPO; kwargs...)
   @ ITensors ~/.julia/packages/ITensors/HjjU3/src/mps/mpo.jl:805
  ...

Stacktrace:
 [1] contract(A::MPO, B::MPO; alg::String, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ ITensors ~/.julia/packages/ITensors/HjjU3/src/mps/mpo.jl:798
 [2] top-level scope
   @ REPL[7]:1

Minimal demonstration of new behavior

using ITensors

R = 3
sites = [Index(2, "Qubit,n=$n") for n in 1:R]
a = replaceprime(randomMPO(sites), 0 => 1, 1 => 2)
b = randomMPO(sites)
ab_ref = contract(a, b; alg="naive")
ab = contract(a, b; alg="densitymatrix")
ab_ref ≈ ab

How Has This Been Tested?

A test will be added in test_mpo.jl that compares the results of contractions of an MPO and an MPS with a dangling bond.

Checklist:

• [x] My code follows the style guidelines of this project. Please run using JuliaFormatter; format(".") in the base directory of the repository (~/.julia/dev/ITensors) to format your code according to our style guidelines.
• [x] I have performed a self-review of my own code.
• [x] I have commented my code, particularly in hard-to-understand areas.
• [x] I have added tests that verify the behavior of the changes I made.
• [x] I have made corresponding changes to the documentation.
• [x] My changes generate no new warnings.
• [x] Any dependent changes have been merged and published in downstream modules.

[mtfishman]

Thanks @shinaoka, this will be useful to have.

I would instead vote for generalizing the function signature of:

function contract(::Algorithm"densitymatrix", A::MPO, ψ::MPS; kwargs...)
  # [...]
end

to:

function contract(::Algorithm"densitymatrix", A::AbstractMPS, B::AbstractMPS; kwargs...)
  # [...]
end

and then returning an object that is typeof(B).

I'm also not such a fan of:

  function _getsimψ_c(i)
    t = copy(ψ_c[i])
    replaceinds!(t, dangling_inds_ψ[i], sim_dangling_inds_ψ[i])
    return t
  end

Why not just use:

replaceinds(ψ_c[i], dangling_inds_ψ[i], sim_dangling_inds_ψ[i])

directly?

[codecov-commenter]

Codecov Report

Merging #1123 (3a4dcfd) into main (7120090) will decrease coverage by 29.29%. The diff coverage is 0.00%.

:exclamation: Current head 3a4dcfd differs from pull request most recent head aa2b347. Consider uploading reports for the commit aa2b347 to get more accurate results

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@@             Coverage Diff             @@
##             main    #1123       +/-   ##
===========================================
- Coverage   82.59%   53.31%   -29.29%     
===========================================
  Files          86       85        -1     
  Lines        8319     7803      -516     
===========================================
- Hits         6871     4160     -2711     
- Misses       1448     3643     +2195     

Impacted Files	Coverage Δ
src/mps/mpo.jl	0.00% <0.00%> (-90.23%)	:arrow_down:

... and 64 files with indirect coverage changes

[shinaoka]

Thank you for the suggestion. I have addressed the issues. I am a bit afraid of "Merging #1123 (3a4dcfd) into main (7120090) will decrease coverage by 29.29%.". What do you think?

[shinaoka]

I have addressed the issues:

• The testset has been moved into inside the testset "MPO Basics".
• "function contract(::Algorithm"densitymatrix", M1::MPO, M2::MPO; kwargs...)::MPO" has been removed.

https://github.com/shinaoka/ITensors.jl/commit/6098a1067eb02e3bb6f9fce45a572547a83acd65

[emstoudenmire]

[test ITensors mps] (this comment ought to run MPS and MPO tests also)

[emstoudenmire]

Looks good to me @shinaoka. Let's see how the tests do and if Matt has more comments.

[github-actions[bot]]

Run ITensors mps tests from comment trigger: succeeded ✅ https://github.com/ITensor/ITensors.jl/actions/runs/5099391690

[github-actions[bot]]

Run ITensors mps tests from comment trigger: succeeded ✅ https://github.com/ITensor/ITensors.jl/actions/runs/5099391690

[shinaoka]

One test on automatic differentiation failed. I got precisely the same error on my Macbook Pro with the latest commit in the main branch. The error seems to be independent of this PR.