Use FillArrays.jl for handling superoperators

[albertomercurio]

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Description

The superoperators are obtained by making the Kronecker product to the given operator. This requires to have the identity matrix.

The previous implementation was using the standard identity I(N), allocating the vector of the diagonal. This is inefficient, as the vector allocates but we already know it is filled by only ones by definition. So, we previously used the Id_cache argument, to avoid to repeatedly allocate.

Here I use instead the Eye constructor from FillArrays.jl. It is a lightweight constructor to replicate the identity matrix. Is has the same size of a number

sizeof(Eye(10000)) # 8 byte

This makes the code way cleaner. Avoiding to define the cache.

The use of FillArrays doens't increase the number of dependencies, as it is already a dependency of many SciML packages.

[Copilot]

Pull Request Overview

This PR refactors superoperator handling to use FillArrays.Eye instead of standard identity matrices I(N), improving memory efficiency and code cleanliness. The lightweight Eye constructor eliminates unnecessary vector allocations while maintaining the same interface.

• Replaced all I(N) identity matrix constructions with Eye(N) in superoperator functions
• Removed Id_cache parameters from public APIs (spre, spost, lindblad_dissipator, liouvillian)
• Added FillArrays.jl as a dependency (already used by other SciML packages)

Reviewed Changes

Copilot reviewed 7 out of 8 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
Project.toml	Added FillArrays dependency with version constraint "1"
src/QuantumToolbox.jl	Imported Eye from FillArrays
src/qobj/superoperators.jl	Replaced I() with Eye() throughout; removed Id_cache parameters from all superoperator functions
src/spin_lattice.jl	Updated multisite_operator to use Eye() in kronecker products
src/time_evolution/smesolve.jl	Removed Id parameter from _spre and _spost calls
src/time_evolution/brmesolve.jl	Removed Id parameter from _spre and _spost calls
src/time_evolution/time_evolution_dynamical.jl	Removed dsf_identity from internal parameters passed between functions
CHANGELOG.md	Documented the change with reference to issue #589

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[ytdHuang]

I suggest we add deprecated warnings for spre, spost, liouvillian, and lindblad_dissipator, and ignore the argument Id_cache, namely

function spre(A::AbstractQuantumObject{Operator}, Id_cache)
    Base.depwarn(
        "The argument `Id_cache` for `spre` is now deprecated, as we now internally use FillArrays.jl, which preserves the same efficiency without requiring this parameter.",
        :spre,
        force = true,
    )
    return spre(A)
end

[ytdHuang]

@TendonFFF

Since our HEOM package relies a lot on Id_cache, can you implement the corresponding changes in HEOM package ?

Basically, just do the similar changes in this PR for HEOM.

[ytdHuang]

@albertomercurio

The documentation build is failing due to the doctest for maximally_mixed_dm.

But since I will change it again in the next PR, we can keep it as it is at the moment.