Zipup fails with a SpaceMismatch on make_time_mpo propagator MPOs #496

Zipup rejects propagator MPOs built by make_time_mpo, failing with a SpaceMismatch.

Its docstring presents Zipup as the single-sweep alternative to the variational algorithms for a finite MPO–MPS product, and applying a propagator MPO is the obvious case for that. But make_time_mpo produces MPOs whose virtual legs are direct sums (SumSpace), and the fused zip-up contraction does not accept them. WII and TaylorCluster fail alike; the same MPO applied variationally is fine.

Reproducer

using MPSKit, MPSKitModels, TensorKit
L = 8
H = transverse_field_ising(FiniteChain(L); g = 2.0)
ψ = FiniteMPS(L, ℂ^2, ℂ^8)

# a plain-tensor FiniteMPO works
Vs = [oneunit(ℂ^3); fill(ℂ^3, L - 1); oneunit(ℂ^3)]
O_plain = FiniteMPO([rand(ComplexF64, Vs[i] ⊗ ℂ^2 ← ℂ^2 ⊗ Vs[i + 1]) for i in 1:L])
approximate((O_plain, ψ), Zipup(; trunc = truncrank(16)))          # OK, ϵ ≈ 2.4e-5

# a propagator MPO does not
O_wii = make_time_mpo(H, 0.05, WII())
approximate((O_wii, ψ), Zipup(; trunc = truncrank(16)))            # SpaceMismatch
approximate(ψ, (O_wii, ψ), DMRG2(; trunc = truncrank(16)))         # OK — variational route is fine

O_taylor = make_time_mpo(H, 0.05, TaylorCluster(; N = 2); tol = 1e-10)
approximate((O_taylor, ψ), Zipup(; trunc = truncrank(16)))         # SpaceMismatch

Error

SpaceMismatch: (⊞(ℂ^2) ⊗ ⊞((ℂ^2)')) ≠ ((ℂ^1 ⊞ ℂ^1) ⊗ ⊞((ℂ^2)'))
  [1] compose                    @ TensorKit/src/spaces/homspace.jl:269
  [2] compose                    @ BlockTensorKit/src/vectorspaces/sumspace.jl:142
  [3] tensorcontract_structure   @ TensorKit/src/tensors/tensoroperations.jl:181
  [6] _fuse_mpo_mps_left         @ src/operators/mpo.jl:306
  [7] zip_left_right!            @ src/algorithms/approximate/zipup.jl:122
  [8] approximate!               @ src/algorithms/approximate/zipup.jl:77

For TaylorCluster(; N = 2) the mismatch is (⊞(ℂ^4) ⊗ ⊞((ℂ^2)')) ≠ ((ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1 ⊞ ℂ^1) ⊗ ⊞((ℂ^2)')) — the fused space is built as a single block of the summed dimension, while the operand carries the individual summands.

Notes

The Zipup testsets in test/algorithms/approximate.jl build their MPOs from dense TensorMaps only (_random_mpo_mps), so no test covers a SumSpace-legged MPO.

Found while documenting Zipup for the docs restructure (#449); the intended make_time_mpo + Zipup recipe had to be dropped.

Version: MPSKit on main at 1c81790 (v0.13.13), Julia 1.12.6.