diff --git a/Project.toml b/Project.toml
index 36d2fce6..d3c0501c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,6 +4,7 @@ authors = ["Michael Goerz <mail@michaelgoerz.net>"]
 version = "0.8.5+dev"
 
 [deps]
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
@@ -25,6 +26,7 @@ QuantumPropagatorsRecursiveArrayToolsExt = "RecursiveArrayTools"
 QuantumPropagatorsStaticArraysExt = "StaticArrays"
 
 [compat]
+ArrayInterface = "7.0"
 OffsetArrays = "1"
 OrdinaryDiffEq = "6.59"
 ProgressMeter = "1"
diff --git a/docs/Project.toml b/docs/Project.toml
index e9975363..c62945d7 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,4 +1,5 @@
 [deps]
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DisplayAs = "0b91fe84-8a4c-11e9-3e1d-67c38462b6d6"
 DocInventories = "43dc2714-ed3b-44b5-b226-857eda1aa7de"
diff --git a/docs/make.jl b/docs/make.jl
index 462e3b5a..b0533025 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -45,6 +45,7 @@ links = InterLinks(
     "StaticArrays" => "https://juliaarrays.github.io/StaticArrays.jl/stable/",
     "ComponentArrays" => "https://sciml.github.io/ComponentArrays.jl/stable/",
     "RecursiveArrayTools" => "https://docs.sciml.ai/RecursiveArrayTools/stable/",
+    "ArrayInterface" => "https://docs.sciml.ai/ArrayInterface/stable/",
     "qutip" => "https://qutip.readthedocs.io/en/qutip-5.0.x/",
 )
 
diff --git a/src/interfaces/operator.jl b/src/interfaces/operator.jl
index 81e0d5f7..435883cf 100644
--- a/src/interfaces/operator.jl
+++ b/src/interfaces/operator.jl
@@ -1,6 +1,7 @@
 using Test
 
 using LinearAlgebra
+import ArrayInterface
 using ..Controls: get_controls, evaluate
 
 
@@ -52,7 +53,8 @@ for two-dimensional arrays:
 * `length(op)` must equal `prod(size(op))`
 * `iterate(op)` must be defined
 * `similar(op)` must be defined and return a mutable array with the same shape
-  and element type
+  and element type. "Mutability" is determined by
+  [`ArrayInterface.ismutable`](@extref).
 * `similar(op, ::Type{S})` must return a mutable array with the same shape and
   element type `S`
 * `similar(op, dims::Dims)` must return a mutable array with the same element
@@ -60,6 +62,9 @@ for two-dimensional arrays:
 * `similar(op, ::Type{S}, dims::Dims)` must return a mutable array with the
   given element type and dimensions
 
+The read-write method `setindex!` is not a requirement for
+`supports_matrix_interface`.
+
 The function returns `true` for a valid operator and `false` for an invalid
 operator. Unless `quiet=true`, it will log an error to indicate which of the
 conditions failed.
@@ -328,9 +333,9 @@ function check_operator(
 
         try
             op2 = similar(op)
-            if !supports_inplace(op2)
+            if !ArrayInterface.ismutable(op2)
                 quiet ||
-                    @error "$(px)`similar(op)` must return a mutable array (`supports_inplace` must be `true`), got $(typeof(op2))"
+                    @error "$(px)`similar(op)` must return a mutable array (`ArrayInterface.ismutable` must be `true`), got $(typeof(op2))"
                 success = false
             end
             if size(op2) != size(op)
@@ -354,9 +359,9 @@ function check_operator(
         try
             S = (eltype(op) == ComplexF64) ? ComplexF32 : ComplexF64
             op2 = similar(op, S)
-            if !supports_inplace(op2)
+            if !ArrayInterface.ismutable(op2)
                 quiet ||
-                    @error "$(px)`similar(op, $S)` must return a mutable array (`supports_inplace` must be `true`), got $(typeof(op2))"
+                    @error "$(px)`similar(op, $S)` must return a mutable array (`ArrayInterface.ismutable` must be `true`), got $(typeof(op2))"
                 success = false
             end
             if size(op2) != size(op)
@@ -380,9 +385,9 @@ function check_operator(
         try
             dims = size(op)
             op2 = similar(op, dims)
-            if !supports_inplace(op2)
+            if !ArrayInterface.ismutable(op2)
                 quiet ||
-                    @error "$(px)`similar(op, dims)` must return a mutable array (`supports_inplace` must be `true`), got $(typeof(op2))"
+                    @error "$(px)`similar(op, dims)` must return a mutable array (`ArrayInterface.ismutable` must be `true`), got $(typeof(op2))"
                 success = false
             end
             if size(op2) != dims
@@ -407,9 +412,9 @@ function check_operator(
             S = (eltype(op) == ComplexF64) ? ComplexF32 : ComplexF64
             dims = size(op)
             op2 = similar(op, S, dims)
-            if !supports_inplace(op2)
+            if !ArrayInterface.ismutable(op2)
                 quiet ||
-                    @error "$(px)`similar(op, $S, dims)` must return a mutable array (`supports_inplace` must be `true`), got $(typeof(op2))"
+                    @error "$(px)`similar(op, $S, dims)` must return a mutable array (`ArrayInterface.ismutable` must be `true`), got $(typeof(op2))"
                 success = false
             end
             if size(op2) != dims
diff --git a/src/interfaces/state.jl b/src/interfaces/state.jl
index f8e88f72..3ba66995 100644
--- a/src/interfaces/state.jl
+++ b/src/interfaces/state.jl
@@ -1,5 +1,6 @@
 using Test
 
+import ArrayInterface
 using LinearAlgebra
 
 
@@ -36,8 +37,8 @@ Any `state` must support the following not-in-place operations:
 If `supports_inplace(state)` is `true`, the `state` must also support the
 following:
 
-* `similar(state)` must be defined and return a valid state of the same type a
-  `state`
+* `similar(state)` must be defined and return a valid state of the same type as
+  the original `state`
 * `copyto!(other, state)` must be defined
 * `fill!(state, c)` must be defined
 * `LinearAlgebra.lmul!(c, state)` for a scalar `c` must be defined
@@ -60,7 +61,8 @@ for one-dimensional arrays:
 * `length(state)` must equal `prod(size(state))`
 * `iterate(state)` must be defined
 * `similar(state)` must be defined and return a mutable vector with the same
-  length and element type.
+  length and element type. "Mutability" is determined by
+  [`ArrayInterface.ismutable`](@extref).
 * `similar(state, ::Type{S})` must return a mutable vector with the same length
   and element type `S`
 * `similar(state, dims::Dims)` must return a mutable array with the same
@@ -454,9 +456,9 @@ function check_state(
 
         try
             st2 = similar(state)
-            if !supports_inplace(st2)
+            if !ArrayInterface.ismutable(st2)
                 quiet ||
-                    @error "$(px)`similar(state)` must return a mutable vector (`supports_inplace` must be `true`), got $(typeof(st2))"
+                    @error "$(px)`similar(state)` must return a mutable vector (`ArrayInterface.ismutable` must be `true`), got $(typeof(st2))"
                 success = false
             end
             if size(st2) != size(state)
@@ -480,9 +482,9 @@ function check_state(
         try
             S = (eltype(state) == ComplexF64) ? ComplexF32 : ComplexF64
             st2 = similar(state, S)
-            if !supports_inplace(st2)
+            if !ArrayInterface.ismutable(st2)
                 quiet ||
-                    @error "$(px)`similar(state, $S)` must return a mutable vector (`supports_inplace` must be `true`), got $(typeof(st2))"
+                    @error "$(px)`similar(state, $S)` must return a mutable vector (`ArrayInterface.ismutable` must be `true`), got $(typeof(st2))"
                 success = false
             end
             if size(st2) != size(state)
@@ -506,9 +508,9 @@ function check_state(
         try
             dims = size(state)
             st2 = similar(state, dims)
-            if !supports_inplace(st2)
+            if !ArrayInterface.ismutable(st2)
                 quiet ||
-                    @error "$(px)`similar(state, dims)` must return a mutable array (`supports_inplace` must be `true`), got $(typeof(st2))"
+                    @error "$(px)`similar(state, dims)` must return a mutable array (`ArrayInterface.ismutable` must be `true`), got $(typeof(st2))"
                 success = false
             end
             if size(st2) != dims
@@ -533,9 +535,9 @@ function check_state(
             S = (eltype(state) == ComplexF64) ? ComplexF32 : ComplexF64
             dims = size(state)
             st2 = similar(state, S, dims)
-            if !supports_inplace(st2)
+            if !ArrayInterface.ismutable(st2)
                 quiet ||
-                    @error "$(px)`similar(state, $S, dims)` must return a mutable array (`supports_inplace` must be `true`), got $(typeof(st2))"
+                    @error "$(px)`similar(state, $S, dims)` must return a mutable array (`ArrayInterface.ismutable` must be `true`), got $(typeof(st2))"
                 success = false
             end
             if size(st2) != dims
diff --git a/src/interfaces/supports_inplace.jl b/src/interfaces/supports_inplace.jl
index 10c4128a..8416ed76 100644
--- a/src/interfaces/supports_inplace.jl
+++ b/src/interfaces/supports_inplace.jl
@@ -2,6 +2,7 @@ import ..Operator
 import ..ScaledOperator
 import LinearAlgebra
 import SparseArrays: SparseMatrixCSC
+import ArrayInterface
 
 """Indicate whether a type supports in-place operations.
 
@@ -22,27 +23,33 @@ see [`QuantumPropagators.Interfaces.check_operator`](@ref).
 
 For operators, a `true` result indicates that the operator can be evaluated
 in-place with [`evaluate!`](@ref), see
-[`QuantumPropagators.Interfaces.check_generator`](@ref).
-
-Note that `supports_inplace` is not quite the same as
-[`Base.ismutabletype`](@extref) and/or [`Base.ismutable`](@extref): When using
-[custom structs](@extref Julia :label:`Mutable-Composite-Types`) for states or
+[`QuantumPropagators.Interfaces.check_generator`](@ref). Again, this is
+intended only as an indicator for what assumptions can be made in the
+implementation of a particular propagator: `supports_inplace` is semantically
+separate from [`Base.ismutabletype`](@extref), [`Base.ismutable`](@extref), or
+similar "traits": When using [custom structs](@extref Julia
+:label:`Mutable-Composite-Types`) for states or
 operators, even if those structs are not defined as `mutable`, they may still
 define the in-place interface (typically because their *components* are
-mutable).
+mutable). Conversely, even types that are "mutable" may want to opt out
+of `evaluate!` for performance reasons.
+
+Mutable abstract arrays ([`ArrayInterface.ismutable`](@extref)) without
+considerable performance issues
+([`ArrayInterface.fast_scalar_indexing`](@extref))
+should support in-place operations.
 """
 supports_inplace(::Type{<:Vector{ComplexF64}}) = true
-supports_inplace(::Type{T}) where {T<:AbstractVector} = ismutabletype(T)  # fallback
-# The fallback doesn't actually guarantee that the required interface implied
-# by `supports_inplace` is fulfilled, but it's a reasonable expectation to
-# have, and the `check_state` function will test it.
 
 supports_inplace(::Type{<:Matrix}) = true
 supports_inplace(::Type{<:Operator}) = true
 supports_inplace(::Type{<:LinearAlgebra.Diagonal}) = true
-supports_inplace(::Type{<:SparseMatrixCSC}) = true
+supports_inplace(::Type{<:SparseMatrixCSC}) = true  # XXX is this a good idea?
 supports_inplace(::Type{<:ScaledOperator{<:Any,OT}}) where {OT} = supports_inplace(OT)
-supports_inplace(::Type{T}) where {T<:AbstractMatrix} = ismutabletype(T)  # fallback
+
+# Fallback (both for operators and states)
+supports_inplace(::Type{T}) where {T<:AbstractArray} =
+    ArrayInterface.ismutable(T) && ArrayInterface.fast_scalar_indexing(T)
 
 # Generic catch-all for types without a specific method (prevents StackOverflow
 # from the value→type fallback below)
diff --git a/src/interfaces/supports_matrix_interface.jl b/src/interfaces/supports_matrix_interface.jl
index 695eb713..34376468 100644
--- a/src/interfaces/supports_matrix_interface.jl
+++ b/src/interfaces/supports_matrix_interface.jl
@@ -9,7 +9,12 @@ returns `true` if `T` implements the
 for two-dimensional arrays. This is `true` for all subtypes of
 `AbstractMatrix`, but may also be `true` for types that implement an array
 interface (`size`, `getindex`, etc.) without declaring themselves subtypes
-of `AbstractMatrix`. Calling `supports_matrix_interface` on an instance
+of `AbstractMatrix`.
+
+A `setindex!` method is not a requirement for `supports_matrix_interface`. That
+is, only the read-interface for matrices is enforced.
+
+Calling `supports_matrix_interface` on an instance
 `x` also works via a convenience fallback that forwards to
 `supports_matrix_interface(typeof(x))`.
 
diff --git a/test/Project.toml b/test/Project.toml
index b00b63d7..3df51a9c 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,4 +1,5 @@
 [deps]
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 ComponentArrays = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66"
 Coverage = "a2441757-f6aa-5fb2-8edb-039e3f45d037"
diff --git a/test/test_invalid_interfaces.jl b/test/test_invalid_interfaces.jl
index 05e792a7..73d5f7d8 100644
--- a/test/test_invalid_interfaces.jl
+++ b/test/test_invalid_interfaces.jl
@@ -179,10 +179,7 @@ end
     end
     @test captured.value ≡ false
     # similar(op): wrong mutability, shape, and eltype
-    @test contains(
-        captured.output,
-        "`similar(op)` must return a mutable array (`supports_inplace` must be `true`)"
-    )
+    @test contains(captured.output, "`similar(op)` must return a mutable array")
     @test contains(
         captured.output,
         "`similar(op)` must return an array with the same shape"
@@ -627,10 +624,7 @@ end
     end
     @test captured.value ≡ false
     # similar(state): wrong mutability, shape, and eltype
-    @test contains(
-        captured.output,
-        "`similar(state)` must return a mutable vector (`supports_inplace` must be `true`)"
-    )
+    @test contains(captured.output, "`similar(state)` must return a mutable vector")
     @test contains(
         captured.output,
         "`similar(state)` must return a vector with the same shape"
diff --git a/test/test_operator_linalg.jl b/test/test_operator_linalg.jl
index 581ad02b..707eaa97 100644
--- a/test/test_operator_linalg.jl
+++ b/test/test_operator_linalg.jl
@@ -1,9 +1,11 @@
 using Test
 using LinearAlgebra
 using QuantumControlTestUtils.RandomObjects: random_matrix, random_state_vector
-using QuantumPropagators.Interfaces: check_operator, supports_matrix_interface
+using QuantumPropagators.Interfaces:
+    check_operator, check_generator, supports_matrix_interface
 import QuantumPropagators.Interfaces: supports_inplace
 import QuantumPropagators.Controls: get_controls, evaluate
+import ArrayInterface
 using StaticArrays: SMatrix, SVector
 
 using QuantumPropagators: Generator, Operator, ScaledOperator
@@ -332,3 +334,27 @@ end
     @test check_operator(SFreeOp; state = Ψ)
 
 end
+
+
+@testset "Hermitian matrix supports in-place operations" begin
+
+    # Test the resolution of
+    # https://github.com/JuliaQuantumControl/QuantumPropagators.jl/issues/102
+
+    Ψ0 = ComplexF64[1, 0]
+    Ĥ = ComplexF64[
+         0   0.5
+        0.5   0
+    ]
+    tlist = collect(range(0.0, 1.0, length = 101))
+    generator = (Hermitian(Ĥ),)
+    op = evaluate(generator, tlist, 1)
+    T = Hermitian{ComplexF64,Matrix{ComplexF64}}
+    @test op isa T
+    @test supports_inplace(T)
+    op2 = similar(op)
+    @test op2 isa T
+    @test ArrayInterface.ismutable(T)
+    @test check_generator(generator; state = Ψ0, tlist)
+
+end