diff --git a/NDTensors/ext/NDTensorsMetalExt/linearalgebra.jl b/NDTensors/ext/NDTensorsMetalExt/linearalgebra.jl
index ce52993c42..f6d692daee 100644
--- a/NDTensors/ext/NDTensorsMetalExt/linearalgebra.jl
+++ b/NDTensors/ext/NDTensorsMetalExt/linearalgebra.jl
@@ -18,14 +18,16 @@ function NDTensors.Unwrap.ql_positive(A::Exposed{<:MtlMatrix})
 end
 
 function LinearAlgebra.eigen(A::Exposed{<:MtlMatrix})
-  D, U = eigen(expose(NDTensors.cpu(A)))
-  return adapt(set_ndims(unwrap_type(A), ndims(D)), D), adapt(unwrap_type(A), U)
+  Dcpu, Ucpu = eigen(expose(NDTensors.cpu(A)))
+  D = adapt(set_ndims(set_eltype(unwrap_type(A), eltype(Dcpu)), ndims(Dcpu)), Dcpu)
+  U = adapt(unwrap_type(A), Ucpu)
+  return D, U
 end
 
 function LinearAlgebra.svd(A::Exposed{<:MtlMatrix}; kwargs...)
   Ucpu, Scpu, Vcpu = svd(expose(NDTensors.cpu(A)); kwargs...)
   U = adapt(unwrap_type(A), Ucpu)
-  S = adapt(set_ndims(unwrap_type(A), ndims(Scpu)), Scpu)
+  S = adapt(set_ndims(set_eltype(unwrap_type(A), eltype(Scpu)), ndims(Scpu)), Scpu)
   V = adapt(unwrap_type(A), Vcpu)
   return U, S, V
 end
diff --git a/NDTensors/src/Unwrap/test/runtests.jl b/NDTensors/src/Unwrap/test/runtests.jl
index c4ff4fd825..127f85cfae 100644
--- a/NDTensors/src/Unwrap/test/runtests.jl
+++ b/NDTensors/src/Unwrap/test/runtests.jl
@@ -4,10 +4,10 @@ using NDTensors
 using LinearAlgebra
 
 include("../../../test/device_list.jl")
-@testset "Testing Unwrap" for dev in devices_list(ARGS)
-  elt = Float32
+@testset "Testing Unwrap $dev, $elt" for dev in devices_list(ARGS),
+  elt in (Float32, ComplexF32)
 
-  v = dev(Vector{elt}(undef, 10))
+  v = dev(randn(elt, 10))
   vt = transpose(v)
   va = v'
 
@@ -39,7 +39,7 @@ include("../../../test/device_list.jl")
   @test typeof(Et) == Exposed{m_type,LinearAlgebra.Transpose{e_type,m_type}}
   @test typeof(Ea) == Exposed{m_type,LinearAlgebra.Adjoint{e_type,m_type}}
 
-  o = dev(Vector{elt})(undef, 1)
+  o = dev(randn(elt, 1))
   expose(o)[] = 2
   @test expose(o)[] == 2
 
@@ -58,17 +58,32 @@ include("../../../test/device_list.jl")
   q, r = Unwrap.qr_positive(expose(mp))
   @test q * r ≈ mp
 
-  square = dev(rand(elt, (10, 10)))
+  square = dev(rand(real(elt), (10, 10)))
   square = (square + transpose(square)) / 2
   ## CUDA only supports Hermitian or Symmetric eigen decompositions
   ## So I symmetrize square and call symetric here
   l, U = eigen(expose(Symmetric(square)))
+  @test eltype(l) == real(elt)
+  @test eltype(U) == real(elt)
+  @test square * U ≈ U * Diagonal(l)
+
+  square = dev(rand(elt, (10, 10)))
+  # Can use `hermitianpart` in Julia 1.10
+  square = (square + square') / 2
+  ## CUDA only supports Hermitian or Symmetric eigen decompositions
+  ## So I symmetrize square and call symetric here
+  l, U = eigen(expose(Hermitian(square)))
+  @test eltype(l) == real(elt)
+  @test eltype(U) == elt
   @test square * U ≈ U * Diagonal(l)
 
   U, S, V, = svd(expose(mp))
+  @test eltype(U) == elt
+  @test eltype(S) == real(elt)
+  @test eltype(V) == elt
   @test U * Diagonal(S) * V' ≈ mp
 
-  cm = dev(fill!(Matrix{elt}(undef, (2, 2)), 0.0))
+  cm = dev(randn(elt, 2, 2))
   mul!(expose(cm), expose(mp), expose(mp'), 1.0, 0.0)
   @test cm ≈ mp * mp'
 
diff --git a/NDTensors/src/blocksparse/blocksparse.jl b/NDTensors/src/blocksparse/blocksparse.jl
index 30d86c28a4..fffd146aeb 100644
--- a/NDTensors/src/blocksparse/blocksparse.jl
+++ b/NDTensors/src/blocksparse/blocksparse.jl
@@ -128,20 +128,26 @@ can_contract(T1::Type{<:BlockSparse}, T2::Type{<:Dense}) = can_contract(T2, T1)
 function promote_rule(
   ::Type{<:BlockSparse{ElT1,VecT1,N}}, ::Type{<:BlockSparse{ElT2,VecT2,N}}
 ) where {ElT1,ElT2,VecT1,VecT2,N}
-  return BlockSparse{promote_type(ElT1, ElT2),promote_type(VecT1, VecT2),N}
+  # Promote the element types properly.
+  ElT = promote_type(ElT1, ElT2)
+  VecT = promote_type(set_eltype(VecT1, ElT), set_eltype(VecT2, ElT))
+  return BlockSparse{ElT,VecT,N}
 end
 
 function promote_rule(
   ::Type{<:BlockSparse{ElT1,VecT1,N1}}, ::Type{<:BlockSparse{ElT2,VecT2,N2}}
 ) where {ElT1,ElT2,VecT1,VecT2,N1,N2}
-  return BlockSparse{promote_type(ElT1, ElT2),promote_type(VecT1, VecT2),NR} where {NR}
+  # Promote the element types properly.
+  ElT = promote_type(ElT1, ElT2)
+  VecT = promote_type(set_eltype(VecT1, ElT), set_eltype(VecT2, ElT))
+  return BlockSparse{ElT,VecT,NR} where {NR}
 end
 
 function promote_rule(
-  ::Type{<:BlockSparse{ElT1,Vector{ElT1},N1}}, ::Type{ElT2}
-) where {ElT1,ElT2<:Number,N1}
+  ::Type{<:BlockSparse{ElT1,VecT1,N1}}, ::Type{ElT2}
+) where {ElT1,VecT1<:AbstractVector{ElT1},ElT2<:Number,N1}
   ElR = promote_type(ElT1, ElT2)
-  VecR = Vector{ElR}
+  VecR = set_eltype(VecT1, ElR)
   return BlockSparse{ElR,VecR,N1}
 end
 
diff --git a/NDTensors/test/ITensors/TestITensorDMRG/TestITensorDMRG.jl b/NDTensors/test/ITensors/TestITensorDMRG/TestITensorDMRG.jl
index 667e2a1f8a..618f2b6ced 100644
--- a/NDTensors/test/ITensors/TestITensorDMRG/TestITensorDMRG.jl
+++ b/NDTensors/test/ITensors/TestITensorDMRG/TestITensorDMRG.jl
@@ -12,5 +12,16 @@ reference_energies = Dict([
 ])
 
 default_rtol(elt::Type) = 10^(0.75 * log10(eps(real(elt))))
+
+is_supported_eltype(dev, elt::Type) = true
+is_supported_eltype(dev::typeof(NDTensors.mtl), elt::Type{Float64}) = false
+function is_supported_eltype(dev::typeof(NDTensors.mtl), elt::Type{<:Complex})
+  return is_supported_eltype(dev, real(elt))
+end
+
+is_broken(dev, elt::Type, conserve_qns::Val) = false
+is_broken(dev::typeof(NDTensors.cu), elt::Type, conserve_qns::Val{true}) = true
+
 include("dmrg.jl")
+
 end
diff --git a/NDTensors/test/ITensors/TestITensorDMRG/dmrg.jl b/NDTensors/test/ITensors/TestITensorDMRG/dmrg.jl
index 2c5a77eddf..ab73f5ff82 100644
--- a/NDTensors/test/ITensors/TestITensorDMRG/dmrg.jl
+++ b/NDTensors/test/ITensors/TestITensorDMRG/dmrg.jl
@@ -1,5 +1,5 @@
-function test_dmrg(elt, N::Integer, dev::Function)
-  sites = siteinds("S=1/2", N)
+function test_dmrg(elt, N::Integer; dev::Function, conserve_qns)
+  sites = siteinds("S=1/2", N; conserve_qns)
 
   os = OpSum()
   for j in 1:(N - 1)
@@ -9,12 +9,13 @@ function test_dmrg(elt, N::Integer, dev::Function)
   end
 
   Random.seed!(1234)
-  psi0 = dev(randomMPS(Float64, sites; linkdims=4))
+  init = j -> isodd(j) ? "↑" : "↓"
+  psi0 = dev(randomMPS(elt, sites, init; linkdims=4))
   H = dev(MPO(elt, os, sites))
 
   nsweeps = 3
   cutoff = [1e-3, 1e-13]
-  noise = [1e-12, 0]
+  noise = [1e-6, 0]
   ## running these with nsweeps = 100 and no maxdim
   ## all problems do not have a maxlinkdim > 32
   maxdim = 32
diff --git a/NDTensors/test/ITensors/TestITensorDMRG/runtests.jl b/NDTensors/test/ITensors/TestITensorDMRG/runtests.jl
index ee6712e9d6..bccc179656 100644
--- a/NDTensors/test/ITensors/TestITensorDMRG/runtests.jl
+++ b/NDTensors/test/ITensors/TestITensorDMRG/runtests.jl
@@ -4,11 +4,19 @@ include("TestITensorDMRG.jl")
 
 include("../../device_list.jl")
 
-@testset "Testing DMRG different backends" begin
-  for dev in devices_list(ARGS),
-    N in [4, 10],
-    elt in (Float32, ComplexF32, Float64, ComplexF64)
+@testset "Test DMRG $dev, $conserve_qns, $elt, $N" for dev in devices_list(ARGS),
+  conserve_qns in [false, true],
+  elt in (Float32, ComplexF32, Float64, ComplexF64),
+  N in [4, 10]
 
-    TestITensorDMRG.test_dmrg(elt, N, dev)
+  if !TestITensorDMRG.is_supported_eltype(dev, elt)
+    continue
+  end
+  if TestITensorDMRG.is_broken(dev, elt, Val(conserve_qns))
+    # TODO: Switch to `@test ... broken=true`, introduced
+    # in Julia 1.7.
+    @test_broken TestITensorDMRG.test_dmrg(elt, N; dev, conserve_qns)
+  else
+    TestITensorDMRG.test_dmrg(elt, N; dev, conserve_qns)
   end
 end
diff --git a/src/mps/dmrg.jl b/src/mps/dmrg.jl
index 116d387e22..eda11f5292 100644
--- a/src/mps/dmrg.jl
+++ b/src/mps/dmrg.jl
@@ -260,10 +260,12 @@ function dmrg(
         ortho = ha == 1 ? "left" : "right"
 
         drho = nothing
-        if noise(sweeps, sw) > 0.0
+        if noise(sweeps, sw) > 0
           @timeit_debug timer "dmrg: noiseterm" begin
-            # Use noise term when determining new MPS basis
-            drho = noise(sweeps, sw) * noiseterm(PH, phi, ortho)
+            # Use noise term when determining new MPS basis.
+            # This is used to preserve the element type of the MPS.
+            elt = real(scalartype(psi))
+            drho = elt(noise(sweeps, sw)) * noiseterm(PH, phi, ortho)
           end
         end